From 65a57d436c08f3ff1e5034b7c70fba2f808eb312 Mon Sep 17 00:00:00 2001
From: Travis Scrimshaw <tscrimsh at umn.edu>
Date: Fri, 19 May 2017 17:27:26 -0500
Subject: [PATCH 001/128] Improving doc and check for (p)Witt algebras.

---
 src/sage/algebras/lie_algebras/examples.py | 9 +++++++++
 src/sage/algebras/lie_algebras/virasoro.py | 2 ++
 2 files changed, 11 insertions(+)

diff --git a/src/sage/algebras/lie_algebras/examples.py b/src/sage/algebras/lie_algebras/examples.py
index 92dbce05411..1ca7fe76b59 100644
--- a/src/sage/algebras/lie_algebras/examples.py
+++ b/src/sage/algebras/lie_algebras/examples.py
@@ -273,6 +273,8 @@ def regular_vector_fields(R):
     r"""
     Return the Lie algebra of regular vector fields on `\CC^{\times}`.
 
+    This is also known as the Witt (Lie) algebra.
+
     .. SEEALSO::
 
         :class:`~sage.algebras.lie_algebras.virasoro.LieAlgebraRegularVectorFields`
@@ -285,10 +287,17 @@ def regular_vector_fields(R):
     from sage.algebras.lie_algebras.virasoro import LieAlgebraRegularVectorFields
     return LieAlgebraRegularVectorFields(R)
 
+witt = regular_vector_fields
+
 def pwitt(R, p):
     r"""
     Return the `p`-Witt Lie algebra over `R`.
 
+    INPUT:
+
+    - ``R`` -- the base ring
+    - ``p`` -- a positive integer that is `0` in ``R``
+
     EXAMPLES::
 
         sage: lie_algebras.pwitt(GF(5), 5)
diff --git a/src/sage/algebras/lie_algebras/virasoro.py b/src/sage/algebras/lie_algebras/virasoro.py
index 24e2e4090df..bc0a212d443 100644
--- a/src/sage/algebras/lie_algebras/virasoro.py
+++ b/src/sage/algebras/lie_algebras/virasoro.py
@@ -169,6 +169,8 @@ def __init__(self, R, p):
             sage: TestSuite(L).run()  # not tested -- universal envelope doesn't work
             sage: L._test_jacobi_identity()
         """
+        if R(p) != 0:
+            raise ValueError("{} is not 0 in {}".format(p, R))
         cat = LieAlgebras(R).FiniteDimensional().WithBasis()
         FinitelyGeneratedLieAlgebra.__init__(self, R, index_set=range(p), category=cat)
         IndexedGenerators.__init__(self, range(p), prefix='d', bracket='[')

From e614c794a478ee5bf48f40b5d3e91c5e718541df Mon Sep 17 00:00:00 2001
From: Travis Scrimshaw <tscrimsh at umn.edu>
Date: Fri, 19 May 2017 21:35:57 -0500
Subject: [PATCH 002/128] Fixed __mul__ for Lie algebra elements to handle
 actions.

---
 .../algebras/lie_algebras/lie_algebra_element.pyx    | 12 +++++++++++-
 1 file changed, 11 insertions(+), 1 deletion(-)

diff --git a/src/sage/algebras/lie_algebras/lie_algebra_element.pyx b/src/sage/algebras/lie_algebras/lie_algebra_element.pyx
index c5b47732616..1540796844a 100644
--- a/src/sage/algebras/lie_algebras/lie_algebra_element.pyx
+++ b/src/sage/algebras/lie_algebras/lie_algebra_element.pyx
@@ -21,7 +21,7 @@ from copy import copy
 
 from sage.misc.misc import repr_lincomb
 from sage.combinat.free_module import CombinatorialFreeModule
-from sage.structure.element cimport have_same_parent, coercion_model
+from sage.structure.element cimport have_same_parent, coercion_model, parent
 from sage.structure.element_wrapper cimport ElementWrapper
 
 # TODO: Inherit from IndexedFreeModuleElement and make cdef once #22632 is merged
@@ -42,6 +42,11 @@ class LieAlgebraElement(CombinatorialFreeModule.Element):
             sage: y*x
             x*y - z
         """
+        # Check if there is an action of self
+        act = parent(y).get_action(self.parent(), self_on_left=False)
+        if act:
+            return act._call_(self, y)
+
         if self.is_zero() or y.is_zero():
             return self.parent().zero()
         if y in self.base_ring():
@@ -281,6 +286,11 @@ cdef class LieAlgebraElementWrapper(ElementWrapper):
             sage: S(elt)  # not tested: needs #16822
             (2,3) - (1,3)
         """
+        # Check if there is an action of self
+        act = parent(x).get_action(self._parent, self_on_left=False)
+        if act:
+            return act._call_(self, x)
+
         if self.value == 0 or x == 0:
             return self._parent.zero()
         if x in self.base_ring():

From c7a49c45a5cdf9f4d49c5fe4518caf23f72be549 Mon Sep 17 00:00:00 2001
From: Travis Scrimshaw <tscrimsh at umn.edu>
Date: Fri, 19 May 2017 21:42:52 -0500
Subject: [PATCH 003/128] Implement chargeless represenation.

---
 .../lie_algebras/lie_algebra_element.pyx      |   8 +
 src/sage/algebras/lie_algebras/virasoro.py    | 186 ++++++++++++++++++
 2 files changed, 194 insertions(+)

diff --git a/src/sage/algebras/lie_algebras/lie_algebra_element.pyx b/src/sage/algebras/lie_algebras/lie_algebra_element.pyx
index 1540796844a..531f2c12460 100644
--- a/src/sage/algebras/lie_algebras/lie_algebra_element.pyx
+++ b/src/sage/algebras/lie_algebras/lie_algebra_element.pyx
@@ -41,6 +41,14 @@ class LieAlgebraElement(CombinatorialFreeModule.Element):
             sage: L.<x,y,z> = LieAlgebra(QQ, {('x','y'): {'z':1}})
             sage: y*x
             x*y - z
+
+        Check that actions work::
+
+            sage: L = lie_algebras.VirasoroAlgebra(QQ)
+            sage: d = L.basis()
+            sage: M = L.chargeless_representation(1/2, 3/4)
+            sage: x = d[-5] * M.basis()[10]
+            33/4*v[5]
         """
         # Check if there is an action of self
         act = parent(y).get_action(self.parent(), self_on_left=False)
diff --git a/src/sage/algebras/lie_algebras/virasoro.py b/src/sage/algebras/lie_algebras/virasoro.py
index bc0a212d443..b7453141ba7 100644
--- a/src/sage/algebras/lie_algebras/virasoro.py
+++ b/src/sage/algebras/lie_algebras/virasoro.py
@@ -26,6 +26,8 @@
 from sage.algebras.lie_algebras.lie_algebra_element import LieAlgebraElement
 from sage.algebras.lie_algebras.lie_algebra import (InfinitelyGeneratedLieAlgebra,
                                                     FinitelyGeneratedLieAlgebra)
+from sage.combinat.free_module import CombinatorialFreeModule
+from sage.structure.element import parent
 
 class LieAlgebraRegularVectorFields(InfinitelyGeneratedLieAlgebra, IndexedGenerators):
     r"""
@@ -472,5 +474,189 @@ def some_elements(self):
         d = self.monomial
         return [d(0), d(2), d(-2), d('c'), self.an_element()]
 
+    def chargeless_representation(self, alpha, beta):
+        return ChargelessVirasoroRepresentation(self, alpha, beta)
+
     Element = LieAlgebraElement
 
+#####################################################################
+## Representations
+
+class ChargelessVirasoroRepresentation(CombinatorialFreeModule):
+    r"""
+    A chargeless representation of the Virasoro algebra.
+
+    Let `L` be the Virasoro algebra over the field `F` of characteristic
+    `0`. For `\alpha, \beta \in R`, we denote `V_{a,b}` as the
+    `(a, b)`-*chargeless representation* of `L`, which is the
+    `F`-span of `\{v_k \mid k \in \ZZ\}` with `L` action
+
+    .. MATH::
+
+        \begin{aligned}
+        d_n \cdot v_k & = (a n + b + k) v_{n+k},
+        \\ c \cdot v_k & = 0,
+        \end{aligned}
+
+    .. NOTE::
+
+        There is a typo in, e.g., [Mat1992]_ and [IK2010]_, where the
+        action is given by `d_n \cdot v_k = (a n + b - k) v_{n+k}`.
+        However, this results is in
+
+        .. MATH::
+
+            x \cdot (y \cdot v) - y \cdot (x \cdot v) = [y, x] cdot v
+            = -[x, y] \cdot v.
+
+    This comes from the action of `d_n = -t^{n+1} \frac{d}{dt}`
+    on `F[t, t^{-1}]` (recall that `V` is the central extension
+    of the algebra of derivations of `F[t, t^{-1}]`), where
+
+    .. MATH::
+
+        V_{a,b} = F[t, t^{-1}] t^(a-b) (dt)^{-a}
+
+    and `v_k = t^{a-b+k} (dz)^{-a}`.
+
+    The chargeless representations are either irreducible or
+    contains exactly two simple subquotients, one of which is the
+    trivial representation and the other is `F[t, t^{-1}] / F`.
+    The non-trivial simple subquotients are called the
+    *intermediate series*.
+
+    The module `V_{a,b}` is irreducible if and only if
+    `a \neq 0, -1` or `b \notin \ZZ`. When `a = 0` and `b \in \ZZ`,
+    then there exists a subrepresentation isomorphic to the trivial
+    representation. If `a = -1` and `b \in \ZZ`, then there exists
+    a subrepresentation `V` such that `V_{a,b} / V` is isomorphic to
+    `K \frac{dt}{t}` and `V` is irreducible.
+
+    In characteristic `p`, the non-trivial simple subquotient is
+    isomorphic to `F[t, t^{-1}] / F[t^p, t^{-p}]`. For `p \neq 2,3`,
+    then the action is given as above.
+
+    EXAMPLES:
+
+    We first construct the irreducible `V_{1/2, 3/4}` and do some
+    basic computations::
+
+        sage: L = lie_algebras.VirasoroAlgebra(QQ)
+        sage: M = L.chargeless_representation(1/2, 3/4)
+        sage: d = L.basis()
+        sage: v = M.basis()
+        sage: d[3] * v[2]
+        17/4*v[5]
+        sage: d[3] * v[-1]
+        5/4*v[2]
+        sage: (d[3] - d[-2]) * (v[-1] + 1/2*v[0] - v[4])
+        5/4*v[-3] + 1/8*v[-2] + 5*v[2] + 9/8*v[3] - 25/4*v[7]
+
+    We construct the reducible `V_{0,2}` and the trivial
+    subrepresentation given by the span of `v_{-2}`. We verify
+    this for `\{d_i \mid -10 \leq i < 10\}::
+
+        sage: M = L.chargeless_representation(0, 2)
+        sage: v = M.basis()
+        sage: all(d[i] * v[-2] == M.zero() for i in range(-10, 10))
+        True
+
+    REFERNCES::
+
+    .. [Mat1992] \O. Mathieu. *Classification of Harish-Chandra
+       modules over the Virasoro Lie algebra*.
+       Invent. Math. **107(2)** (1992), pp. 225–234.
+
+    .. [IK2010] Kenji Iohara and Yoshiyuki Koga.
+       *Representation Theory of the Virasora Algebra*. 
+       Springer, (2010).
+    """
+    def __init__(self, V, a, b):
+        """
+        Initialize ``self``.
+
+        EXAMPLES::
+
+            sage: L = lie_algebras.VirasoroAlgebra(QQ)
+            sage: M = L.chargeless_representation(1/2, 3/4)
+            sage: TestSuite(M).run()
+        """
+        self._a = a
+        self._b = b
+        self._V = V
+        if V.base_ring().characteristic() in [2,3]:
+            raise NotImplementedError("not implemented for characteristic 2,3")
+        CombinatorialFreeModule.__init__(self, V.base_ring(), ZZ,
+                                         prefix='v')
+
+    def _repr_(self):
+        """
+        Return a string representation of ``self``.
+
+        EXAMPLES::
+
+            sage: L = lie_algebras.VirasoroAlgebra(QQ)
+            sage: L.chargeless_representation(1/2, 3/4)
+            Chargeless representation (1/2, 1/2) of
+             The Virasoro algebra over Rational Field
+        """
+        return "Chargeless representation ({}, {}) of {}".format(
+                    self._a, self._a, self._V)
+
+    def parameters(self):
+        """
+        Return the parameters `(a, b)` of ``self``.
+
+        EXAMPLES::
+
+            sage: L = lie_algebras.VirasoroAlgebra(QQ)
+            sage: M = L.chargeless_representation(1/2, 3/4)
+            sage: M.parameters()
+            (1/2, 3/4)
+        """
+        return (self._a, self._b)
+
+    def virasoro_algebra(self):
+        """
+        Return the Virasoro algebra ``self`` is a representation of.
+
+        EXAMPLES::
+
+            sage: L = lie_algebras.VirasoroAlgebra(QQ)
+            sage: M = L.chargeless_representation(1/2, 3/4)
+            sage: M.virasoro_algebra() is L
+            True
+        """
+        return self._V
+
+    class Element(CombinatorialFreeModule.Element):
+        def _acted_upon_(self, scalar, self_on_left=False):
+            """
+            Return the action of ``scalar`` on ``self``.
+
+            EXAMPLES::
+
+                sage: L = lie_algebras.VirasoroAlgebra(QQ)
+                sage: d = L.basis()
+                sage: M = L.chargeless_representation(1/2, 3/4)
+                sage: x = d[-5] * M.an_element() + M.basis()[10]; x
+                -33/4*v[-6] - 7/4*v[-5] - 9/4*v[-4] + v[10]
+                sage: d[2] * x
+                561/16*v[-4] + 91/16*v[-3] + 81/16*v[-2] + 47/4*v[12]
+
+                sage: v = M.basis()
+                sage: all(d[i]*(d[j]*v[k]) - d[j]*(d[i]*v[k]) == d[i].bracket(d[j])*v[k]
+                ....:     for i in range(-5, 5) for j in range(-5, 5) for k in range(-5, 5))
+                True
+            """
+            P = self.parent()
+            # We implement only a left action
+            if not self_on_left and scalar in P._V:
+                scalar = P._V(scalar)
+                return P.sum_of_terms((n+k, (P._a * n + P._b + k) * cv * cm)
+                                      for n,cv in scalar.monomial_coefficients(copy=False).items() if n != 'c'
+                                      for k,cm in self.monomial_coefficients(copy=False).items())
+            return CombinatorialFreeModule.Element._acted_upon_(self, scalar, self_on_left)
+
+        _rmul_ = _lmul_ = _acted_upon_
+

From 8069b1838180e4c3aac306d8ac93af1f88efb21b Mon Sep 17 00:00:00 2001
From: Travis Scrimshaw <tscrimsh at umn.edu>
Date: Sat, 20 May 2017 02:12:55 -0500
Subject: [PATCH 004/128] Changing bracket convention for Witt and Virasoro.
 Implementing Verma modules.

---
 src/doc/en/reference/references/index.rst  |   8 +
 src/sage/algebras/lie_algebras/virasoro.py | 432 ++++++++++++++++++---
 2 files changed, 396 insertions(+), 44 deletions(-)

diff --git a/src/doc/en/reference/references/index.rst b/src/doc/en/reference/references/index.rst
index 1c608568049..aa4df7d2205 100644
--- a/src/doc/en/reference/references/index.rst
+++ b/src/doc/en/reference/references/index.rst
@@ -898,6 +898,10 @@ REFERENCES:
 
 **I**
 
+.. [IK2010] Kenji Iohara and Yoshiyuki Koga.
+            *Representation Theory of the Virasoro Algebra*. 
+            Springer, (2010).
+
 .. [IR1990] \K. Ireland and M. Rosen, *A Classical Introduction to
             Modern Number Theory*, Springer-Verlag, GTM volume
             84, 1990.
@@ -1200,6 +1204,10 @@ REFERENCES:
 
 **M**
 
+.. [Mat1992] \O. Mathieu. *Classification of Harish-Chandra
+             modules over the Virasoro Lie algebra*.
+             Invent. Math. **107(2)** (1992), pp. 225-234.
+
 .. [Mat2002] Jiří Matousek, "Lectures on Discrete Geometry", Springer,
              2002
 
diff --git a/src/sage/algebras/lie_algebras/virasoro.py b/src/sage/algebras/lie_algebras/virasoro.py
index b7453141ba7..87d01bf8191 100644
--- a/src/sage/algebras/lie_algebras/virasoro.py
+++ b/src/sage/algebras/lie_algebras/virasoro.py
@@ -27,7 +27,6 @@
 from sage.algebras.lie_algebras.lie_algebra import (InfinitelyGeneratedLieAlgebra,
                                                     FinitelyGeneratedLieAlgebra)
 from sage.combinat.free_module import CombinatorialFreeModule
-from sage.structure.element import parent
 
 class LieAlgebraRegularVectorFields(InfinitelyGeneratedLieAlgebra, IndexedGenerators):
     r"""
@@ -103,13 +102,13 @@ def bracket_on_basis(self, i, j):
 
             sage: L = lie_algebras.regular_vector_fields(QQ)
             sage: L.bracket_on_basis(2, -2)
-            -4*d[0]
+            4*d[0]
             sage: L.bracket_on_basis(2, 4)
-            2*d[6]
+            -2*d[6]
             sage: L.bracket_on_basis(4, 4)
             0
         """
-        return self.term(i + j, j - i)
+        return self.term(i + j, i - j)
 
     def _an_element_(self):
         """
@@ -149,7 +148,7 @@ class WittLieAlgebra_charp(FinitelyGeneratedLieAlgebra, IndexedGenerators):
 
     .. MATH::
 
-        [d_i, d_j] = (j - i) d_{i+j},
+        [d_i, d_j] = (i - j) d_{i+j},
 
     where the `i+j` on the right hand side is identified with its
     remainder modulo `p`.
@@ -220,15 +219,15 @@ def bracket_on_basis(self, i, j):
 
             sage: L = lie_algebras.pwitt(Zmod(5), 5)
             sage: L.bracket_on_basis(2, 3)
-            d[0]
-            sage: L.bracket_on_basis(3, 2)
             4*d[0]
+            sage: L.bracket_on_basis(3, 2)
+            d[0]
             sage: L.bracket_on_basis(2, 2)
             0
             sage: L.bracket_on_basis(1, 3)
-            2*d[4]
+            3*d[4]
         """
-        return self.term((i + j) % self._p, j - i)
+        return self.term((i + j) % self._p, i - j)
 
     def _an_element_(self):
         """
@@ -439,13 +438,13 @@ def bracket_on_basis(self, i, j):
             sage: d.bracket_on_basis('c', 2)
             0
             sage: d.bracket_on_basis(2, -2)
-            -4*d[0] - 1/2*c
+            4*d[0] + 1/2*c
         """
         if i == 'c' or j == 'c':
             return self.zero()
-        ret = self._from_dict({i + j: j-i})
+        ret = self._from_dict({i + j: i-j})
         if i == -j:
-            ret += (j ** 3 - j) / 12 * self.c()
+            ret += (i ** 3 - i) / 12 * self.c()
         return ret
 
     def _an_element_(self):
@@ -474,15 +473,48 @@ def some_elements(self):
         d = self.monomial
         return [d(0), d(2), d(-2), d('c'), self.an_element()]
 
-    def chargeless_representation(self, alpha, beta):
-        return ChargelessVirasoroRepresentation(self, alpha, beta)
+    def chargeless_representation(self, a, b):
+        """
+        Return the chargeless representation of ``self`` with
+        parameters ``a`` and ``b``.
+
+        .. SEEALSO::
+
+            :class:`~sage.algebras.lie_algebras.virasoro.ChargelessRepresentation`
+
+        EXAMPLES::
+
+            sage: L = lie_algebras.VirasoroAlgebra(QQ)
+            sage: L.chargeless_representation(3, 2)
+            Chargeless representation (3, 2) of
+             The Virasoro algebra over Rational Field
+        """
+        return ChargelessRepresentation(self, a, b)
+
+    def verma_module(self, c, h):
+        """
+        Return the Verma module with central charge ``c`` and
+        conformal (or highest) weight ``h``.
+
+        .. SEEALSO::
+
+            :class:`~sage.algebras.lie_algebras.virasoro.VermaModule`
+
+        EXAMPLES::
+
+            sage: L = lie_algebras.VirasoroAlgebra(QQ)
+            sage: L.verma_module(3, 2)
+            Verma module with charge 3 and confromal weight 2 of
+             The Virasoro algebra over Rational Field
+        """
+        return VermaModule(self, c, h)
 
     Element = LieAlgebraElement
 
 #####################################################################
 ## Representations
 
-class ChargelessVirasoroRepresentation(CombinatorialFreeModule):
+class ChargelessRepresentation(CombinatorialFreeModule):
     r"""
     A chargeless representation of the Virasoro algebra.
 
@@ -494,21 +526,10 @@ class ChargelessVirasoroRepresentation(CombinatorialFreeModule):
     .. MATH::
 
         \begin{aligned}
-        d_n \cdot v_k & = (a n + b + k) v_{n+k},
+        d_n \cdot v_k & = (a n + b - k) v_{n+k},
         \\ c \cdot v_k & = 0,
         \end{aligned}
 
-    .. NOTE::
-
-        There is a typo in, e.g., [Mat1992]_ and [IK2010]_, where the
-        action is given by `d_n \cdot v_k = (a n + b - k) v_{n+k}`.
-        However, this results is in
-
-        .. MATH::
-
-            x \cdot (y \cdot v) - y \cdot (x \cdot v) = [y, x] cdot v
-            = -[x, y] \cdot v.
-
     This comes from the action of `d_n = -t^{n+1} \frac{d}{dt}`
     on `F[t, t^{-1}]` (recall that `V` is the central extension
     of the algebra of derivations of `F[t, t^{-1}]`), where
@@ -546,30 +567,25 @@ class ChargelessVirasoroRepresentation(CombinatorialFreeModule):
         sage: d = L.basis()
         sage: v = M.basis()
         sage: d[3] * v[2]
-        17/4*v[5]
+        1/4*v[5]
         sage: d[3] * v[-1]
-        5/4*v[2]
+        13/4*v[2]
         sage: (d[3] - d[-2]) * (v[-1] + 1/2*v[0] - v[4])
-        5/4*v[-3] + 1/8*v[-2] + 5*v[2] + 9/8*v[3] - 25/4*v[7]
+        -3/4*v[-3] + 1/8*v[-2] - v[2] + 9/8*v[3] + 7/4*v[7]
 
     We construct the reducible `V_{0,2}` and the trivial
-    subrepresentation given by the span of `v_{-2}`. We verify
+    subrepresentation given by the span of `v_2`. We verify
     this for `\{d_i \mid -10 \leq i < 10\}::
 
         sage: M = L.chargeless_representation(0, 2)
         sage: v = M.basis()
-        sage: all(d[i] * v[-2] == M.zero() for i in range(-10, 10))
+        sage: all(d[i] * v[2] == M.zero() for i in range(-10, 10))
         True
 
     REFERNCES::
 
-    .. [Mat1992] \O. Mathieu. *Classification of Harish-Chandra
-       modules over the Virasoro Lie algebra*.
-       Invent. Math. **107(2)** (1992), pp. 225–234.
-
-    .. [IK2010] Kenji Iohara and Yoshiyuki Koga.
-       *Representation Theory of the Virasora Algebra*. 
-       Springer, (2010).
+    - [Mat1992]_
+    - [IK2010]_
     """
     def __init__(self, V, a, b):
         """
@@ -597,11 +613,11 @@ def _repr_(self):
 
             sage: L = lie_algebras.VirasoroAlgebra(QQ)
             sage: L.chargeless_representation(1/2, 3/4)
-            Chargeless representation (1/2, 1/2) of
+            Chargeless representation (1/2, 3/4) of
              The Virasoro algebra over Rational Field
         """
         return "Chargeless representation ({}, {}) of {}".format(
-                    self._a, self._a, self._V)
+                    self._a, self._b, self._V)
 
     def parameters(self):
         """
@@ -640,9 +656,9 @@ def _acted_upon_(self, scalar, self_on_left=False):
                 sage: d = L.basis()
                 sage: M = L.chargeless_representation(1/2, 3/4)
                 sage: x = d[-5] * M.an_element() + M.basis()[10]; x
-                -33/4*v[-6] - 7/4*v[-5] - 9/4*v[-4] + v[10]
+                -9/4*v[-6] - 7/4*v[-5] - 33/4*v[-4] + v[10]
                 sage: d[2] * x
-                561/16*v[-4] + 91/16*v[-3] + 81/16*v[-2] + 47/4*v[12]
+                -279/16*v[-4] - 189/16*v[-3] - 759/16*v[-2] - 33/4*v[12]
 
                 sage: v = M.basis()
                 sage: all(d[i]*(d[j]*v[k]) - d[j]*(d[i]*v[k]) == d[i].bracket(d[j])*v[k]
@@ -653,10 +669,338 @@ def _acted_upon_(self, scalar, self_on_left=False):
             # We implement only a left action
             if not self_on_left and scalar in P._V:
                 scalar = P._V(scalar)
-                return P.sum_of_terms((n+k, (P._a * n + P._b + k) * cv * cm)
+                return P.sum_of_terms((n+k, (P._a * n + P._b - k) * cv * cm)
                                       for n,cv in scalar.monomial_coefficients(copy=False).items() if n != 'c'
                                       for k,cm in self.monomial_coefficients(copy=False).items())
             return CombinatorialFreeModule.Element._acted_upon_(self, scalar, self_on_left)
 
         _rmul_ = _lmul_ = _acted_upon_
 
+class VermaModule(CombinatorialFreeModule):
+    """
+    A Verma module of the Virasoro algebra.
+
+    The Virasoro algebra admits a triangle decomposition of
+
+    .. MATH::
+
+        V_- \oplus R d_0 \oplus R \hat{c} \oplus V_+,
+
+    where `V_-` (resp. `V_+`) is the span of `\{d_i \mid i < 0\}`
+    (resp. `\{d_i \mid i > 0\}`). We can construct the *Verma module*
+    `M_{c,h}` as the induced representation of the `R d_0 \oplus
+    R \hat{c} \oplus V_+` representation `R_{c,H} = Rv`, where
+
+    .. MATH::
+
+        V_+ v = 0, \qquad \hat{c} v = c v, \qquad d_0 v = h v.
+
+    Therefore, we have a basis of `M_{c,h}`
+
+    .. MATH::
+
+        \{ L_{i_1} \cdots L_{i_k} v \mid i_1 \leq \cdots \leq i_k < 0 \}.
+
+    Moreover, the Verma modules are the free objects in the category of
+    highest weight representations of `V` and are indecomposable.
+    The Verma module `M_{c,h}` is irreducible for generic values of `c`
+    and `h` and when it is reducible, the quotient by the maximal
+    submodule is the unique irreducible highest weight representation
+    `V_{c,h}`.
+
+    EXAMPLES:
+
+    We construct a Verma module and do some basic computations::
+
+        sage: L = lie_algebras.VirasoroAlgebra(QQ)
+        sage: M = L.verma_module(3, 0)
+        sage: d = L.basis()
+        sage: v = M.highest_weight_vector()
+        sage: d[3] * v
+        0
+        sage: d[-3] * v
+        d[-3]*v
+        sage: d[-1] * (d[-3] * v)
+        2*d[-4]*v + d[-3]*d[-1]*v
+        sage: d[2] * (d[-1] * (d[-3] * v))
+        12*d[-2]*v + 5*d[-1]*d[-1]*v
+
+    We verify that `d_{-1} v` is a singular vector for
+    `\{d_i \mid 1 \leq i < 20\}`::
+
+        sage: w = M.basis()[-1]; w
+        d[-1]*v
+        sage: all(d[i] * w == M.zero() for i in range(1,20))
+        True
+
+    We also verify a singular vector for `V_{-2,1}`::
+
+        sage: M = L.verma_module(-2, 1)
+        sage: B = M.basis()
+        sage: w = B[-1,-1] - 2 * B[-2]
+        sage: d = L.basis()
+        sage: all(d[i] * w == M.zero() for i in range(1,20))
+        True
+
+    REFERENCES:
+
+    - :wikipedia:`Virasoro_algebra#Representation_theory`
+    """
+    @staticmethod
+    def __classcall_private__(cls, V, c, h):
+        """
+        Normalize input to ensure a unique representation.
+
+        EXAMPLES::
+
+            sage: L = lie_algebras.VirasoroAlgebra(QQ)
+            sage: M = L.verma_module(3, 1/2)
+            sage: M2 = L.verma_module(int(3), 1/2)
+            sage: M is M2
+            True
+        """
+        R = V.base_ring()
+        return super(VermaModule, cls).__classcall__(cls, V, R(c), R(h))
+
+    @staticmethod
+    def _partition_to_neg_tuple(x):
+        """
+        Helper function to convert a partition to an increasing
+        sequence of negative numbers.
+
+        EXAMPLES::
+
+            sage: from sage.algebras.lie_algebras.virasoro import VermaModule
+            sage: VermaModule._partition_to_neg_tuple([3,2,2,1])
+            (-3, -2, -2, -1)
+        """
+        # The entries of the partition are likely ints, but we need to
+        #   make sure they are Integers.
+        return tuple([ZZ(-i) for i in x])
+
+    def __init__(self, V, c, h):
+        """
+        Initialize ``self``.
+
+        EXAMPLES::
+
+            sage: L = lie_algebras.VirasoroAlgebra(QQ)
+            sage: M = L.verma_module(3, 1/2)
+            sage: TestSuite(M).run()
+        """
+        self._c = c
+        self._h = h
+        self._V = V
+        from sage.combinat.partition import _Partitions
+        indices = _Partitions.map(VermaModule._partition_to_neg_tuple)
+        CombinatorialFreeModule.__init__(self, V.base_ring(),
+                                         indices, prefix='v')
+
+    def _repr_term(self, k):
+        """
+        Return a string representation for the term indexed by ``k``.
+
+        EXAMPLES::
+
+            sage: L = lie_algebras.VirasoroAlgebra(QQ)
+            sage: M = L.verma_module(1, -2)
+            sage: M._repr_term((-3,-2,-2,-1))
+            'd[-3]*d[-2]*d[-2]*d[-1]*v'
+        """
+        if not k:
+            return 'v'
+        d = self._V.basis()
+        return '*'.join(repr(d[i]) for i in k) + '*v'
+
+    def _latex_term(self, k):
+        """
+        Return a latex representation for the term indexed by ``k``.
+
+        EXAMPLES::
+
+            sage: L = lie_algebras.VirasoroAlgebra(QQ)
+            sage: M = L.verma_module(1, -2)
+            sage: M._latex_term((-3,-2,-2,-1))
+            'd_{-3} d_{-2} d_{-2} d_{-1} v'
+        """
+        if not k:
+            return 'v'
+        d = self._V.basis()
+        from sage.misc.latex import latex
+        return ' '.join(latex(d[i]) for i in k) + ' v'
+
+    def _repr_(self):
+        """
+        Return a string representation of ``self``.
+
+        EXAMPLES::
+
+            sage: L = lie_algebras.VirasoroAlgebra(QQ)
+            sage: M = L.verma_module(3, 0)
+            sage: M
+            Verma module with charge 3 and confromal weight 0 of
+             The Virasoro algebra over Rational Field
+        """
+        return "Verma module with charge {} and confromal weight {} of {}".format(
+                    self._c, self._h, self._V)
+
+    def _monomial(self, index):
+        """
+        TESTS::
+
+            sage: L = lie_algebras.VirasoroAlgebra(QQ)
+            sage: M = L.verma_module(3, 0)
+            sage: v = M.basis()
+            sage: v[-3]  # indirect doctest
+            d[-3]*v
+            sage: v[-3,-2,-2]  # indirect doctest
+            d[-3]*d[-2]*d[-2]*v
+        """
+        if index in ZZ:
+            if index >= 0:
+                raise ValueError("sequence must have non-positive entries")
+            index = (index,)
+        return super(VermaModule, self)._monomial(index)
+
+    def central_charge(self):
+        """
+        Return the central charge of ``self``.
+
+        EXAMPLES::
+
+            sage: L = lie_algebras.VirasoroAlgebra(QQ)
+            sage: M = L.verma_module(3, 0)
+            sage: M.central_charge()
+            3
+        """
+        return self._c
+
+    def conformal_weight(self):
+        """
+        Return the conformal weight of ``self``.
+
+        EXAMPLES::
+
+            sage: L = lie_algebras.VirasoroAlgebra(QQ)
+            sage: M = L.verma_module(3, 0)
+            sage: M.conformal_weight()
+            3
+        """
+        return self._c
+
+    def virasoro_algebra(self):
+        """
+        Return the Virasoro algebra ``self`` is a representation of.
+
+        EXAMPLES::
+
+            sage: L = lie_algebras.VirasoroAlgebra(QQ)
+            sage: M = L.verma_module(1/2, 3/4)
+            sage: M.virasoro_algebra() is L
+            True
+        """
+        return self._V
+
+    @cached_method
+    def highest_weight_vector(self):
+        """
+        Return the highest weight vector of ``self``.
+
+        EXAMPLES::
+
+            sage: L = lie_algebras.VirasoroAlgebra(QQ)
+            sage: M = L.verma_module(-2/7, 3)
+            sage: M.highest_weight_vector()
+            v
+        """
+        return self.monomial(())
+
+    def _d_action_on_basis(self, n, k):
+        """
+        Return the action of `d_n` on `v_k`.
+
+        EXAMPLES::
+
+            sage: L = lie_algebras.VirasoroAlgebra(QQ)
+            sage: M = L.verma_module(-2/7, 3)
+            sage: M._d_action_on_basis(-3, ())
+            d[-3]*v
+            sage: M._d_action_on_basis(0, ())
+            3*v
+            sage: M._d_action_on_basis('c', ())
+            -2/7*v
+            sage: M._d_action_on_basis('c', (-4,-2,-2,-1))
+            -2/7*d[-4]*d[-2]*d[-2]*d[-1]*v
+            sage: M._d_action_on_basis(3, (-4,-2,-2,-1))
+            7*d[-5]*d[-1]*v + 60*d[-4]*d[-2]*v + 15*d[-4]*d[-1]*d[-1]*v
+             + 14*d[-3]*d[-2]*d[-1]*v + 7*d[-2]*d[-2]*d[-1]*d[-1]*v
+            sage: M._d_action_on_basis(-1, (-4,-2,-2,-1))
+            d[-9]*d[-1]*v + d[-5]*d[-4]*d[-1]*v + 3*d[-5]*d[-2]*d[-2]*d[-1]*v
+             + 2*d[-4]*d[-3]*d[-2]*d[-1]*v + d[-4]*d[-2]*d[-2]*d[-1]*d[-1]*v
+        """
+        # c acts my multiplication by self._c on all elements
+        if n == 'c':
+            return self.term(k, self._c)
+
+        # when k corresponds to the highest weight vector
+        if not k:
+            if n > 0:
+                return self.zero()
+            if n == 0:
+                return self.term(k, self._h)
+            return self.monomial((n,))
+
+        # The basis are eigenvectors for d_0
+        if n == 0:
+            return self.term(k, self._h - sum(k))
+
+        # We keep things in order
+        if n <= k[0]:
+            return self.monomial((n,) + k)
+
+        # [L_n, L_m] v = L_n L_m v - L_m L_n v
+        # L_n L_m v = L_m L_n v + [L_n, L_m] v
+        d = self._V.basis()
+        m = k[0]
+        k = k[1:]
+        # We need to explicitly call the action as this method is
+        #   used in discovering the action
+        return (self._d_action_on_basis(n, k)._acted_upon_(d[m], False)
+                + self.monomial(k)._acted_upon_(d[n].bracket(d[m]), False))
+
+    class Element(CombinatorialFreeModule.Element):
+        def _acted_upon_(self, scalar, self_on_left=False):
+            """
+            Return the action of ``scalar`` on ``self``.
+
+            EXAMPLES::
+
+                sage: L = lie_algebras.VirasoroAlgebra(QQ)
+                sage: d = L.basis()
+                sage: M = L.verma_module(1/2, 3/4)
+                sage: x = d[-5] * M.an_element() + M.basis()[-10]; x
+                d[-10]*v + 2*d[-5]*v + 3*d[-5]*d[-2]*v + 2*d[-5]*d[-1]*v
+                sage: d[2] * x
+                12*d[-8]*v + 39/4*d[-5]*v + 14*d[-3]*v + 21*d[-3]*d[-2]*v
+                 + 14*d[-3]*d[-1]*v
+                sage: v = M.highest_weight_vector()
+                sage: d[2] * (d[-2] * v)
+                13/4*v
+
+                sage: it = iter(M.basis())
+                sage: B = [it.next() for _ in range(10)]
+                sage: all(d[i]*(d[j]*v) - d[j]*(d[i]*v) == d[i].bracket(d[j])*v
+                ....:     for i in range(-5, 5) for j in range(-5, 5) for v in B)
+                True
+            """
+            P = self.parent()
+            # We implement only a left action
+            if not self_on_left and scalar in P._V:
+                scalar = P._V(scalar)
+                return P.linear_combination((P._d_action_on_basis(n, k), cv * cm)
+                                            for n,cv in scalar.monomial_coefficients(copy=False).items()
+                                            for k,cm in self.monomial_coefficients(copy=False).items())
+            return CombinatorialFreeModule.Element._acted_upon_(self, scalar, self_on_left)
+
+        _rmul_ = _lmul_ = _acted_upon_
+

From aaeb1c9a7258a17d66391260ed05d299360ebfaf Mon Sep 17 00:00:00 2001
From: Travis Scrimshaw <tscrimsh at umn.edu>
Date: Sat, 20 May 2017 10:05:43 -0500
Subject: [PATCH 005/128] Updating documentation.

---
 src/sage/algebras/lie_algebras/virasoro.py | 9 +++++++--
 1 file changed, 7 insertions(+), 2 deletions(-)

diff --git a/src/sage/algebras/lie_algebras/virasoro.py b/src/sage/algebras/lie_algebras/virasoro.py
index 87d01bf8191..8ed3036fa00 100644
--- a/src/sage/algebras/lie_algebras/virasoro.py
+++ b/src/sage/algebras/lie_algebras/virasoro.py
@@ -37,10 +37,15 @@ class LieAlgebraRegularVectorFields(InfinitelyGeneratedLieAlgebra, IndexedGenera
 
     .. MATH::
 
-        [d_i, d_j] = (j - i) d_{i+j}.
+        [d_i, d_j] = (i - j) d_{i+j}.
 
     This is also known as the Witt (Lie) algebra.
 
+    .. NOTE::
+
+        This differs from some conventions (e.g., [Ka1990]_), where
+        we have `d'_i \mapsto -d_i`.
+
     REFERENCES:
 
     - :wikipedia:`Witt_algebra`
@@ -284,7 +289,7 @@ class VirasoroAlgebra(InfinitelyGeneratedLieAlgebra, IndexedGenerators):
 
     .. MATH::
 
-        [d_i, d_j] = (j - i) d_{i+j} + \frac{1}{12}(j^3 - j) \delta_{i,-j} c
+        [d_i, d_j] = (i - j) d_{i+j} + \frac{1}{12}(i^3 - i) \delta_{i,-j} c
 
     and
 

From 5b88fd72731ae7669a95ec78b66e28badc46c092 Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?Fr=C3=A9d=C3=A9ric=20Chapoton?=
 <chapoton@math.univ-lyon1.fr>
Date: Wed, 13 Sep 2017 22:06:48 +0200
Subject: [PATCH 006/128] trac 3313 lift from SL_m(Z/N) to SL_m(Z)

---
 src/sage/modular/local_comp/liftings.py | 79 ++++++++++++++++++++++++-
 1 file changed, 78 insertions(+), 1 deletion(-)

diff --git a/src/sage/modular/local_comp/liftings.py b/src/sage/modular/local_comp/liftings.py
index d5f59f97ffb..6ab7088b34d 100644
--- a/src/sage/modular/local_comp/liftings.py
+++ b/src/sage/modular/local_comp/liftings.py
@@ -6,9 +6,11 @@
 problems.
 """
 
-from sage.rings.all import ZZ, Zmod
+from sage.rings.all import ZZ
 from sage.arith.all import crt, inverse_mod
 from sage.modular.modsym.p1list import lift_to_sl2z
+from copy import copy
+
 
 def lift_to_gamma1(g, m, n):
     r"""
@@ -162,3 +164,78 @@ def lift_ramified(g, p, u, n):
     d = d - p**u * r * b
     # assert (c - g[2]) % p**(u+1) == 0
     return [a,b,c,d]
+
+
+def lift_for_SL(A, N):
+    r"""
+    Lift a matrix `A` from `SL_m(\ZZ / N\ZZ)` to `SL_m(\ZZ)`.
+
+    Follows Shimura, Lemma 1.38, p. 21.
+
+    EXAMPLES::
+
+
+        sage: from sage.modular.local_comp.liftings import lift_for_SL
+        sage: N = 11
+        sage: A = matrix(ZZ, 4, 4, [6, 0, 0, 9, 1, 6, 9, 4, 4, 4, 8, 0, 4, 0, 0, 8])
+        sage: A.det()
+        144
+        sage: A.change_ring(Zmod(N)).det()
+        1
+        sage: L = lift_for_SL(A, N)
+        sage: L.det()
+        1
+        sage: (L - A) * Mod(1, N) == 0
+        True
+
+        sage: N = 19
+        sage: B = matrix(ZZ, 4, 4, [1, 6, 10, 4, 4, 14, 15, 4, 13, 0, 1, 15, 15, 15, 17, 10])
+        sage: B.det()
+        4447
+        sage: B.change_ring(Zmod(N)).det()
+        1
+        sage: L = lift_for_SL(B, N)
+        sage: L.det()
+        1
+        sage: (L - B) * Mod(1, N) == 0
+        True
+    """
+    from sage.matrix.constructor import matrix
+    from sage.matrix.special import identity_matrix, diagonal_matrix, block_diagonal_matrix
+    from sage.misc.misc_c import prod
+
+    m = A.nrows()
+    if m == 1:
+        return identity_matrix(1)
+
+    D, U, V = A.smith_form()
+    diag = diagonal_matrix([-1] + [1] * (m - 1))
+    if U.det() == -1 :
+        U = diag * U
+    if V.det() == -1 :
+        V = V * diag
+    D = U * A * V
+
+    a = [D[i, i] for i in range(m)]
+    b = prod(a[1:])
+    W = identity_matrix(m)
+    W[0, 0] = b
+    W[1, 0] = b - 1
+    W[0, 1] = 1
+
+    X = identity_matrix(m)
+    X[0, 1] = -a[1]
+
+    Ap = copy(D)
+    Ap[0, 0] = 1
+    Ap[1, 0] = 1 - a[0]
+    Ap[1, 1] *= a[0]
+
+    Cp = diagonal_matrix(a[1:])
+    Cp[0, 0] *= a[0]
+    C = lift_for_SL(Cp, N)
+
+    Cpp = block_diagonal_matrix(identity_matrix(1), C)
+    Cpp[1, 0] = 1 - a[0]
+
+    return (~U * ~W * Cpp * ~X * ~V).change_ring(ZZ)

From defa4706cbdb23d70b615160387d39e41fe8a6a5 Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?Fr=C3=A9d=C3=A9ric=20Chapoton?=
 <chapoton@math.univ-lyon1.fr>
Date: Thu, 14 Sep 2017 10:35:49 +0200
Subject: [PATCH 007/128] trac 3313 make the tests appear

---
 src/sage/modular/local_comp/liftings.py | 20 ++++++++++++--------
 1 file changed, 12 insertions(+), 8 deletions(-)

diff --git a/src/sage/modular/local_comp/liftings.py b/src/sage/modular/local_comp/liftings.py
index 6ab7088b34d..c9e54543aac 100644
--- a/src/sage/modular/local_comp/liftings.py
+++ b/src/sage/modular/local_comp/liftings.py
@@ -58,15 +58,17 @@ def lift_to_gamma1(g, m, n):
         [1, 0, 0, 1]
     """
     if m == 1:
-        return [ZZ(1),ZZ(0),ZZ(0),ZZ(1)]
-    a,b,c,d = [ZZ(x) for x in g]
-    if not (a*d - b*c) % m == 1:
-        raise ValueError( "Determinant is {0} mod {1}, should be 1".format((a*d - b*c) % m, m) )
+        return [ZZ.one(), ZZ.zero(), ZZ.zero(), ZZ.one()]
+    a, b, c, d = [ZZ(x) for x in g]
+    det = (a * d - b * c) % m
+    if det != 1:
+        raise ValueError("Determinant is {0} mod {1}, should be 1".format(det, m))
     c2 = crt(c, 0, m, n)
     d2 = crt(d, 1, m, n)
-    a3,b3,c3,d3 = [ZZ(_) for _ in lift_to_sl2z(c2,d2,m*n)]
+    a3,b3,c3,d3 = [ZZ(_) for _ in lift_to_sl2z(c2, d2, m * n)]
     r = (a3*b - b3*a) % m
-    return [a3 + r*c3, b3 + r*d3, c3, d3]
+    return [a3 + r * c3, b3 + r * d3, c3, d3]
+
 
 def lift_matrix_to_sl2z(A, N):
     r"""
@@ -76,7 +78,7 @@ def lift_matrix_to_sl2z(A, N):
 
     This is a special case of :func:`~lift_to_gamma1`, and is coded as such.
 
-    TESTS::
+    EXAMPLES::
 
         sage: from sage.modular.local_comp.liftings import lift_matrix_to_sl2z
         sage: lift_matrix_to_sl2z([10, 11, 3, 11], 19)
@@ -90,6 +92,7 @@ def lift_matrix_to_sl2z(A, N):
     """
     return lift_to_gamma1(A, N, 1)
 
+
 def lift_gen_to_gamma1(m, n):
     r"""
     Return four integers defining a matrix in `\mathrm{SL}_2(\ZZ)` which is
@@ -116,6 +119,7 @@ def lift_gen_to_gamma1(m, n):
     """
     return lift_to_gamma1([0,-1,1,0], m, n)
 
+
 def lift_uniformiser_odd(p, u, n):
     r"""
     Construct a matrix over `\ZZ` whose determinant is `p`, and which is
@@ -134,7 +138,7 @@ def lift_uniformiser_odd(p, u, n):
         <type 'sage.rings.integer.Integer'>
     """
     g = lift_gen_to_gamma1(p**u, n)
-    return [p*g[0], g[1], p*g[2], g[3]]
+    return [p * g[0], g[1], p * g[2], g[3]]
 
 
 def lift_ramified(g, p, u, n):

From 5856470d89a78a17e0b783837502babbc69dfc43 Mon Sep 17 00:00:00 2001
From: Moritz Firsching <moritz@math.fu-berlin.de>
Date: Tue, 22 Aug 2017 17:04:18 +0200
Subject: [PATCH 008/128] don't invoke Graphics3d() for empty plot

---
 src/sage/geometry/polyhedron/plot.py | 13 +++++++------
 1 file changed, 7 insertions(+), 6 deletions(-)

diff --git a/src/sage/geometry/polyhedron/plot.py b/src/sage/geometry/polyhedron/plot.py
index 2a51bf6540e..38cf6c73c05 100644
--- a/src/sage/geometry/polyhedron/plot.py
+++ b/src/sage/geometry/polyhedron/plot.py
@@ -1244,17 +1244,18 @@ def render_3d(self, point_opts={}, line_opts={}, polygon_opts={}):
             sage: Polyhedron(vertices=[[1,1,1]]).plot()                        # point in R^3
             Graphics3d Object
         """
-        from sage.plot.plot3d.base import Graphics3d
-        plt = Graphics3d()
+        pplt = None
+        lplt = None
+        pgplt = None
         if isinstance(point_opts, dict):
             point_opts.setdefault('width', 3)
-            plt += self.render_vertices_3d(**point_opts)
+            pplt = self.render_vertices_3d(**point_opts)
         if isinstance(line_opts, dict):
             line_opts.setdefault('width', 3)
-            plt += self.render_wireframe_3d(**line_opts)
+            lplt = self.render_wireframe_3d(**line_opts)
         if isinstance(polygon_opts, dict):
-            plt += self.render_solid_3d(**polygon_opts)
-        return plt
+            pgplt = self.render_solid_3d(**polygon_opts)
+        return pplt + lplt + pgplt
 
     def tikz(self, view=[0, 0, 1], angle=0, scale=2,
              edge_color='blue!95!black', facet_color='blue!95!black',

From 244aff04a43c3c581799828dcdde9820149b7add Mon Sep 17 00:00:00 2001
From: Moritz Firsching <moritz@math.fu-berlin.de>
Date: Tue, 22 Aug 2017 17:11:40 +0200
Subject: [PATCH 009/128] added doctest

---
 src/sage/geometry/polyhedron/plot.py | 9 +++++++++
 1 file changed, 9 insertions(+)

diff --git a/src/sage/geometry/polyhedron/plot.py b/src/sage/geometry/polyhedron/plot.py
index 38cf6c73c05..79aa9b5e1f5 100644
--- a/src/sage/geometry/polyhedron/plot.py
+++ b/src/sage/geometry/polyhedron/plot.py
@@ -1243,6 +1243,15 @@ def render_3d(self, point_opts={}, line_opts={}, polygon_opts={}):
             Graphics3d Object
             sage: Polyhedron(vertices=[[1,1,1]]).plot()                        # point in R^3
             Graphics3d Object
+
+        The origin is no included, if it is not in the polyhedron (:trac:`23555`)::
+
+            sage: Q = Polyhedron([[100],[101]])
+            sage: P = Q*Q*Q; P
+            A 3-dimensional polyhedron in ZZ^3 defined as the convex hull of 8 vertices
+            sage: p = P.plot()
+            sage: p.bounding_box()
+            ((100.0, 100.0, 100.0), (101.0, 101.0, 101.0))
         """
         pplt = None
         lplt = None

From 856df773df5de6e55e060c5f526e15302e68be28 Mon Sep 17 00:00:00 2001
From: Moritz Firsching <moritz@math.fu-berlin.de>
Date: Mon, 11 Sep 2017 11:57:13 +0200
Subject: [PATCH 010/128] prevent adding of 'None'

---
 src/sage/geometry/polyhedron/plot.py | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/src/sage/geometry/polyhedron/plot.py b/src/sage/geometry/polyhedron/plot.py
index 79aa9b5e1f5..7b92111e262 100644
--- a/src/sage/geometry/polyhedron/plot.py
+++ b/src/sage/geometry/polyhedron/plot.py
@@ -1264,7 +1264,7 @@ def render_3d(self, point_opts={}, line_opts={}, polygon_opts={}):
             lplt = self.render_wireframe_3d(**line_opts)
         if isinstance(polygon_opts, dict):
             pgplt = self.render_solid_3d(**polygon_opts)
-        return pplt + lplt + pgplt
+        return sum(_ for _ in [pplt, lplt, pgplt] if _ != None)
 
     def tikz(self, view=[0, 0, 1], angle=0, scale=2,
              edge_color='blue!95!black', facet_color='blue!95!black',

From 3f02385aa21d875917a5aef1a26013f1005d56e4 Mon Sep 17 00:00:00 2001
From: Moritz Firsching <moritz@math.fu-berlin.de>
Date: Thu, 14 Sep 2017 20:53:40 +0200
Subject: [PATCH 011/128] typo

---
 src/sage/geometry/polyhedron/plot.py | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/src/sage/geometry/polyhedron/plot.py b/src/sage/geometry/polyhedron/plot.py
index 7b92111e262..03092097093 100644
--- a/src/sage/geometry/polyhedron/plot.py
+++ b/src/sage/geometry/polyhedron/plot.py
@@ -1244,7 +1244,7 @@ def render_3d(self, point_opts={}, line_opts={}, polygon_opts={}):
             sage: Polyhedron(vertices=[[1,1,1]]).plot()                        # point in R^3
             Graphics3d Object
 
-        The origin is no included, if it is not in the polyhedron (:trac:`23555`)::
+        The origin is not included, if it is not in the polyhedron (:trac:`23555`)::
 
             sage: Q = Polyhedron([[100],[101]])
             sage: P = Q*Q*Q; P

From 650c674e0a2cb3fb9370ea1a2dfffb5494a72831 Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?Fr=C3=A9d=C3=A9ric=20Chapoton?=
 <chapoton@math.univ-lyon1.fr>
Date: Tue, 19 Sep 2017 18:36:03 +0200
Subject: [PATCH 012/128] trac 3313 added ref to shimura

---
 src/doc/en/reference/references/index.rst | 8 ++++++--
 src/sage/modular/local_comp/liftings.py   | 7 +++----
 2 files changed, 9 insertions(+), 6 deletions(-)

diff --git a/src/doc/en/reference/references/index.rst b/src/doc/en/reference/references/index.rst
index 8fb702d9be6..e7f12118bfb 100644
--- a/src/doc/en/reference/references/index.rst
+++ b/src/doc/en/reference/references/index.rst
@@ -1861,8 +1861,12 @@ REFERENCES:
             Reduction*. Advances in Cryptology - EUROCRYPT '95. LNCS
             Volume 921, 1995, pp 1-12.
 
-.. [Shr2004] Shreve, S. Stochastic Calculus for Finance II:
-             Continuous-Time Models.  New York: Springer, 2004
+.. [Shimura] Goro Shimura, *Introduction to the arithmetic theory of
+             automorphic functions*, Publications of the Mathematical
+             Society of Japan, 11
+
+.. [Shr2004] \S. Shreve, *Stochastic Calculus for Finance II:
+             Continuous-Time Models*.  New York: Springer, 2004
 
 .. [SIHMAS2011] \K. Shibutani, T. Isobe, H. Hiwatari, A. Mitsuda, T. Akishita,
                 and T. Shirai, *Piccolo: An ultra-lightweight block-cipher*; in
diff --git a/src/sage/modular/local_comp/liftings.py b/src/sage/modular/local_comp/liftings.py
index c9e54543aac..5cdb9ab25c9 100644
--- a/src/sage/modular/local_comp/liftings.py
+++ b/src/sage/modular/local_comp/liftings.py
@@ -174,11 +174,10 @@ def lift_for_SL(A, N):
     r"""
     Lift a matrix `A` from `SL_m(\ZZ / N\ZZ)` to `SL_m(\ZZ)`.
 
-    Follows Shimura, Lemma 1.38, p. 21.
+    This follows [Shimura]_, Lemma 1.38, p. 21.
 
     EXAMPLES::
 
-
         sage: from sage.modular.local_comp.liftings import lift_for_SL
         sage: N = 11
         sage: A = matrix(ZZ, 4, 4, [6, 0, 0, 9, 1, 6, 9, 4, 4, 4, 8, 0, 4, 0, 0, 8])
@@ -214,9 +213,9 @@ def lift_for_SL(A, N):
 
     D, U, V = A.smith_form()
     diag = diagonal_matrix([-1] + [1] * (m - 1))
-    if U.det() == -1 :
+    if U.det() == -1:
         U = diag * U
-    if V.det() == -1 :
+    if V.det() == -1:
         V = V * diag
     D = U * A * V
 

From ad028d68d1d4ae02a46c12e625f90fe5154b6f21 Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?Fran=C3=A7ois=20Bissey?= <frp.bissey@gmail.com>
Date: Wed, 8 Nov 2017 10:23:12 +1300
Subject: [PATCH 013/128] upgrade giac to 1.4.9-19. Remove patches that are
 obsolte

---
 build/pkgs/giac/checksums.ini                 |  6 +-
 build/pkgs/giac/package-version.txt           |  2 +-
 build/pkgs/giac/patches/README.txt            |  3 -
 .../pkgs/giac/patches/cSolveorder-check.patch | 11 ----
 build/pkgs/giac/patches/libpng16.patch        | 62 -------------------
 build/pkgs/giac/spkg-src                      |  4 +-
 6 files changed, 6 insertions(+), 82 deletions(-)
 delete mode 100644 build/pkgs/giac/patches/cSolveorder-check.patch
 delete mode 100644 build/pkgs/giac/patches/libpng16.patch

diff --git a/build/pkgs/giac/checksums.ini b/build/pkgs/giac/checksums.ini
index 27861689d59..421ba0b54ec 100644
--- a/build/pkgs/giac/checksums.ini
+++ b/build/pkgs/giac/checksums.ini
@@ -1,4 +1,4 @@
 tarball=giac-VERSION.tar.bz2
-sha1=79503a2c2ee1ffe996727d09ebe6c6be3554434c
-md5=ad15340533a7308f30b739bc36991a56
-cksum=2233538356
+sha1=ace4620c664e796a7cf8243eebdf5789dfd77540
+md5=c8b2ff00ec478116aa5902d96de69bfb
+cksum=4247205719
diff --git a/build/pkgs/giac/package-version.txt b/build/pkgs/giac/package-version.txt
index dc0a2966fad..15350262215 100644
--- a/build/pkgs/giac/package-version.txt
+++ b/build/pkgs/giac/package-version.txt
@@ -1 +1 @@
-1.2.3.47.p0
+1.4.9.19
diff --git a/build/pkgs/giac/patches/README.txt b/build/pkgs/giac/patches/README.txt
index 691aca83157..93e759e6cc5 100644
--- a/build/pkgs/giac/patches/README.txt
+++ b/build/pkgs/giac/patches/README.txt
@@ -6,6 +6,3 @@
     (xcas, qcas). http://xcas.e.ujf-grenoble.fr/XCAS/viewtopic.php?f=4&t=1555.
     The macos-ifactor patch enables pari in ifactor under osx because the problem can't be 
     reproduced with the spkg library.
-
-*   the pari2.8 patch is because some outputs in the check suite differs when giac is built
-    with pari 2.8 vs 2.7. (One more keyword and a different ordering in a sum)
diff --git a/build/pkgs/giac/patches/cSolveorder-check.patch b/build/pkgs/giac/patches/cSolveorder-check.patch
deleted file mode 100644
index 08a155138b7..00000000000
--- a/build/pkgs/giac/patches/cSolveorder-check.patch
+++ /dev/null
@@ -1,11 +0,0 @@
---- a/check/TP16-sol.cas.out1	2016-07-16 14:21:09.000000000 +0200
-+++ b/check/TP16-sol.cas.out1	2016-09-14 14:08:07.110527423 +0200
-@@ -48,7 +48,7 @@
- "Done",
- [-sqrt(13)-1,sqrt(13)-1,4],
- y^2+6*sqrt(13)+18,y^2-6*sqrt(13)+18,y^2,
---sqrt(6)*I*sqrt(sqrt(13)+3),sqrt(6)*I*sqrt(sqrt(13)+3),-sqrt(6)*sqrt(sqrt(13)-3),sqrt(6)*sqrt(sqrt(13)-3),0,
-+sqrt(6)*I*sqrt(sqrt(13)+3),-sqrt(6)*I*sqrt(sqrt(13)+3),-sqrt(6)*sqrt(sqrt(13)-3),sqrt(6)*sqrt(sqrt(13)-3),0,
- "No such variable u",
- x^2+1/4*y^2+1/9*z^2-1,
- x^2+y^2+z^2-u,
diff --git a/build/pkgs/giac/patches/libpng16.patch b/build/pkgs/giac/patches/libpng16.patch
deleted file mode 100644
index b6ba599c4e5..00000000000
--- a/build/pkgs/giac/patches/libpng16.patch
+++ /dev/null
@@ -1,62 +0,0 @@
-Make sure libpng 1.6x as provided by sage is used.
---- giac/configure.in	2017-06-19 13:50:43.676339211 +0000
-+++ giac.patched/configure.in	2017-06-19 13:51:38.986548183 +0000
-@@ -100,7 +100,7 @@
- 	[ if test "x$enableval" = "xno"; then CONFIG_PNG="no"; fi], [])
-   
- if test "x$CONFIG_PNG" = "xyes"; then 
--   AC_CHECK_HEADERS(png.h, AC_CHECK_LIB(png,main))
-+   AC_CHECK_HEADERS(png.h, AC_CHECK_LIB(png16,main))
- fi
- 
-   
---- giac/configure	2017-05-28 12:54:29.000000000 +0000
-+++ giac.patched/configure	2017-06-19 13:51:54.826611543 +0000
-@@ -15482,13 +15550,13 @@
-   cat >>confdefs.h <<_ACEOF
- #define HAVE_PNG_H 1
- _ACEOF
-- { $as_echo "$as_me:${as_lineno-$LINENO}: checking for main in -lpng" >&5
--$as_echo_n "checking for main in -lpng... " >&6; }
--if ${ac_cv_lib_png_main+:} false; then :
-+ { $as_echo "$as_me:${as_lineno-$LINENO}: checking for main in -lpng16" >&5
-+$as_echo_n "checking for main in -lpng16... " >&6; }
-+if ${ac_cv_lib_png16_main+:} false; then :
-   $as_echo_n "(cached) " >&6
- else
-   ac_check_lib_save_LIBS=$LIBS
--LIBS="-lpng  $LIBS"
-+LIBS="-lpng16  $LIBS"
- cat confdefs.h - <<_ACEOF >conftest.$ac_ext
- /* end confdefs.h.  */
- 
-@@ -15502,22 +15570,22 @@
- }
- _ACEOF
- if ac_fn_cxx_try_link "$LINENO"; then :
--  ac_cv_lib_png_main=yes
-+  ac_cv_lib_png16_main=yes
- else
--  ac_cv_lib_png_main=no
-+  ac_cv_lib_png16_main=no
- fi
- rm -f core conftest.err conftest.$ac_objext \
-     conftest$ac_exeext conftest.$ac_ext
- LIBS=$ac_check_lib_save_LIBS
- fi
--{ $as_echo "$as_me:${as_lineno-$LINENO}: result: $ac_cv_lib_png_main" >&5
--$as_echo "$ac_cv_lib_png_main" >&6; }
--if test "x$ac_cv_lib_png_main" = xyes; then :
-+{ $as_echo "$as_me:${as_lineno-$LINENO}: result: $ac_cv_lib_png16_main" >&5
-+$as_echo "$ac_cv_lib_png16_main" >&6; }
-+if test "x$ac_cv_lib_png16_main" = xyes; then :
-   cat >>confdefs.h <<_ACEOF
--#define HAVE_LIBPNG 1
-+#define HAVE_LIBPNG16 1
- _ACEOF
- 
--  LIBS="-lpng $LIBS"
-+  LIBS="-lpng16 $LIBS"
- 
- fi
- 
diff --git a/build/pkgs/giac/spkg-src b/build/pkgs/giac/spkg-src
index 6706f87ed38..7637c596b87 100755
--- a/build/pkgs/giac/spkg-src
+++ b/build/pkgs/giac/spkg-src
@@ -14,8 +14,8 @@ fi
 set -e
 
 # TODO on the next update: l71 switch from gz to bz2 as wished in #18826
-VERSION="1.2.3"
-VERSIONREV="47"
+VERSION="1.4.9"
+VERSIONREV="19"
 
 # The upstream tarball name is: giac"$SOURCEORIG".tar.gz
 SOURCEORIG=_"$VERSION"-"$VERSIONREV"

From 9141f652ae719f1db96f33eaa096ad5ab4e545c3 Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?Fran=C3=A7ois=20Bissey?= <frp.bissey@gmail.com>
Date: Wed, 8 Nov 2017 10:25:22 +1300
Subject: [PATCH 014/128] adopt
 https://anonscm.debian.org/cgit/debian-science/packages/sagemath.git/tree/debian/patches/u1-version-giac-1.2.3.57.patch
 from debian which is valid for all giac after 1.2.3-57

---
 src/sage/interfaces/giac.py | 4 ++--
 1 file changed, 2 insertions(+), 2 deletions(-)

diff --git a/src/sage/interfaces/giac.py b/src/sage/interfaces/giac.py
index 0742cf896e6..0649a26d991 100644
--- a/src/sage/interfaces/giac.py
+++ b/src/sage/interfaces/giac.py
@@ -714,14 +714,14 @@ def _true_symbol(self):
         EXAMPLES::
 
             sage: giac._true_symbol()
-            '1'
+            'true'
 
         ::
 
             sage: giac(2) == giac(2)
             True
         """
-        return '1'
+        return 'true'
 
     def _assign_symbol(self):
         """

From 6bee3fca54bf50cfbd7a82e71d899b7ddafacb89 Mon Sep 17 00:00:00 2001
From: John Cremona <john.cremona@gmail.com>
Date: Sun, 12 Nov 2017 16:33:27 +0000
Subject: [PATCH 015/128] #10017: fix construction of order elements from list,
 and number field reduced basis

---
 src/sage/rings/number_field/number_field.py | 19 ++++++++++++++++++-
 src/sage/rings/number_field/order.py        | 18 ++++++++++++++++++
 2 files changed, 36 insertions(+), 1 deletion(-)

diff --git a/src/sage/rings/number_field/number_field.py b/src/sage/rings/number_field/number_field.py
index 70fdaea0351..4dfcd07bb2a 100644
--- a/src/sage/rings/number_field/number_field.py
+++ b/src/sage/rings/number_field/number_field.py
@@ -5589,6 +5589,22 @@ def reduced_basis(self, prec=None):
             [-1, -1/2*t^5 + 1/2*t^4 + 3*t^3 - 3/2*t^2 - 4*t - 1/2, t, 1/2*t^5 + 1/2*t^4 - 4*t^3 - 5/2*t^2 + 7*t + 1/2, 1/2*t^5 - 1/2*t^4 - 2*t^3 + 3/2*t^2 - 1/2, 1/2*t^5 - 1/2*t^4 - 3*t^3 + 5/2*t^2 + 4*t - 5/2]
             sage: CyclotomicField(12).reduced_basis()
             [1, zeta12^2, zeta12, zeta12^3]
+
+        TESTS:
+
+        See (:trac:`10017`)::
+
+            sage: x = polygen(QQ)
+            sage: k = NumberField(x^6 + 2218926655879913714112*x^4 - 32507675650290949030789018433536*x^3 + 4923635504174417014460581055002374467948544*x^2 - 3666074010564497464129951249279114076897746988630016*x + 264187244046129768986806800244258952598300346857154900812365824,'a')
+            sage: new_basis = k.reduced_basis()
+            sage: [c.minpoly() for c in new_basis]
+            [x - 1,
+             x^6 + 3*x^5 + 258*x^4 + 511*x^3 + 3564*x^2 + 3309*x + 2347,
+             x^6 - 24*x^5 + 6126*x^4 - 312664*x^3 + 5407566*x^2 - 33643572*x + 95921443,
+             x^6 + 18*x^5 + 3366*x^4 + 82008*x^3 + 886962*x^2 - 840726*x + 5521647,
+             x^6 + 27*x^5 + 9579*x^4 + 623358*x^3 + 5060091*x^2 - 139224285*x + 880944177,
+             x^6 - 72*x^5 + 65286*x^4 - 10762768*x^3 + 473072922*x^2 - 2502686322*x + 54227921641]
+
         """
         if self.is_totally_real():
             try:
@@ -5619,7 +5635,8 @@ def reduced_basis(self, prec=None):
         else:
             M = self.Minkowski_embedding(self.integral_basis(), prec=prec)
             T = pari(M).qflll().sage()
-            self.__reduced_basis = [ self(v.list()) for v in T.columns() ]
+            ZK = self.ring_of_integers()
+            self.__reduced_basis = [ ZK(v.list()) for v in T.columns() ]
             if prec is None:
                 ## this is the default choice for Minkowski_embedding
                 self.__reduced_basis_prec = 53
diff --git a/src/sage/rings/number_field/order.py b/src/sage/rings/number_field/order.py
index bf79b8f1eee..cf20dbf72c0 100644
--- a/src/sage/rings/number_field/order.py
+++ b/src/sage/rings/number_field/order.py
@@ -1129,6 +1129,7 @@ def _element_constructor_(self, x):
 
         EXAMPLES::
 
+            sage: x = polygen(QQ)
             sage: k.<z> = NumberField(x^2 - 389)
             sage: m = k.order(3*z); m
             Order in Number Field in z with defining polynomial x^2 - 389
@@ -1136,9 +1137,26 @@ def _element_constructor_(self, x):
             6*z
             sage: k(m(6*z))
             6*z
+
+        If ``x`` is a list or tuple the element constructed is the
+        linear combination of the generators with these coefficients
+        (see :trac:`10017`)::
+
+            sage: x = polygen(QQ)
+            sage: K.<a> = NumberField(x^3-10)
+            sage: ZK = K.ring_of_integers()
+            sage: ZK.basis()
+            [1/3*a^2 + 1/3*a + 1/3, a, a^2]
+            sage: ZK([1,2,3])
+            10/3*a^2 + 7/3*a + 1/3
+            sage: K([1,2,3])
+            3*a^2 + 2*a + 1
+
         """
         if is_Element(x) and x.parent() is self:
             return x
+        if isinstance(x,list) or isinstance(x,tuple):
+            x = sum(xi*gi for xi,gi in zip(x,self.gens()))
         if not is_Element(x) or x.parent() is not self._K:
             x = self._K(x)
         V, _, embedding = self._K.vector_space()

From 5d51b3260b6bec7eacc24aca4f469ee1ba8b4572 Mon Sep 17 00:00:00 2001
From: John Cremona <john.cremona@gmail.com>
Date: Tue, 21 Nov 2017 13:05:09 +0000
Subject: [PATCH 016/128] #10017 added 2 lines to new doctest

---
 src/sage/rings/number_field/number_field.py | 3 ++-
 1 file changed, 2 insertions(+), 1 deletion(-)

diff --git a/src/sage/rings/number_field/number_field.py b/src/sage/rings/number_field/number_field.py
index 4dfcd07bb2a..0cd1dd4f26c 100644
--- a/src/sage/rings/number_field/number_field.py
+++ b/src/sage/rings/number_field/number_field.py
@@ -5604,7 +5604,8 @@ def reduced_basis(self, prec=None):
              x^6 + 18*x^5 + 3366*x^4 + 82008*x^3 + 886962*x^2 - 840726*x + 5521647,
              x^6 + 27*x^5 + 9579*x^4 + 623358*x^3 + 5060091*x^2 - 139224285*x + 880944177,
              x^6 - 72*x^5 + 65286*x^4 - 10762768*x^3 + 473072922*x^2 - 2502686322*x + 54227921641]
-
+            sage: R = k.order(new_basis)
+            sage: assert R.discriminant()==k.discriminant()
         """
         if self.is_totally_real():
             try:

From 8b3eb02ede88e3de6bf03cc54f8565b2a0ef3bcf Mon Sep 17 00:00:00 2001
From: John Cremona <john.cremona@gmail.com>
Date: Tue, 21 Nov 2017 14:24:59 +0000
Subject: [PATCH 017/128] #10017 minor changes to docstring

---
 src/sage/rings/number_field/number_field.py | 5 +++--
 1 file changed, 3 insertions(+), 2 deletions(-)

diff --git a/src/sage/rings/number_field/number_field.py b/src/sage/rings/number_field/number_field.py
index 0cd1dd4f26c..a692372458c 100644
--- a/src/sage/rings/number_field/number_field.py
+++ b/src/sage/rings/number_field/number_field.py
@@ -5592,7 +5592,7 @@ def reduced_basis(self, prec=None):
 
         TESTS:
 
-        See (:trac:`10017`)::
+        Check that the bug reported at :trac:`10017` is fixed::
 
             sage: x = polygen(QQ)
             sage: k = NumberField(x^6 + 2218926655879913714112*x^4 - 32507675650290949030789018433536*x^3 + 4923635504174417014460581055002374467948544*x^2 - 3666074010564497464129951249279114076897746988630016*x + 264187244046129768986806800244258952598300346857154900812365824,'a')
@@ -5605,7 +5605,8 @@ def reduced_basis(self, prec=None):
              x^6 + 27*x^5 + 9579*x^4 + 623358*x^3 + 5060091*x^2 - 139224285*x + 880944177,
              x^6 - 72*x^5 + 65286*x^4 - 10762768*x^3 + 473072922*x^2 - 2502686322*x + 54227921641]
             sage: R = k.order(new_basis)
-            sage: assert R.discriminant()==k.discriminant()
+            sage: R.discriminant()==k.discriminant()
+            True
         """
         if self.is_totally_real():
             try:

From 1add357c497b6630fb4a5c022f4caec6318a5ee0 Mon Sep 17 00:00:00 2001
From: "Erik M. Bray" <erik.bray@lri.fr>
Date: Tue, 21 Nov 2017 12:14:32 +0000
Subject: [PATCH 018/128] Add a doctest output fixup to replace <type '...'>
 with <class '...'> so that such tests can pass on Python 3.

---
 src/sage/doctest/parsing.py | 78 ++++++++++++++++++++++++++++++++++---
 1 file changed, 73 insertions(+), 5 deletions(-)

diff --git a/src/sage/doctest/parsing.py b/src/sage/doctest/parsing.py
index 96a77d793a9..4f600fa78ac 100644
--- a/src/sage/doctest/parsing.py
+++ b/src/sage/doctest/parsing.py
@@ -113,6 +113,46 @@ def remove_unicode_u(string):
     return string
 
 
+_type_repr_re = re.compile(r"<type '(?P<name>[^']+)'>")
+
+def normalize_type_repr(s):
+    """
+    Converts the repr of type objects (e.g. ``int``, ``float``) from their
+    Python 2 representation to their Python 3 representation.
+
+    In Python 2, the repr of built-in types like ``int`` is like ``<type
+    'int'>``, whereas user-defined pure Python classes are displayed as
+    ``<class 'classname'>``.  On Python 3 this was normalized so that
+    built-in types are represented the same as user-defined classes (e.g.
+    ``<class 'int'>``.
+
+    This simply normalizes all class/type reprs to the Python 3 convention for
+    the sake of output checking.
+
+    EXAMPLES::
+
+        sage: from sage.doctest.parsing import normalize_type_repr
+        sage: s = "<type 'int'>"
+        sage: normalize_type_repr(s)
+        "<class 'int'>"
+        sage: normalize_type_repr(repr(float))
+        "<class 'float'>"
+
+    This can work on multi-line output as well::
+
+        sage: s = "The desired output was <class 'int'>\n" \
+        ....:     "The received output was <type 'int'>"
+        sage: print(normalize_type_repr(s))
+        The desired output was <class 'int'>
+        The received output was <class 'int'>
+    """
+
+    def subst(m):
+        return "<class '{0}'>".format(m.group('name'))
+
+    return _type_repr_re.sub(subst, s)
+
+
 def parse_optional_tags(string):
     """
     Returns a set consisting of the optional tags from the following
@@ -874,6 +914,14 @@ def check_output(self, want, got, optionflags):
             [u'Fermat',  u'Euler']
             sage: c = u'you'; c
             u'you'
+
+        Also allowance for the difference in reprs of ``type`` instances (i.e.
+        classes) between Python 2 and Python 3::
+
+            sage: int
+            <class 'int'>
+            sage: float
+            <type 'float'>
         """
         got = self.human_readable_escape_sequences(got)
         if isinstance(want, MarkedOutput):
@@ -899,13 +947,33 @@ def check_output(self, want, got, optionflags):
                 return all(a.overlaps(b) for a, b in zip(want_intervals, got_values))
 
         ok = doctest.OutputChecker.check_output(self, want, got, optionflags)
-        if ok or ('u"' not in want and "u'" not in want):
+
+        if ok:
             return ok
 
-        # accept the same answer where strings have unicode prefix u
-        # for smoother transition to python3
-        if not six.PY2:
-            want = remove_unicode_u(want)
+        # Possibly fix up the desired output to account for the difference in
+        # reprs of some objects between Python 2 and Python 3
+        # Since most of the tests are currently written for Python 2 the only
+        # fixups we perform right now are on Python 3
+        if six.PY2:
+            repr_fixups = []
+        else:
+            repr_fixups = [
+                (lambda g, w: 'u"' in w or "u'" in w, remove_unicode_u),
+                (lambda g, w: '<class' in g and '<type' in w,
+                 normalize_type_repr)
+            ]
+
+        did_fixup = False
+        for quick_check, fixup in repr_fixups:
+            do_fixup = quick_check(got, want)
+            if do_fixup:
+                want = fixup(want)
+                did_fixup = True
+
+        if not did_fixup:
+            # Return the same result as before
+            return ok
 
         return doctest.OutputChecker.check_output(self, want, got, optionflags)
 

From e12b67fda63bf721cf519c4553c5abef0e8553ef Mon Sep 17 00:00:00 2001
From: "Erik M. Bray" <erik.bray@lri.fr>
Date: Tue, 28 Nov 2017 11:09:46 +0000
Subject: [PATCH 019/128] Fix docstring--the normalization is currently not
 performed on Python 2

---
 src/sage/doctest/parsing.py | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/src/sage/doctest/parsing.py b/src/sage/doctest/parsing.py
index 4f600fa78ac..b1c615ed98d 100644
--- a/src/sage/doctest/parsing.py
+++ b/src/sage/doctest/parsing.py
@@ -919,7 +919,7 @@ def check_output(self, want, got, optionflags):
         classes) between Python 2 and Python 3::
 
             sage: int
-            <class 'int'>
+            <type 'int'>
             sage: float
             <type 'float'>
         """

From a889c310d1ced386492facc9412fd13e4285227f Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?Fr=C3=A9d=C3=A9ric=20Chapoton?=
 <chapoton@math.univ-lyon1.fr>
Date: Thu, 30 Nov 2017 17:54:59 +0100
Subject: [PATCH 020/128] trac 3313 some enhancements

---
 src/sage/modular/local_comp/liftings.py | 80 ++++++++++++++++---------
 1 file changed, 52 insertions(+), 28 deletions(-)

diff --git a/src/sage/modular/local_comp/liftings.py b/src/sage/modular/local_comp/liftings.py
index 5cdb9ab25c9..7bb67a76faa 100644
--- a/src/sage/modular/local_comp/liftings.py
+++ b/src/sage/modular/local_comp/liftings.py
@@ -20,6 +20,12 @@ def lift_to_gamma1(g, m, n):
     `\begin{pmatrix} 1 & * \\ 0 & 1 \end{pmatrix} \pmod n`. Here `m` and `n`
     must be coprime.
 
+    INPUT:
+
+    - ``g`` -- list of 4 integers defining a `2 \times 2` matrix
+
+    - `m`, `n` -- coprime positive integers
+
     Here `m` and `n` should be coprime positive integers. Either of `m` and `n`
     can be `1`. If `n = 1`, this still makes perfect sense; this is what is
     called by the function :func:`~lift_matrix_to_sl2z`. If `m = 1` this is a
@@ -78,6 +84,12 @@ def lift_matrix_to_sl2z(A, N):
 
     This is a special case of :func:`~lift_to_gamma1`, and is coded as such.
 
+    INPUT:
+
+    - ``A`` -- list of 4 integers defining a `2 \times 2` matrix
+
+    - `N` -- positive integer
+
     EXAMPLES::
 
         sage: from sage.modular.local_comp.liftings import lift_matrix_to_sl2z
@@ -102,6 +114,10 @@ def lift_gen_to_gamma1(m, n):
 
     This is a special case of :func:`~lift_to_gamma1`, and is coded as such.
 
+    INPUT:
+
+    - `m`, `n` -- coprime positive integers
+
     EXAMPLES::
 
         sage: from sage.modular.local_comp.liftings import lift_gen_to_gamma1
@@ -170,75 +186,83 @@ def lift_ramified(g, p, u, n):
     return [a,b,c,d]
 
 
-def lift_for_SL(A, N):
+def lift_for_SL(A):
     r"""
     Lift a matrix `A` from `SL_m(\ZZ / N\ZZ)` to `SL_m(\ZZ)`.
 
     This follows [Shimura]_, Lemma 1.38, p. 21.
 
+    INPUT:
+
+    - ``A`` -- a square matrix with coefficients in `\ZZ / N\ZZ`
+
     EXAMPLES::
 
         sage: from sage.modular.local_comp.liftings import lift_for_SL
-        sage: N = 11
-        sage: A = matrix(ZZ, 4, 4, [6, 0, 0, 9, 1, 6, 9, 4, 4, 4, 8, 0, 4, 0, 0, 8])
+        sage: A = matrix(Zmod(11), 4, 4, [6, 0, 0, 9, 1, 6, 9, 4, 4, 4, 8, 0, 4, 0, 0, 8])
         sage: A.det()
-        144
-        sage: A.change_ring(Zmod(N)).det()
         1
-        sage: L = lift_for_SL(A, N)
+        sage: L = lift_for_SL(A)
         sage: L.det()
         1
-        sage: (L - A) * Mod(1, N) == 0
+        sage: (L - A) == 0
         True
 
-        sage: N = 19
-        sage: B = matrix(ZZ, 4, 4, [1, 6, 10, 4, 4, 14, 15, 4, 13, 0, 1, 15, 15, 15, 17, 10])
+        sage: B = matrix(Zmod(19), 4, 4, [1, 6, 10, 4, 4, 14, 15, 4, 13, 0, 1, 15, 15, 15, 17, 10])
         sage: B.det()
-        4447
-        sage: B.change_ring(Zmod(N)).det()
         1
-        sage: L = lift_for_SL(B, N)
+        sage: L = lift_for_SL(B)
         sage: L.det()
         1
-        sage: (L - B) * Mod(1, N) == 0
+        sage: (L - B) == 0
         True
+
+    TESTS::
+
+        sage: A = matrix(Zmod(7), 2, [1,0,0,1])
+        sage: L = lift_for_SL(A)
+        sage: L.parent()
+        Full MatrixSpace of 2 by 2 dense matrices over Integer Ring
+
+        sage: A = matrix(Zmod(7), 1, [1])
+        sage: L = lift_for_SL(A); L
+        [1]
     """
     from sage.matrix.constructor import matrix
     from sage.matrix.special import identity_matrix, diagonal_matrix, block_diagonal_matrix
     from sage.misc.misc_c import prod
 
+    N = A.parent().base_ring().characteristic()
+
     m = A.nrows()
     if m == 1:
-        return identity_matrix(1)
+        return identity_matrix(ZZ, 1)
 
-    D, U, V = A.smith_form()
+    AZZ = A .change_ring(ZZ)
+    D, U, V = AZZ.smith_form()
     diag = diagonal_matrix([-1] + [1] * (m - 1))
     if U.det() == -1:
         U = diag * U
     if V.det() == -1:
         V = V * diag
-    D = U * A * V
+    D = U * AZZ * V
 
     a = [D[i, i] for i in range(m)]
     b = prod(a[1:])
-    W = identity_matrix(m)
-    W[0, 0] = b
-    W[1, 0] = b - 1
-    W[0, 1] = 1
 
-    X = identity_matrix(m)
-    X[0, 1] = -a[1]
+    Winv = identity_matrix(m)
+    Winv[1, 0] = 1 - b
+    Winv[0, 1] = -1
+    Winv[1, 1] = b
 
-    Ap = copy(D)
-    Ap[0, 0] = 1
-    Ap[1, 0] = 1 - a[0]
-    Ap[1, 1] *= a[0]
+    Xinv = identity_matrix(m)
+    Xinv[0, 1] = a[1]
 
     Cp = diagonal_matrix(a[1:])
     Cp[0, 0] *= a[0]
-    C = lift_for_SL(Cp, N)
+    C = lift_for_SL(Cp)
 
     Cpp = block_diagonal_matrix(identity_matrix(1), C)
     Cpp[1, 0] = 1 - a[0]
 
-    return (~U * ~W * Cpp * ~X * ~V).change_ring(ZZ)
+    return (~U * Winv * Cpp * Xinv * ~V).change_ring(ZZ)

From f58b626dbd062617c585412ffc9c9a51c1a0f1a2 Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?Fr=C3=A9d=C3=A9ric=20Chapoton?=
 <chapoton@math.univ-lyon1.fr>
Date: Wed, 6 Dec 2017 13:41:19 +0100
Subject: [PATCH 021/128] trac 3313 some details, allow ZZ matrices as input
 again

---
 src/sage/modular/local_comp/liftings.py | 30 ++++++++++++++++++++-----
 1 file changed, 25 insertions(+), 5 deletions(-)

diff --git a/src/sage/modular/local_comp/liftings.py b/src/sage/modular/local_comp/liftings.py
index 7bb67a76faa..97b26b2028b 100644
--- a/src/sage/modular/local_comp/liftings.py
+++ b/src/sage/modular/local_comp/liftings.py
@@ -186,7 +186,7 @@ def lift_ramified(g, p, u, n):
     return [a,b,c,d]
 
 
-def lift_for_SL(A):
+def lift_for_SL(A, N=None):
     r"""
     Lift a matrix `A` from `SL_m(\ZZ / N\ZZ)` to `SL_m(\ZZ)`.
 
@@ -194,7 +194,10 @@ def lift_for_SL(A):
 
     INPUT:
 
-    - ``A`` -- a square matrix with coefficients in `\ZZ / N\ZZ`
+    - ``A`` -- a square matrix with coefficients in `\ZZ / N\ZZ` (or `\ZZ`)
+
+    - ``N`` -- the modulus (optional) required only if the matrix ``A``
+      has coefficients in `\ZZ`
 
     EXAMPLES::
 
@@ -219,6 +222,11 @@ def lift_for_SL(A):
 
     TESTS::
 
+        sage: lift_for_SL(matrix(3,3,[1,2,0,3,4,0,0,0,1]),3)
+        [10 14  3]
+        [ 9 10  3]
+        [ 3  3  1]
+
         sage: A = matrix(Zmod(7), 2, [1,0,0,1])
         sage: L = lift_for_SL(A)
         sage: L.parent()
@@ -227,12 +235,24 @@ def lift_for_SL(A):
         sage: A = matrix(Zmod(7), 1, [1])
         sage: L = lift_for_SL(A); L
         [1]
+
+        sage: A = matrix(ZZ, 2, [1,0,0,1])
+        sage: lift_for_SL(A)
+        Traceback (most recent call last):
+        ...
+        ValueError: you must choose the modulus
     """
     from sage.matrix.constructor import matrix
-    from sage.matrix.special import identity_matrix, diagonal_matrix, block_diagonal_matrix
+    from sage.matrix.special import (identity_matrix, diagonal_matrix,
+                                     block_diagonal_matrix)
     from sage.misc.misc_c import prod
 
-    N = A.parent().base_ring().characteristic()
+    ring = A.parent().base_ring()
+    if N is None:
+        if ring is ZZ:
+            raise ValueError('you must choose the modulus')
+        else:
+            N = ring.characteristic()
 
     m = A.nrows()
     if m == 1:
@@ -260,7 +280,7 @@ def lift_for_SL(A):
 
     Cp = diagonal_matrix(a[1:])
     Cp[0, 0] *= a[0]
-    C = lift_for_SL(Cp)
+    C = lift_for_SL(Cp, N)
 
     Cpp = block_diagonal_matrix(identity_matrix(1), C)
     Cpp[1, 0] = 1 - a[0]

From 42108d59dd989161960dbab4933eeae4cd7d05dc Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?Fr=C3=A9d=C3=A9ric=20Chapoton?=
 <chapoton@math.univ-lyon1.fr>
Date: Wed, 6 Dec 2017 17:59:39 +0100
Subject: [PATCH 022/128] trac 3313 one more enhancement

---
 src/sage/modular/local_comp/liftings.py | 3 +--
 1 file changed, 1 insertion(+), 2 deletions(-)

diff --git a/src/sage/modular/local_comp/liftings.py b/src/sage/modular/local_comp/liftings.py
index 97b26b2028b..a0e70b090c7 100644
--- a/src/sage/modular/local_comp/liftings.py
+++ b/src/sage/modular/local_comp/liftings.py
@@ -265,9 +265,8 @@ def lift_for_SL(A, N=None):
         U = diag * U
     if V.det() == -1:
         V = V * diag
-    D = U * AZZ * V
 
-    a = [D[i, i] for i in range(m)]
+    a = [U.row(i) * AZZ * V.column(i) for i in range(m)]
     b = prod(a[1:])
 
     Winv = identity_matrix(m)

From 2a0765a947feef6e61d4bff50dde7635c1711198 Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?Fr=C3=A9d=C3=A9ric=20Chapoton?=
 <chapoton@math.univ-lyon1.fr>
Date: Sat, 9 Dec 2017 08:57:12 +0100
Subject: [PATCH 023/128] trac 3313 add random tests

---
 src/sage/modular/local_comp/liftings.py | 16 +++++++++++-----
 1 file changed, 11 insertions(+), 5 deletions(-)

diff --git a/src/sage/modular/local_comp/liftings.py b/src/sage/modular/local_comp/liftings.py
index a0e70b090c7..cf322e6adbe 100644
--- a/src/sage/modular/local_comp/liftings.py
+++ b/src/sage/modular/local_comp/liftings.py
@@ -178,12 +178,12 @@ def lift_ramified(g, p, u, n):
         sage: type(lift_ramified([8,2,12,2], 3, 2, 23)[0])
         <type 'sage.rings.integer.Integer'>
     """
-    a,b,c,d = lift_to_gamma1(g, p**u, n)
-    r = crt( (c - g[2]) / p**u * inverse_mod(a, p), 0, p, n)
+    a, b, c, d = lift_to_gamma1(g, p**u, n)
+    r = crt((c - g[2]) / p**u * inverse_mod(a, p), 0, p, n)
     c = c - p**u * r * a
     d = d - p**u * r * b
     # assert (c - g[2]) % p**(u+1) == 0
-    return [a,b,c,d]
+    return [a, b, c, d]
 
 
 def lift_for_SL(A, N=None):
@@ -241,6 +241,12 @@ def lift_for_SL(A, N=None):
         Traceback (most recent call last):
         ...
         ValueError: you must choose the modulus
+
+        sage: for _ in range(100):
+        ....:     d = randint(0, 10)
+        ....:     p = choice([2,3,5,7,11])
+        ....:     M = random_matrix(Zmod(p), d, algorithm='unimodular')
+        ....:     assert lift_for_SL(M).det() == 1
     """
     from sage.matrix.constructor import matrix
     from sage.matrix.special import (identity_matrix, diagonal_matrix,
@@ -255,8 +261,8 @@ def lift_for_SL(A, N=None):
             N = ring.characteristic()
 
     m = A.nrows()
-    if m == 1:
-        return identity_matrix(ZZ, 1)
+    if m <= 1:
+        return identity_matrix(ZZ, m)
 
     AZZ = A .change_ring(ZZ)
     D, U, V = AZZ.smith_form()

From 1ac7481f53517fb772e709a5c9ee1a217572b870 Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?Fran=C3=A7ois=20Bissey?= <frp.bissey@gmail.com>
Date: Mon, 11 Dec 2017 14:33:05 +1300
Subject: [PATCH 024/128] rebase on ticket #24214

---
 build/pkgs/giac/spkg-install | 27 +++------------------------
 1 file changed, 3 insertions(+), 24 deletions(-)

diff --git a/build/pkgs/giac/spkg-install b/build/pkgs/giac/spkg-install
index bdd8df6cb8d..7221fa4e661 100644
--- a/build/pkgs/giac/spkg-install
+++ b/build/pkgs/giac/spkg-install
@@ -3,12 +3,6 @@
 ###########################################
 
 
-if [ "$SAGE_LOCAL" = "" ]; then
-   echo "SAGE_LOCAL undefined ... exiting";
-   echo "Maybe run 'sage -sh'?"
-   exit 1
-fi
-
 #############################################################
 #    Environment Variables
 #############################################################
@@ -50,22 +44,13 @@ if [ "$UNAME" = "Darwin" ]; then
     DISABLENLS="--disable-nls"
 fi
 
-./configure --prefix="$SAGE_LOCAL" --disable-gui --disable-ao --disable-lapack "$DISABLENLS"
-
-if [ $? -ne 0 ]; then
-    exit 1
-fi
+sdh_configure --disable-gui --disable-ao --disable-lapack "$DISABLENLS"
 
 #############################################################
 #   Build
 #############################################################
 
-echo "Building  giac..."
-$MAKE
-
-if [ $? -ne 0 ]; then
-    exit 1
-fi
+sdh_make
 
 #############################################################
 #   Clean old install
@@ -88,11 +73,5 @@ rm -rf ${SAGE_LOCAL}/include/giac
 #############################################################
 #   Install
 #############################################################
-echo "Installing giac..."
-$MAKE install
-if [ $? -ne 0 ]; then
-    echo >&2 "Error installing Giac."
-    exit 1
-fi
-
 
+sdh_make_install

From a0ce68334dfc95d6a3adf237d1c4b95e8be68f2a Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?Fran=C3=A7ois=20Bissey?= <frp.bissey@gmail.com>
Date: Tue, 12 Dec 2017 09:33:31 +1300
Subject: [PATCH 025/128] update giac to 1.4.9.39

---
 build/pkgs/giac/checksums.ini       | 6 +++---
 build/pkgs/giac/package-version.txt | 2 +-
 build/pkgs/giac/spkg-src            | 2 +-
 3 files changed, 5 insertions(+), 5 deletions(-)

diff --git a/build/pkgs/giac/checksums.ini b/build/pkgs/giac/checksums.ini
index 421ba0b54ec..1da1baceb03 100644
--- a/build/pkgs/giac/checksums.ini
+++ b/build/pkgs/giac/checksums.ini
@@ -1,4 +1,4 @@
 tarball=giac-VERSION.tar.bz2
-sha1=ace4620c664e796a7cf8243eebdf5789dfd77540
-md5=c8b2ff00ec478116aa5902d96de69bfb
-cksum=4247205719
+sha1=7ba617ef29dde72bb927a0e92541e8a30325a7a4
+md5=45dfd01ee167cc0221d07e54db0c28e2
+cksum=1393477559
diff --git a/build/pkgs/giac/package-version.txt b/build/pkgs/giac/package-version.txt
index 15350262215..1ccdedf3c0c 100644
--- a/build/pkgs/giac/package-version.txt
+++ b/build/pkgs/giac/package-version.txt
@@ -1 +1 @@
-1.4.9.19
+1.4.9.39
diff --git a/build/pkgs/giac/spkg-src b/build/pkgs/giac/spkg-src
index 7637c596b87..9d52f68ac00 100755
--- a/build/pkgs/giac/spkg-src
+++ b/build/pkgs/giac/spkg-src
@@ -15,7 +15,7 @@ set -e
 
 # TODO on the next update: l71 switch from gz to bz2 as wished in #18826
 VERSION="1.4.9"
-VERSIONREV="19"
+VERSIONREV="39"
 
 # The upstream tarball name is: giac"$SOURCEORIG".tar.gz
 SOURCEORIG=_"$VERSION"-"$VERSIONREV"

From e020df5a647c1c49df1aaf0819f5e673dba43ece Mon Sep 17 00:00:00 2001
From: Mark <mark00bell@gmail.com>
Date: Fri, 29 Dec 2017 10:08:51 +0000
Subject: [PATCH 026/128] Initial version of get_integral_point method.

---
 src/sage/geometry/polyhedron/base.py | 32 ++++++++++++++++++++++++++++
 1 file changed, 32 insertions(+)

diff --git a/src/sage/geometry/polyhedron/base.py b/src/sage/geometry/polyhedron/base.py
index 2c88b51c8ca..bc32341fe22 100644
--- a/src/sage/geometry/polyhedron/base.py
+++ b/src/sage/geometry/polyhedron/base.py
@@ -5286,6 +5286,38 @@ def integral_points(self, threshold=100000):
         # assert all(self.contains(p) for p in points)   # slow
         return tuple(points)
 
+    def get_integral_point(self, index, **kwds):
+
+        def count(eqns, ieqs):
+            return Polyhedron(eqns=self.equations_list() + extra_eqns, ieqs=self.inequalities_list() + extra_ieqs).integral_points_count(**kwds)
+
+        if not 0 <= index < count([], []):
+            raise IndexError('polytope index out of range')
+
+        D = self.ambient_dim()
+        lower_bounds, upper_bounds = self.bounding_box()
+        coordinate = []
+        extra_eqns = []  # For the components of the coordinate that we have already found.
+        for i in range(D):
+            lower, upper = lower_bounds[i], upper_bounds[i]
+            while lower < upper-1:
+                guess = (lower + upper) // 2  # > lower.
+                # Build new inequalities corresponding to: lower <= x_i < guess.
+                lower_guess_ieqs = [
+                    [-lower] + [0] * i + [1] + [0] * (D - i - 1),
+                    [guess-1] + [0] * i + [-1] + [0] * (D - i - 1),
+                    ]
+                lower_guess_count = count(extra_eqns, lower_guess_ieqs)
+                if lower_guess_count > index:  # Move upper down to guess.
+                    upper = guess
+                    index -= 0
+                else:  # lower_guess_count <= index:  # Move lower up to guess.
+                    lower = guess
+                    index -= lower_guess_count
+            coordinate.append(lower)
+            extra_eqns.append([-lower] + [0] * i + [1] + [0] * (D - i - 1))
+        return vector(ZZ, coordinate)
+
     @cached_method
     def combinatorial_automorphism_group(self, vertex_graph_only=False):
         """

From ca57e1572dca036778b287418a18968f2461565c Mon Sep 17 00:00:00 2001
From: Mark <mark00bell@gmail.com>
Date: Fri, 29 Dec 2017 11:02:35 +0000
Subject: [PATCH 027/128] Added docstring and more comments.

---
 src/sage/geometry/polyhedron/base.py | 41 ++++++++++++++++++++++++++--
 1 file changed, 39 insertions(+), 2 deletions(-)

diff --git a/src/sage/geometry/polyhedron/base.py b/src/sage/geometry/polyhedron/base.py
index bc32341fe22..a7ca2a38fc4 100644
--- a/src/sage/geometry/polyhedron/base.py
+++ b/src/sage/geometry/polyhedron/base.py
@@ -5287,8 +5287,43 @@ def integral_points(self, threshold=100000):
         return tuple(points)
 
     def get_integral_point(self, index, **kwds):
+        r"""
+        Return the integral point self.integral_points()[index].
+
+        However, so long as self.integral_points_count() does not need to enumerate
+        all integral points, neither does this method. Hence this method can be
+        significantly faster.
+
+        INPUT:
+
+        - ``index`` -- integer. The index of the integral point to be found. If this is
+        not in [0, ``self.integral_point_count()``), an ``IndexError`` is raised.
+
+        OUTPUT:
+
+        The integral point in the polyhedron which appears at the given index in the
+        list of integral points returned by self.integral_points(). Note that the
+        points in this list are sorted, first by their first component and then by
+        their second component and so on.
+        If the polyhedron is not compact, a ``ValueError`` is raised.
+
+        EXAMPLES::
+
+            sage: P = Polyhedron(vertices=[(-1,-1),(1,0),(1,1),(0,1)])
+            sage: P.get_integral_point(1)
+            (0, 0)
+            sage: P.get_integral_point(4)
+            (1, 1)
+            sage: P.integral_points()
+            ((-1, -1), (0, 0), (0, 1), (1, 0), (1, 1))
+        """
+
+        if not self.is_compact():
+            raise ValueError('Can only enumerate points in a compact polyhedron.')
 
         def count(eqns, ieqs):
+            r""" Return the number of integral points in this polytope intersected with the one given by eqns and ieqs. """
+
             return Polyhedron(eqns=self.equations_list() + extra_eqns, ieqs=self.inequalities_list() + extra_ieqs).integral_points_count(**kwds)
 
         if not 0 <= index < count([], []):
@@ -5297,8 +5332,8 @@ def count(eqns, ieqs):
         D = self.ambient_dim()
         lower_bounds, upper_bounds = self.bounding_box()
         coordinate = []
-        extra_eqns = []  # For the components of the coordinate that we have already found.
-        for i in range(D):
+        extra_eqns = []  # Constraints from the components of the coordinate that we have already found.
+        for i in range(D):  # Now compute the ith component of coordinate.
             lower, upper = lower_bounds[i], upper_bounds[i]
             while lower < upper-1:
                 guess = (lower + upper) // 2  # > lower.
@@ -5307,6 +5342,7 @@ def count(eqns, ieqs):
                     [-lower] + [0] * i + [1] + [0] * (D - i - 1),
                     [guess-1] + [0] * i + [-1] + [0] * (D - i - 1),
                     ]
+                # Find out how many integral points are in this range.
                 lower_guess_count = count(extra_eqns, lower_guess_ieqs)
                 if lower_guess_count > index:  # Move upper down to guess.
                     upper = guess
@@ -5314,6 +5350,7 @@ def count(eqns, ieqs):
                 else:  # lower_guess_count <= index:  # Move lower up to guess.
                     lower = guess
                     index -= lower_guess_count
+            # Record the new component that we have found.
             coordinate.append(lower)
             extra_eqns.append([-lower] + [0] * i + [1] + [0] * (D - i - 1))
         return vector(ZZ, coordinate)

From f77150616b41c22805b4988e4d83613d8827ac7a Mon Sep 17 00:00:00 2001
From: Mark <mark00bell@gmail.com>
Date: Sat, 30 Dec 2017 20:55:53 +0000
Subject: [PATCH 028/128] Fixed docstring whitespace.

---
 src/sage/geometry/polyhedron/base.py | 6 +++---
 1 file changed, 3 insertions(+), 3 deletions(-)

diff --git a/src/sage/geometry/polyhedron/base.py b/src/sage/geometry/polyhedron/base.py
index a7ca2a38fc4..5736d70c624 100644
--- a/src/sage/geometry/polyhedron/base.py
+++ b/src/sage/geometry/polyhedron/base.py
@@ -5291,13 +5291,13 @@ def get_integral_point(self, index, **kwds):
         Return the integral point self.integral_points()[index].
 
         However, so long as self.integral_points_count() does not need to enumerate
-        all integral points, neither does this method. Hence this method can be
-        significantly faster.
+        all integral points, neither does this method. Hence it can be significantly
+        faster.
 
         INPUT:
 
         - ``index`` -- integer. The index of the integral point to be found. If this is
-        not in [0, ``self.integral_point_count()``), an ``IndexError`` is raised.
+          not in [0, ``self.integral_point_count()``), an ``IndexError`` is raised.
 
         OUTPUT:
 

From 626e399a80d8d8627fafa6b1a4102524995f86e5 Mon Sep 17 00:00:00 2001
From: Mark <mark00bell@gmail.com>
Date: Sat, 30 Dec 2017 21:31:14 +0000
Subject: [PATCH 029/128] Fixed line widths and fencepost error in upper bound.

---
 src/sage/geometry/polyhedron/base.py | 46 ++++++++++++++++++++--------
 1 file changed, 33 insertions(+), 13 deletions(-)

diff --git a/src/sage/geometry/polyhedron/base.py b/src/sage/geometry/polyhedron/base.py
index 5736d70c624..90018ded0e0 100644
--- a/src/sage/geometry/polyhedron/base.py
+++ b/src/sage/geometry/polyhedron/base.py
@@ -5290,22 +5290,38 @@ def get_integral_point(self, index, **kwds):
         r"""
         Return the integral point self.integral_points()[index].
 
-        However, so long as self.integral_points_count() does not need to enumerate
-        all integral points, neither does this method. Hence it can be significantly
-        faster.
+        However, so long as self.integral_points_count() does not need to
+        enumerate all integral points, neither does this method. Hence it can be
+        significantly faster.
 
         INPUT:
 
-        - ``index`` -- integer. The index of the integral point to be found. If this is
-          not in [0, ``self.integral_point_count()``), an ``IndexError`` is raised.
+        - ``index`` -- integer. The index of the integral point to be found. If
+          this is not in [0, ``self.integral_point_count()``), an ``IndexError``
+          is raised.
+
+        - ``**kwds`` -- optional keyword parameters that are passed to
+          :meth:`self.integral_points_count`.
 
         OUTPUT:
 
-        The integral point in the polyhedron which appears at the given index in the
-        list of integral points returned by self.integral_points(). Note that the
-        points in this list are sorted, first by their first component and then by
-        their second component and so on.
-        If the polyhedron is not compact, a ``ValueError`` is raised.
+        The integral point in the polyhedron which appears at the given index in
+        the list of integral points returned by self.integral_points(). Note
+        that the points in this list are sorted first by their first component
+        and then by their second component and so on.  If the polyhedron is not
+        compact, a ``ValueError`` is raised.
+
+        ALGORITHM:
+
+        The function computes each of the components of the requested point in
+        turn.  To compute x_i, the ith component, it bisects the the upper and
+        lower bounds on x_i given by the bounding box. At each bisection, it
+        uses :meth:`integral_points_count` to determine on which side of the
+        bisecting hyperplane the requested point lies.
+
+        .. SEEALSO::
+
+            :meth:`integral_points_count`.
 
         EXAMPLES::
 
@@ -5316,6 +5332,10 @@ def get_integral_point(self, index, **kwds):
             (1, 1)
             sage: P.integral_points()
             ((-1, -1), (0, 0), (0, 1), (1, 0), (1, 1))
+
+            sage: Q = Polyhedron([(1,3), (2, 7), (9, 77)])
+            sage: [Q.get_integral_point(i) for i in range(Q.integral_points_count())] == list(Q.integral_points())
+            True
         """
 
         if not self.is_compact():
@@ -5324,7 +5344,7 @@ def get_integral_point(self, index, **kwds):
         def count(eqns, ieqs):
             r""" Return the number of integral points in this polytope intersected with the one given by eqns and ieqs. """
 
-            return Polyhedron(eqns=self.equations_list() + extra_eqns, ieqs=self.inequalities_list() + extra_ieqs).integral_points_count(**kwds)
+            return Polyhedron(eqns=self.equations_list() + eqns, ieqs=self.inequalities_list() + ieqs).integral_points_count(**kwds)
 
         if not 0 <= index < count([], []):
             raise IndexError('polytope index out of range')
@@ -5333,8 +5353,8 @@ def count(eqns, ieqs):
         lower_bounds, upper_bounds = self.bounding_box()
         coordinate = []
         extra_eqns = []  # Constraints from the components of the coordinate that we have already found.
-        for i in range(D):  # Now compute the ith component of coordinate.
-            lower, upper = lower_bounds[i], upper_bounds[i]
+        for i in range(D):  # Now compute x_i, the ith component of coordinate.
+            lower, upper = lower_bounds[i], upper_bounds[i] + 1  # So lower <= x_i < upper.
             while lower < upper-1:
                 guess = (lower + upper) // 2  # > lower.
                 # Build new inequalities corresponding to: lower <= x_i < guess.

From c46460d6180b59171c4422a31203994f21567ffb Mon Sep 17 00:00:00 2001
From: Mark <mark00bell@gmail.com>
Date: Sat, 30 Dec 2017 23:39:31 +0000
Subject: [PATCH 030/128] Added sorting comments to docstring and
 random_integral_point method.

---
 src/sage/geometry/polyhedron/base.py | 42 ++++++++++++++++++++++++----
 1 file changed, 36 insertions(+), 6 deletions(-)

diff --git a/src/sage/geometry/polyhedron/base.py b/src/sage/geometry/polyhedron/base.py
index 90018ded0e0..899e5698723 100644
--- a/src/sage/geometry/polyhedron/base.py
+++ b/src/sage/geometry/polyhedron/base.py
@@ -5288,7 +5288,7 @@ def integral_points(self, threshold=100000):
 
     def get_integral_point(self, index, **kwds):
         r"""
-        Return the integral point self.integral_points()[index].
+        Return the integral point sorted(self.integral_points())[index].
 
         However, so long as self.integral_points_count() does not need to
         enumerate all integral points, neither does this method. Hence it can be
@@ -5305,11 +5305,11 @@ def get_integral_point(self, index, **kwds):
 
         OUTPUT:
 
-        The integral point in the polyhedron which appears at the given index in
-        the list of integral points returned by self.integral_points(). Note
-        that the points in this list are sorted first by their first component
-        and then by their second component and so on.  If the polyhedron is not
-        compact, a ``ValueError`` is raised.
+        The integral point in the polyhedron which appears at the given index
+        in the sorted list of integral points returned by
+        self.integral_points(). Note that the points in this list are sorted
+        first by their first component and then by their second component and
+        so on.  If the polyhedron is not compact, a ``ValueError`` is raised.
 
         ALGORITHM:
 
@@ -5375,6 +5375,36 @@ def count(eqns, ieqs):
             extra_eqns.append([-lower] + [0] * i + [1] + [0] * (D - i - 1))
         return vector(ZZ, coordinate)
 
+    def random_integral_point(self, **kwds):
+        r"""
+        Return an integral point in this polyhedron chosen uniformly at random.
+
+        INPUT:
+
+        - ``**kwds`` -- optional keyword parameters that are passed to
+          :meth:`self.get_integral_point`.
+
+        OUTPUT:
+
+        The integral point in the polyhedron chosen uniformly at random.
+        If the polyhedron is not compact, a ``ValueError`` is raised.
+
+        .. SEEALSO::
+
+            :meth:`get_integral_point`.
+
+        EXAMPLES::
+
+            sage: P = Polyhedron(vertices=[(-1,-1),(1,0),(1,1),(0,1)])
+            sage: P.random_integral_point()  # random
+            (0, 0)
+            sage: P.random_integral_point() in P.integral_points()
+            True
+        """
+
+        index = random.randint(0, self.integral_points_count()-1)
+        return self.get_integral_point(index)
+
     @cached_method
     def combinatorial_automorphism_group(self, vertex_graph_only=False):
         """

From 82a64d2f6eb533c16413c681a8d89c130283fa1c Mon Sep 17 00:00:00 2001
From: Mark <mark00bell@gmail.com>
Date: Sat, 30 Dec 2017 23:44:14 +0000
Subject: [PATCH 031/128] Added missing import.

---
 src/sage/geometry/polyhedron/base.py | 1 +
 1 file changed, 1 insertion(+)

diff --git a/src/sage/geometry/polyhedron/base.py b/src/sage/geometry/polyhedron/base.py
index 899e5698723..6dd0f1dcc93 100644
--- a/src/sage/geometry/polyhedron/base.py
+++ b/src/sage/geometry/polyhedron/base.py
@@ -17,6 +17,7 @@
 from __future__ import division, print_function, absolute_import
 
 import itertools
+import random
 import six
 from sage.structure.element import Element, coerce_binop, is_Vector
 from sage.structure.richcmp import rich_to_bool, op_NE

From 11aabdd974fba81accf9966584a159fba8621c2e Mon Sep 17 00:00:00 2001
From: Mark <mark00bell@gmail.com>
Date: Sun, 31 Dec 2017 12:10:48 +0000
Subject: [PATCH 032/128] Added check to make sure there are integral points
 before sampling and doctests for the different errors.

---
 src/sage/geometry/polyhedron/base.py | 38 ++++++++++++++++++++++++----
 1 file changed, 33 insertions(+), 5 deletions(-)

diff --git a/src/sage/geometry/polyhedron/base.py b/src/sage/geometry/polyhedron/base.py
index 6dd0f1dcc93..bf85d447b97 100644
--- a/src/sage/geometry/polyhedron/base.py
+++ b/src/sage/geometry/polyhedron/base.py
@@ -39,6 +39,8 @@
 
 from sage.misc.superseded import deprecated_function_alias
 
+from sage.categories.sets_cat import EmptySetError
+
 #########################################################################
 # Notes if you want to implement your own backend:
 #
@@ -5335,8 +5337,14 @@ def get_integral_point(self, index, **kwds):
             ((-1, -1), (0, 0), (0, 1), (1, 0), (1, 1))
 
             sage: Q = Polyhedron([(1,3), (2, 7), (9, 77)])
-            sage: [Q.get_integral_point(i) for i in range(Q.integral_points_count())] == list(Q.integral_points())
+            sage: [Q.get_integral_point(i) for i in range(Q.integral_points_count())] == sorted(Q.integral_points())
             True
+
+            sage: R = Polyhedron(vertices=[[1/2, 1/3]], rays=[[1, 1]])
+            sage: R.get_integral_point(0)
+            Traceback (most recent call last):
+            ...
+            ValueError: ...
         """
 
         if not self.is_compact():
@@ -5387,8 +5395,10 @@ def random_integral_point(self, **kwds):
 
         OUTPUT:
 
-        The integral point in the polyhedron chosen uniformly at random.
-        If the polyhedron is not compact, a ``ValueError`` is raised.
+        The integral point in the polyhedron chosen uniformly at random. If the
+        polyhedron is not compact, a ``ValueError`` is raised.  If the
+        polyhedron does not contain any integral points, an ``EmptySetError`` is
+        raised.
 
         .. SEEALSO::
 
@@ -5401,10 +5411,28 @@ def random_integral_point(self, **kwds):
             (0, 0)
             sage: P.random_integral_point() in P.integral_points()
             True
+
+            sage: Q = Polyhedron(vertices=[(2, 1/3)], rays=[(1, 2)])
+            sage: Q.random_integral_point()
+            Traceback (most recent call last):
+            ...
+            ValueError: ...
+
+            sage: R = Polyhedron(vertices=[(1/2, 0), (1, 1/2), (0, 1/2)])
+            sage: R.random_integral_point()
+            Traceback (most recent call last):
+            ...
+            EmptySetError: ...
         """
 
-        index = random.randint(0, self.integral_points_count()-1)
-        return self.get_integral_point(index)
+        if not self.is_compact():
+            raise ValueError('Can only sample integral points in a compact polyhedron.')
+
+        count = self.integral_points_count()
+        if count == 0:
+            raise EmptySetError('Polyhedron does not contain any integral points.')
+
+        return self.get_integral_point(random.randint(0, count-1))
 
     @cached_method
     def combinatorial_automorphism_group(self, vertex_graph_only=False):

From 4e76f7d28eb839bac153ea682e50707c5bdb4754 Mon Sep 17 00:00:00 2001
From: Mark <mark00bell@gmail.com>
Date: Sun, 31 Dec 2017 13:32:00 +0000
Subject: [PATCH 033/128] Using current_randstate() instead of random.

---
 src/sage/geometry/polyhedron/base.py | 4 ++--
 1 file changed, 2 insertions(+), 2 deletions(-)

diff --git a/src/sage/geometry/polyhedron/base.py b/src/sage/geometry/polyhedron/base.py
index bf85d447b97..fddd20e25db 100644
--- a/src/sage/geometry/polyhedron/base.py
+++ b/src/sage/geometry/polyhedron/base.py
@@ -17,13 +17,13 @@
 from __future__ import division, print_function, absolute_import
 
 import itertools
-import random
 import six
 from sage.structure.element import Element, coerce_binop, is_Vector
 from sage.structure.richcmp import rich_to_bool, op_NE
 
 from sage.misc.all import cached_method, prod
 from sage.misc.package import is_package_installed, PackageNotFoundError
+from sage.misc.randstate import current_randstate
 
 from sage.rings.all import QQ, ZZ, AA
 from sage.rings.real_double import RDF
@@ -5432,7 +5432,7 @@ def random_integral_point(self, **kwds):
         if count == 0:
             raise EmptySetError('Polyhedron does not contain any integral points.')
 
-        return self.get_integral_point(random.randint(0, count-1))
+        return self.get_integral_point(current_randstate().python_random().randint(0, count-1))
 
     @cached_method
     def combinatorial_automorphism_group(self, vertex_graph_only=False):

From 99683415186c9890bc065fe0883f383fd2bd0019 Mon Sep 17 00:00:00 2001
From: Mark <mark00bell@gmail.com>
Date: Sun, 31 Dec 2017 13:56:50 +0000
Subject: [PATCH 034/128] Fixed upper and lower bounds to be integers.

---
 src/sage/geometry/polyhedron/base.py | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/src/sage/geometry/polyhedron/base.py b/src/sage/geometry/polyhedron/base.py
index fddd20e25db..a58e934b176 100644
--- a/src/sage/geometry/polyhedron/base.py
+++ b/src/sage/geometry/polyhedron/base.py
@@ -5363,7 +5363,7 @@ def count(eqns, ieqs):
         coordinate = []
         extra_eqns = []  # Constraints from the components of the coordinate that we have already found.
         for i in range(D):  # Now compute x_i, the ith component of coordinate.
-            lower, upper = lower_bounds[i], upper_bounds[i] + 1  # So lower <= x_i < upper.
+            lower, upper = ceil(lower_bounds[i]), floor(upper_bounds[i]) + 1  # So lower <= x_i < upper.
             while lower < upper-1:
                 guess = (lower + upper) // 2  # > lower.
                 # Build new inequalities corresponding to: lower <= x_i < guess.

From a632bf6ffe46d7cdb412a4504200e047e5852322 Mon Sep 17 00:00:00 2001
From: Vincent Delecroix <20100.delecroix@gmail.com>
Date: Sun, 31 Dec 2017 13:54:50 +0100
Subject: [PATCH 035/128] 23418: number fields are infinite

---
 .../coercion_and_categories.rst                 |  3 ++-
 src/sage/categories/homset.py                   |  6 +++---
 src/sage/categories/number_fields.py            |  9 +++++++--
 src/sage/misc/c3_controlled.pyx                 |  3 ++-
 src/sage/rings/number_field/number_field.py     | 17 +++++++++++++++--
 src/sage/rings/rational_field.py                |  2 ++
 6 files changed, 31 insertions(+), 9 deletions(-)

diff --git a/src/doc/en/thematic_tutorials/coercion_and_categories.rst b/src/doc/en/thematic_tutorials/coercion_and_categories.rst
index e1e1872a5fe..552a4a6b045 100644
--- a/src/doc/en/thematic_tutorials/coercion_and_categories.rst
+++ b/src/doc/en/thematic_tutorials/coercion_and_categories.rst
@@ -879,7 +879,8 @@ The four axioms requested for coercions
       rational field is a homomorphism of euclidean domains::
 
           sage: QQ.coerce_map_from(ZZ).category_for()
-          Join of Category of euclidean domains and Category of metric spaces
+          Join of Category of euclidean domains and Category of infinite sets
+          and Category of metric spaces
 
       .. end of output
 
diff --git a/src/sage/categories/homset.py b/src/sage/categories/homset.py
index 6e6abee4363..272ddacb692 100644
--- a/src/sage/categories/homset.py
+++ b/src/sage/categories/homset.py
@@ -47,8 +47,6 @@
 
 - Simon King (2013-02): added examples
 """
-from __future__ import absolute_import
-
 #*****************************************************************************
 #  Copyright (C) 2005 David Kohel <kohel@maths.usyd.edu>, William Stein <wstein@gmail.com>
 #
@@ -64,6 +62,8 @@
 #                  http://www.gnu.org/licenses/
 #*****************************************************************************
 
+from __future__ import absolute_import, print_function
+
 from sage.categories.category import Category
 from . import morphism
 from sage.structure.parent import Parent, Set_generic
@@ -402,7 +402,7 @@ def Hom(X, Y, category=None, check=True):
                 #   will be called twice.
                 # - This is bound to fail if X is an extension type and
                 #   does not actually inherit from category.parent_class
-                H = category.parent_class._Hom_(X, Y, category = category)
+                H = X.category().parent_class._Hom_(X, Y, category = category)
             except (AttributeError, TypeError):
                 # By default, construct a plain homset.
                 H = Homset(X, Y, category = category, check=check)
diff --git a/src/sage/categories/number_fields.py b/src/sage/categories/number_fields.py
index a1c6336e656..0317f520a5e 100644
--- a/src/sage/categories/number_fields.py
+++ b/src/sage/categories/number_fields.py
@@ -26,6 +26,11 @@ class NumberFields(Category_singleton):
         sage: C
         Category of number fields
 
+    By definition, it is infinite::
+
+        sage: NumberFields().Infinite() is NumberFields()
+        True
+
     Notice that the rational numbers `\QQ` *are* considered as
     an object in this category::
 
@@ -58,9 +63,9 @@ def super_categories(self):
         EXAMPLES::
 
             sage: NumberFields().super_categories()
-            [Category of fields]
+            [Category of infinite fields]
         """
-        return[Fields()]
+        return [Fields().Infinite()]
 
     def __contains__(self, x):
         r"""
diff --git a/src/sage/misc/c3_controlled.pyx b/src/sage/misc/c3_controlled.pyx
index 38b3b7577f7..831b20f6829 100644
--- a/src/sage/misc/c3_controlled.pyx
+++ b/src/sage/misc/c3_controlled.pyx
@@ -346,7 +346,8 @@ doctest::
      Category of finite dimensional hopf algebras with basis over Rational Field,
      Category of finite enumerated permutation groups,
      Category of finite weyl groups,
-     Category of group algebras over Rational Field]
+     Category of group algebras over Rational Field,
+     Category of number fields]
 
 AUTHOR:
 
diff --git a/src/sage/rings/number_field/number_field.py b/src/sage/rings/number_field/number_field.py
index 9dbf23b8cf2..61af24d0ab8 100644
--- a/src/sage/rings/number_field/number_field.py
+++ b/src/sage/rings/number_field/number_field.py
@@ -120,6 +120,7 @@
 from sage.misc.misc_c import prod
 from sage.categories.homset import End
 from sage.rings.all import Infinity
+from sage.categories.number_fields import NumberFields
 
 import sage.rings.ring
 from sage.misc.latex import latex_variable_name
@@ -142,6 +143,7 @@
 from itertools import count
 from builtins import zip
 
+_NumberFields = NumberFields()
 
 def is_NumberFieldHomsetCodomain(codomain):
     """
@@ -520,6 +522,18 @@ def NumberField(polynomial, name=None, check=True, names=None, embedding=None, l
         ...
         TypeError: You must specify the name of the generator.
 
+    Check that we can construct morphisms to matrix space (:trac:`23418`)::
+
+        sage: t = polygen(QQ)
+        sage: K = NumberField(t^4 - 2, 'a')
+        sage: K.hom([K.gen().matrix()])
+        Ring morphism:
+          From: Number Field in a with defining polynomial x^4 - 2
+          To:   Full MatrixSpace of 4 by 4 dense matrices over Rational Field
+          Defn: a |--> [0 1 0 0]
+                       [0 0 1 0]
+                       [0 0 0 1]
+                       [2 0 0 0]
     """
     if names is not None:
         name = names
@@ -1327,8 +1341,7 @@ def __init__(self, polynomial, name, latex_name,
         self._assume_disc_small = assume_disc_small
         self._maximize_at_primes = maximize_at_primes
         self._structure = structure
-        from sage.categories.number_fields import NumberFields
-        default_category = NumberFields()
+        default_category = _NumberFields
         if category is None:
             category = default_category
         else:
diff --git a/src/sage/rings/rational_field.py b/src/sage/rings/rational_field.py
index 64be36a52bc..29823505821 100644
--- a/src/sage/rings/rational_field.py
+++ b/src/sage/rings/rational_field.py
@@ -39,6 +39,8 @@
     True
     sage: RationalField() is RationalField()
     True
+    sage: Q in Fields().Infinite()
+    True
 
 AUTHORS:
 

From 911bfdc8fa652202ad3bc128d97d26ca46c978e5 Mon Sep 17 00:00:00 2001
From: Mark <mark00bell@gmail.com>
Date: Sun, 31 Dec 2017 15:05:31 +0000
Subject: [PATCH 036/128] Returned point is now immutable.

---
 src/sage/geometry/polyhedron/base.py | 4 +++-
 1 file changed, 3 insertions(+), 1 deletion(-)

diff --git a/src/sage/geometry/polyhedron/base.py b/src/sage/geometry/polyhedron/base.py
index a58e934b176..3b8c46ba45f 100644
--- a/src/sage/geometry/polyhedron/base.py
+++ b/src/sage/geometry/polyhedron/base.py
@@ -5382,7 +5382,9 @@ def count(eqns, ieqs):
             # Record the new component that we have found.
             coordinate.append(lower)
             extra_eqns.append([-lower] + [0] * i + [1] + [0] * (D - i - 1))
-        return vector(ZZ, coordinate)
+        point = vector(ZZ, coordinate)
+        point.set_immutable()
+        return point
 
     def random_integral_point(self, **kwds):
         r"""

From 73af99173b5cdec874342eb1bcd04e3c2bb857b7 Mon Sep 17 00:00:00 2001
From: Mark <mark00bell@gmail.com>
Date: Sun, 31 Dec 2017 15:13:25 +0000
Subject: [PATCH 037/128] More explict error cases.

---
 src/sage/geometry/polyhedron/base.py | 6 +++---
 1 file changed, 3 insertions(+), 3 deletions(-)

diff --git a/src/sage/geometry/polyhedron/base.py b/src/sage/geometry/polyhedron/base.py
index 3b8c46ba45f..c0921b34227 100644
--- a/src/sage/geometry/polyhedron/base.py
+++ b/src/sage/geometry/polyhedron/base.py
@@ -5350,14 +5350,14 @@ def get_integral_point(self, index, **kwds):
         if not self.is_compact():
             raise ValueError('Can only enumerate points in a compact polyhedron.')
 
+        if not 0 <= index < self.integral_points_count():
+            raise IndexError('polytope index out of range')
+
         def count(eqns, ieqs):
             r""" Return the number of integral points in this polytope intersected with the one given by eqns and ieqs. """
 
             return Polyhedron(eqns=self.equations_list() + eqns, ieqs=self.inequalities_list() + ieqs).integral_points_count(**kwds)
 
-        if not 0 <= index < count([], []):
-            raise IndexError('polytope index out of range')
-
         D = self.ambient_dim()
         lower_bounds, upper_bounds = self.bounding_box()
         coordinate = []

From 5aea167963a784f90cdd6a576f7f0e446b288666 Mon Sep 17 00:00:00 2001
From: Mark <mark00bell@gmail.com>
Date: Sun, 31 Dec 2017 15:39:02 +0000
Subject: [PATCH 038/128] Rewitten to repeatedly intersect the polyhedron with
 halfspaces.

---
 src/sage/geometry/polyhedron/base.py | 31 +++++++++++-----------------
 1 file changed, 12 insertions(+), 19 deletions(-)

diff --git a/src/sage/geometry/polyhedron/base.py b/src/sage/geometry/polyhedron/base.py
index c0921b34227..288c5e211f7 100644
--- a/src/sage/geometry/polyhedron/base.py
+++ b/src/sage/geometry/polyhedron/base.py
@@ -5353,35 +5353,28 @@ def get_integral_point(self, index, **kwds):
         if not 0 <= index < self.integral_points_count():
             raise IndexError('polytope index out of range')
 
-        def count(eqns, ieqs):
-            r""" Return the number of integral points in this polytope intersected with the one given by eqns and ieqs. """
-
-            return Polyhedron(eqns=self.equations_list() + eqns, ieqs=self.inequalities_list() + ieqs).integral_points_count(**kwds)
-
         D = self.ambient_dim()
         lower_bounds, upper_bounds = self.bounding_box()
         coordinate = []
-        extra_eqns = []  # Constraints from the components of the coordinate that we have already found.
+        P = self
         for i in range(D):  # Now compute x_i, the ith component of coordinate.
             lower, upper = ceil(lower_bounds[i]), floor(upper_bounds[i]) + 1  # So lower <= x_i < upper.
             while lower < upper-1:
                 guess = (lower + upper) // 2  # > lower.
-                # Build new inequalities corresponding to: lower <= x_i < guess.
-                lower_guess_ieqs = [
-                    [-lower] + [0] * i + [1] + [0] * (D - i - 1),
-                    [guess-1] + [0] * i + [-1] + [0] * (D - i - 1),
-                    ]
-                # Find out how many integral points are in this range.
-                lower_guess_count = count(extra_eqns, lower_guess_ieqs)
-                if lower_guess_count > index:  # Move upper down to guess.
+                # Build new polyhedron by intersecting P with the halfspace {x_i < guess}.
+                P_lt_guess = P.intersection(Polyhedron(ieqs=[[guess-1] + [0] * i + [-1] + [0] * (D - i - 1)]))
+                # Avoid computing P_geq_guess = P.intersection{x_i >= guess} right now, it might not be needed.
+                P_lt_guess_count = P_lt_guess.integral_points_count()
+                if P_lt_guess_count > index:  # Move upper down to guess.
                     upper = guess
                     index -= 0
-                else:  # lower_guess_count <= index:  # Move lower up to guess.
+                    P = P_lt_guess
+                else:  # P_lt_guess_count <= index:  # Move lower up to guess.
                     lower = guess
-                    index -= lower_guess_count
-            # Record the new component that we have found.
-            coordinate.append(lower)
-            extra_eqns.append([-lower] + [0] * i + [1] + [0] * (D - i - 1))
+                    index -= P_lt_guess_count
+                    P_geq_guess = P.intersection(Polyhedron(ieqs=[[-guess] + [0] * i + [1] + [0] * (D - i - 1)]))
+                    P = P_geq_guess
+            coordinate.append(lower)  # Record the new component that we have found.
         point = vector(ZZ, coordinate)
         point.set_immutable()
         return point

From ff28e93eda39a2ff8a83dc8cf68af3d36f5d7976 Mon Sep 17 00:00:00 2001
From: Mark <mark00bell@gmail.com>
Date: Mon, 1 Jan 2018 14:36:23 +0000
Subject: [PATCH 039/128] Construct halfspaces using self.parent() to stay in
 the same ring.

---
 src/sage/geometry/polyhedron/base.py | 7 ++++---
 1 file changed, 4 insertions(+), 3 deletions(-)

diff --git a/src/sage/geometry/polyhedron/base.py b/src/sage/geometry/polyhedron/base.py
index 288c5e211f7..66be2434517 100644
--- a/src/sage/geometry/polyhedron/base.py
+++ b/src/sage/geometry/polyhedron/base.py
@@ -5357,13 +5357,14 @@ def get_integral_point(self, index, **kwds):
         lower_bounds, upper_bounds = self.bounding_box()
         coordinate = []
         P = self
+        S = self.parent()
         for i in range(D):  # Now compute x_i, the ith component of coordinate.
             lower, upper = ceil(lower_bounds[i]), floor(upper_bounds[i]) + 1  # So lower <= x_i < upper.
             while lower < upper-1:
                 guess = (lower + upper) // 2  # > lower.
                 # Build new polyhedron by intersecting P with the halfspace {x_i < guess}.
-                P_lt_guess = P.intersection(Polyhedron(ieqs=[[guess-1] + [0] * i + [-1] + [0] * (D - i - 1)]))
-                # Avoid computing P_geq_guess = P.intersection{x_i >= guess} right now, it might not be needed.
+                P_lt_guess = P.intersection(S(ieqs=[[guess-1] + [0] * i + [-1] + [0] * (D - i - 1)]))
+                # Avoid computing P_geq_guess = P.intersection({x_i >= guess}) right now, it might not be needed.
                 P_lt_guess_count = P_lt_guess.integral_points_count()
                 if P_lt_guess_count > index:  # Move upper down to guess.
                     upper = guess
@@ -5372,7 +5373,7 @@ def get_integral_point(self, index, **kwds):
                 else:  # P_lt_guess_count <= index:  # Move lower up to guess.
                     lower = guess
                     index -= P_lt_guess_count
-                    P_geq_guess = P.intersection(Polyhedron(ieqs=[[-guess] + [0] * i + [1] + [0] * (D - i - 1)]))
+                    P_geq_guess = P.intersection(S(ieqs=[[-guess] + [0] * i + [1] + [0] * (D - i - 1)]))
                     P = P_geq_guess
             coordinate.append(lower)  # Record the new component that we have found.
         point = vector(ZZ, coordinate)

From 8d3f64162697d0580f8b7657ace4ee703a27bd03 Mon Sep 17 00:00:00 2001
From: Mark <mark00bell@gmail.com>
Date: Tue, 2 Jan 2018 16:13:12 +0000
Subject: [PATCH 040/128] Using correct syntax for creating halfspaces via
 parent.

---
 src/sage/geometry/polyhedron/base.py | 4 ++--
 1 file changed, 2 insertions(+), 2 deletions(-)

diff --git a/src/sage/geometry/polyhedron/base.py b/src/sage/geometry/polyhedron/base.py
index 66be2434517..a5caf01ae45 100644
--- a/src/sage/geometry/polyhedron/base.py
+++ b/src/sage/geometry/polyhedron/base.py
@@ -5363,7 +5363,7 @@ def get_integral_point(self, index, **kwds):
             while lower < upper-1:
                 guess = (lower + upper) // 2  # > lower.
                 # Build new polyhedron by intersecting P with the halfspace {x_i < guess}.
-                P_lt_guess = P.intersection(S(ieqs=[[guess-1] + [0] * i + [-1] + [0] * (D - i - 1)]))
+                P_lt_guess = P.intersection(S(None, ([[guess-1] + [0] * i + [-1] + [0] * (D - i - 1)], [])))
                 # Avoid computing P_geq_guess = P.intersection({x_i >= guess}) right now, it might not be needed.
                 P_lt_guess_count = P_lt_guess.integral_points_count()
                 if P_lt_guess_count > index:  # Move upper down to guess.
@@ -5373,7 +5373,7 @@ def get_integral_point(self, index, **kwds):
                 else:  # P_lt_guess_count <= index:  # Move lower up to guess.
                     lower = guess
                     index -= P_lt_guess_count
-                    P_geq_guess = P.intersection(S(ieqs=[[-guess] + [0] * i + [1] + [0] * (D - i - 1)]))
+                    P_geq_guess = P.intersection(S(None, ([[-guess] + [0] * i + [1] + [0] * (D - i - 1)], [])))
                     P = P_geq_guess
             coordinate.append(lower)  # Record the new component that we have found.
         point = vector(ZZ, coordinate)

From ed313737d7579954968b5feee89ada4901cdd5e3 Mon Sep 17 00:00:00 2001
From: Mark <mark00bell@gmail.com>
Date: Tue, 2 Jan 2018 17:48:31 +0000
Subject: [PATCH 041/128] Reworked docstring.

---
 src/sage/geometry/polyhedron/base.py | 30 +++++++++++++---------------
 1 file changed, 14 insertions(+), 16 deletions(-)

diff --git a/src/sage/geometry/polyhedron/base.py b/src/sage/geometry/polyhedron/base.py
index a5caf01ae45..9707e92fccc 100644
--- a/src/sage/geometry/polyhedron/base.py
+++ b/src/sage/geometry/polyhedron/base.py
@@ -5291,11 +5291,13 @@ def integral_points(self, threshold=100000):
 
     def get_integral_point(self, index, **kwds):
         r"""
-        Return the integral point sorted(self.integral_points())[index].
+        Return the ``index``-th integral point in this polyhedron.
 
-        However, so long as self.integral_points_count() does not need to
-        enumerate all integral points, neither does this method. Hence it can be
-        significantly faster.
+        This is equivalent to sorted(self.integral_points())[index]. However,
+        so long as self.integral_points_count() does not need to enumerate all
+        integral points, neither does this method. Hence it can be
+        significantly faster. If the polyhedron is not compact, a
+        ``ValueError`` is raised.
 
         INPUT:
 
@@ -5306,18 +5308,10 @@ def get_integral_point(self, index, **kwds):
         - ``**kwds`` -- optional keyword parameters that are passed to
           :meth:`self.integral_points_count`.
 
-        OUTPUT:
-
-        The integral point in the polyhedron which appears at the given index
-        in the sorted list of integral points returned by
-        self.integral_points(). Note that the points in this list are sorted
-        first by their first component and then by their second component and
-        so on.  If the polyhedron is not compact, a ``ValueError`` is raised.
-
         ALGORITHM:
 
         The function computes each of the components of the requested point in
-        turn.  To compute x_i, the ith component, it bisects the the upper and
+        turn. To compute x_i, the ith component, it bisects the the upper and
         lower bounds on x_i given by the bounding box. At each bisection, it
         uses :meth:`integral_points_count` to determine on which side of the
         bisecting hyperplane the requested point lies.
@@ -5333,8 +5327,12 @@ def get_integral_point(self, index, **kwds):
             (0, 0)
             sage: P.get_integral_point(4)
             (1, 1)
-            sage: P.integral_points()
-            ((-1, -1), (0, 0), (0, 1), (1, 0), (1, 1))
+            sage: sorted(P.integral_points())
+            [(-1, -1), (0, 0), (0, 1), (1, 0), (1, 1)]
+            sage: P.get_integral_point(5)
+            Traceback (most recent call last):
+            ...
+            IndexError: ...
 
             sage: Q = Polyhedron([(1,3), (2, 7), (9, 77)])
             sage: [Q.get_integral_point(i) for i in range(Q.integral_points_count())] == sorted(Q.integral_points())
@@ -5392,7 +5390,7 @@ def random_integral_point(self, **kwds):
         OUTPUT:
 
         The integral point in the polyhedron chosen uniformly at random. If the
-        polyhedron is not compact, a ``ValueError`` is raised.  If the
+        polyhedron is not compact, a ``ValueError`` is raised. If the
         polyhedron does not contain any integral points, an ``EmptySetError`` is
         raised.
 

From f8350785ffca7f2078cc1fd6537c77288eb05eb0 Mon Sep 17 00:00:00 2001
From: Mark <mark00bell@gmail.com>
Date: Tue, 2 Jan 2018 18:54:32 +0000
Subject: [PATCH 042/128] Added code fragment markers to docstring.

---
 src/sage/geometry/polyhedron/base.py | 8 ++++----
 1 file changed, 4 insertions(+), 4 deletions(-)

diff --git a/src/sage/geometry/polyhedron/base.py b/src/sage/geometry/polyhedron/base.py
index 9707e92fccc..3ccf3644739 100644
--- a/src/sage/geometry/polyhedron/base.py
+++ b/src/sage/geometry/polyhedron/base.py
@@ -5293,10 +5293,10 @@ def get_integral_point(self, index, **kwds):
         r"""
         Return the ``index``-th integral point in this polyhedron.
 
-        This is equivalent to sorted(self.integral_points())[index]. However,
-        so long as self.integral_points_count() does not need to enumerate all
-        integral points, neither does this method. Hence it can be
-        significantly faster. If the polyhedron is not compact, a
+        This is equivalent to ``sorted(self.integral_points())[index]``.
+        However, so long as self.integral_points_count() does not need to
+        enumerate all integral points, neither does this method. Hence it can
+        be significantly faster. If the polyhedron is not compact, a
         ``ValueError`` is raised.
 
         INPUT:

From cdbc67dafaa65dc2de3cc81c57ef17a0e5b1e209 Mon Sep 17 00:00:00 2001
From: Travis Scrimshaw <tcscrims at gmail.com>
Date: Wed, 3 Jan 2018 00:50:01 -0600
Subject: [PATCH 043/128] Reverting change and adding test showing the
 behavior.

---
 src/sage/categories/homset.py | 32 ++++++++++++++++++++++++++++++--
 1 file changed, 30 insertions(+), 2 deletions(-)

diff --git a/src/sage/categories/homset.py b/src/sage/categories/homset.py
index 272ddacb692..b22ae9a1469 100644
--- a/src/sage/categories/homset.py
+++ b/src/sage/categories/homset.py
@@ -343,6 +343,34 @@ def Hom(X, Y, category=None, check=True):
         si... = ... pg_Hom(si..., si..., ...) ...
         sage: Q == loads(dumps(Q))
         True
+
+    Check that the ``_Hom_`` method of the ``category`` input is used::
+
+        sage: from sage.categories.category_types import Category_over_base_ring
+        sage: class ModulesWithHom(Category_over_base_ring):
+        ....:     def super_categories(self):
+        ....:         return [Modules(self.base_ring())]
+        ....:     class ParentMethods:
+        ....:         def _Hom_(self, Y, category=None):
+        ....:             print("Modules")
+        ....:             raise TypeError
+        sage: class AlgebrasWithHom(Category_over_base_ring):
+        ....:     def super_categories(self):
+        ....:         return [Algebras(self.base_ring()), ModulesWithHom(self.base_ring())]
+        ....:     class ParentMethods:
+        ....:         def _Hom_(self, Y, category=None):
+        ....:             R = self.base_ring()
+        ....:             if category is not None and category.is_subcategory(Algebras(R)):
+        ....:                 print("Algebras")
+        ....:             raise TypeError
+        sage: from sage.structure.element import Element
+        sage: class Foo(Parent):
+        ....:     _no_generic_basering_coercion = True
+        ....:     class Element(Element):
+        ....:         pass
+        sage: X = Foo(base=QQ, category=AlgebrasWithHom(QQ))
+        sage: H = Hom(X, X, ModulesWithHom(QQ))
+        Modules
     """
     # This should use cache_function instead
     # However some special handling is currently needed for
@@ -402,10 +430,10 @@ def Hom(X, Y, category=None, check=True):
                 #   will be called twice.
                 # - This is bound to fail if X is an extension type and
                 #   does not actually inherit from category.parent_class
-                H = X.category().parent_class._Hom_(X, Y, category = category)
+                H = category.parent_class._Hom_(X, Y, category=category)
             except (AttributeError, TypeError):
                 # By default, construct a plain homset.
-                H = Homset(X, Y, category = category, check=check)
+                H = Homset(X, Y, category=category, check=check)
     _cache[key] = H
     if isinstance(X, UniqueRepresentation) and isinstance(Y, UniqueRepresentation):
         if not isinstance(H, WithEqualityById):

From b7f3fa69fae7ca1119968e2805230a67d60c21d8 Mon Sep 17 00:00:00 2001
From: Travis Scrimshaw <tcscrims at gmail.com>
Date: Wed, 3 Jan 2018 01:14:42 -0600
Subject: [PATCH 044/128] Special handling of the join categories for Hom.

---
 src/sage/categories/homset.py | 34 +++++++++++++++++++++++-----------
 1 file changed, 23 insertions(+), 11 deletions(-)

diff --git a/src/sage/categories/homset.py b/src/sage/categories/homset.py
index b22ae9a1469..9364ac5cacc 100644
--- a/src/sage/categories/homset.py
+++ b/src/sage/categories/homset.py
@@ -64,7 +64,7 @@
 
 from __future__ import absolute_import, print_function
 
-from sage.categories.category import Category
+from sage.categories.category import Category, JoinCategory
 from . import morphism
 from sage.structure.parent import Parent, Set_generic
 from sage.misc.fast_methods import WithEqualityById
@@ -422,16 +422,28 @@ def Hom(X, Y, category=None, check=True):
         try: # _Hom_ hook from the parent
             H = X._Hom_(Y, category)
         except (AttributeError, TypeError):
-            try:
-                # Workaround in case the above fails, but the category
-                # also provides a _Hom_ hook.
-                # FIXME:
-                # - If X._Hom_ actually comes from category and fails, it
-                #   will be called twice.
-                # - This is bound to fail if X is an extension type and
-                #   does not actually inherit from category.parent_class
-                H = category.parent_class._Hom_(X, Y, category=category)
-            except (AttributeError, TypeError):
+            # Workaround in case the above fails, but the category
+            # also provides a _Hom_ hook.
+            # FIXME:
+            # - If X._Hom_ actually comes from category and fails, it
+            #   will be called twice.
+            # - This is bound to fail if X is an extension type and
+            #   does not actually inherit from category.parent_class
+            # For join categories, we check all of the direct super
+            #   categories as the parent_class of the join category is
+            #   not (necessarily) inherited and join categories do not
+            #   implement a _Hom_ (see trac #23418).
+            if not isinstance(category, JoinCategory):
+                cats = [category]
+            else:
+                cats = category.super_categories()
+            H = None
+            for C in cats:
+                try:
+                    H = C.parent_class._Hom_(X, Y, category=category)
+                except (AttributeError, TypeError):
+                    pass
+            if H is None:
                 # By default, construct a plain homset.
                 H = Homset(X, Y, category=category, check=check)
     _cache[key] = H

From bf01aa19df338890295dfe5ac99a1a300399f1cb Mon Sep 17 00:00:00 2001
From: Travis Scrimshaw <tcscrims at gmail.com>
Date: Wed, 3 Jan 2018 10:24:33 -0600
Subject: [PATCH 045/128] Break out once H is found.

---
 src/sage/categories/homset.py | 1 +
 1 file changed, 1 insertion(+)

diff --git a/src/sage/categories/homset.py b/src/sage/categories/homset.py
index 9364ac5cacc..11a45af98b3 100644
--- a/src/sage/categories/homset.py
+++ b/src/sage/categories/homset.py
@@ -441,6 +441,7 @@ def Hom(X, Y, category=None, check=True):
             for C in cats:
                 try:
                     H = C.parent_class._Hom_(X, Y, category=category)
+                    break
                 except (AttributeError, TypeError):
                     pass
             if H is None:

From f7e095abe7c5b5e56a5e4b18df991b37a841e68a Mon Sep 17 00:00:00 2001
From: Mark <mark00bell@gmail.com>
Date: Fri, 5 Jan 2018 01:11:19 +0000
Subject: [PATCH 046/128] Actually passing on kwds.

---
 src/sage/geometry/polyhedron/base.py | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/src/sage/geometry/polyhedron/base.py b/src/sage/geometry/polyhedron/base.py
index 3ccf3644739..5b3c025ecd7 100644
--- a/src/sage/geometry/polyhedron/base.py
+++ b/src/sage/geometry/polyhedron/base.py
@@ -5426,7 +5426,7 @@ def random_integral_point(self, **kwds):
         if count == 0:
             raise EmptySetError('Polyhedron does not contain any integral points.')
 
-        return self.get_integral_point(current_randstate().python_random().randint(0, count-1))
+        return self.get_integral_point(current_randstate().python_random().randint(0, count-1), **kwds)
 
     @cached_method
     def combinatorial_automorphism_group(self, vertex_graph_only=False):

From f585b5ec67fd3048ab35c7b5cd800306563ebeed Mon Sep 17 00:00:00 2001
From: Mark <mark00bell@gmail.com>
Date: Fri, 5 Jan 2018 16:23:02 +0000
Subject: [PATCH 047/128] Using **kwds in get_integral_point and doctesting
 these.

---
 src/sage/geometry/polyhedron/base.py | 16 ++++++++++++++--
 1 file changed, 14 insertions(+), 2 deletions(-)

diff --git a/src/sage/geometry/polyhedron/base.py b/src/sage/geometry/polyhedron/base.py
index 5b3c025ecd7..21cff50c223 100644
--- a/src/sage/geometry/polyhedron/base.py
+++ b/src/sage/geometry/polyhedron/base.py
@@ -5337,6 +5337,12 @@ def get_integral_point(self, index, **kwds):
             sage: Q = Polyhedron([(1,3), (2, 7), (9, 77)])
             sage: [Q.get_integral_point(i) for i in range(Q.integral_points_count())] == sorted(Q.integral_points())
             True
+            sage: Q.get_integral_point(0, explicit_enumeration_threshold=0, triangulation='cddlib')
+            (1, 3)
+            sage: Q.get_integral_point(0, explicit_enumeration_threshold=0, triangulation='cddlib', foo=True)
+            Traceback (most recent call last):
+            ...
+            RuntimeError: ...
 
             sage: R = Polyhedron(vertices=[[1/2, 1/3]], rays=[[1, 1]])
             sage: R.get_integral_point(0)
@@ -5348,7 +5354,7 @@ def get_integral_point(self, index, **kwds):
         if not self.is_compact():
             raise ValueError('Can only enumerate points in a compact polyhedron.')
 
-        if not 0 <= index < self.integral_points_count():
+        if not 0 <= index < self.integral_points_count(**kwds):
             raise IndexError('polytope index out of range')
 
         D = self.ambient_dim()
@@ -5363,7 +5369,7 @@ def get_integral_point(self, index, **kwds):
                 # Build new polyhedron by intersecting P with the halfspace {x_i < guess}.
                 P_lt_guess = P.intersection(S(None, ([[guess-1] + [0] * i + [-1] + [0] * (D - i - 1)], [])))
                 # Avoid computing P_geq_guess = P.intersection({x_i >= guess}) right now, it might not be needed.
-                P_lt_guess_count = P_lt_guess.integral_points_count()
+                P_lt_guess_count = P_lt_guess.integral_points_count(**kwds)
                 if P_lt_guess_count > index:  # Move upper down to guess.
                     upper = guess
                     index -= 0
@@ -5405,6 +5411,12 @@ def random_integral_point(self, **kwds):
             (0, 0)
             sage: P.random_integral_point() in P.integral_points()
             True
+            sage: P.random_integral_point(explicit_enumeration_threshold=0, triangulation='cddlib')  # random
+            (1, 1)
+            sage: P.random_integral_point(explicit_enumeration_threshold=0, triangulation='cddlib', foo=7)
+            Traceback (most recent call last):
+            ...
+            RuntimeError: ...
 
             sage: Q = Polyhedron(vertices=[(2, 1/3)], rays=[(1, 2)])
             sage: Q.random_integral_point()

From ed9bdefe2b193843cba5fe794b0dfd1e3cdcc2b9 Mon Sep 17 00:00:00 2001
From: Mark <mark00bell@googlemail.com>
Date: Sat, 6 Jan 2018 21:50:55 +0000
Subject: [PATCH 048/128] Docstring typo.

---
 src/sage/geometry/polyhedron/base.py | 6 +++---
 1 file changed, 3 insertions(+), 3 deletions(-)

diff --git a/src/sage/geometry/polyhedron/base.py b/src/sage/geometry/polyhedron/base.py
index 21cff50c223..09ac396f7c9 100644
--- a/src/sage/geometry/polyhedron/base.py
+++ b/src/sage/geometry/polyhedron/base.py
@@ -5311,9 +5311,9 @@ def get_integral_point(self, index, **kwds):
         ALGORITHM:
 
         The function computes each of the components of the requested point in
-        turn. To compute x_i, the ith component, it bisects the the upper and
-        lower bounds on x_i given by the bounding box. At each bisection, it
-        uses :meth:`integral_points_count` to determine on which side of the
+        turn. To compute x_i, the ith component, it bisects the upper and lower
+        bounds on x_i given by the bounding box. At each bisection, it uses
+        :meth:`integral_points_count` to determine on which side of the
         bisecting hyperplane the requested point lies.
 
         .. SEEALSO::

From 999c34b778d27ef2545425e3a6daee50d4ecab47 Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?Fr=C3=A9d=C3=A9ric=20Chapoton?=
 <chapoton@math.univ-lyon1.fr>
Date: Sun, 7 Jan 2018 21:04:44 +0100
Subject: [PATCH 049/128] trac 24487 add colored example + picture to
 list_plot3d

---
 src/sage/plot/plot3d/list_plot3d.py | 20 ++++++++++++++++++++
 1 file changed, 20 insertions(+)

diff --git a/src/sage/plot/plot3d/list_plot3d.py b/src/sage/plot/plot3d/list_plot3d.py
index 50a4b9196ea..858ff56ed69 100644
--- a/src/sage/plot/plot3d/list_plot3d.py
+++ b/src/sage/plot/plot3d/list_plot3d.py
@@ -213,6 +213,7 @@ def list_plot3d(v, interpolation_type='default', texture="automatic", point_list
             return list_plot3d_array_of_arrays(v, interpolation_type, texture, **kwds)
     raise TypeError("v must be a matrix or list")
 
+
 def list_plot3d_matrix(m, texture, **kwds):
     """
     A 3-dimensional plot of a surface defined by a matrix ``M``
@@ -249,6 +250,24 @@ def list_plot3d_matrix(m, texture, **kwds):
         Graphics3d Object
         sage: list_plot3d(m, texture='yellow', interpolation_type='linear') # indirect doctest
         Graphics3d Object
+
+    Here is a colored example, using a colormap and a coloring function
+    which must take values in (0, 1)::
+
+        sage: cm = colormaps.rainbow
+        sage: cf = lambda x, y: ((2*(x-y)/n)**2) % 1
+        sage: n = 20
+        sage: list_plot3d(matrix(RDF, n, [cos(pi*(i+j)/n) for i in [1..n]
+        ....:   for j in [1..n]]), color=(cf,cm))
+        Graphics3d Object
+
+    .. PLOT::
+
+        cm = colormaps.rainbow
+        cf = lambda x, y: ((2*(x-y)/n)**2) % 1
+        n = 20
+        expl = list_plot3d(matrix(RDF, n, [cos(pi*(i+j)/n) for i in [1..n] for j in [1..n]]), color=(cf,cm))
+        sphinx_plot(expl)    
     """
     from .parametric_surface import ParametricSurface
     f = lambda i,j: (i, j, float(m[int(i), int(j)]))
@@ -257,6 +276,7 @@ def list_plot3d_matrix(m, texture, **kwds):
     G._set_extra_kwds(kwds)
     return G
 
+
 def list_plot3d_array_of_arrays(v, interpolation_type, texture, **kwds):
     """
     A 3-dimensional plot of a surface defined by a list of lists ``v``

From 03848aed408223cf9fb6978ed374bc10ea1ab71d Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?Fr=C3=A9d=C3=A9ric=20Chapoton?=
 <chapoton@math.univ-lyon1.fr>
Date: Mon, 8 Jan 2018 20:15:41 +0100
Subject: [PATCH 050/128] trac 24493 remove deprecated SymplecticGraph

---
 src/sage/graphs/generators/classical_geometries.py | 6 +-----
 src/sage/graphs/graph_generators.py                | 1 -
 2 files changed, 1 insertion(+), 6 deletions(-)

diff --git a/src/sage/graphs/generators/classical_geometries.py b/src/sage/graphs/generators/classical_geometries.py
index 8a3f67170ce..0c036ac22ee 100644
--- a/src/sage/graphs/generators/classical_geometries.py
+++ b/src/sage/graphs/generators/classical_geometries.py
@@ -49,9 +49,7 @@ def SymplecticPolarGraph(d, q, algorithm=None):
 
     Computation of the spectrum of `Sp(6,2)`::
 
-        sage: g = graphs.SymplecticGraph(6,2)
-        doctest:...: DeprecationWarning: SymplecticGraph is deprecated. Please use sage.graphs.generators.classical_geometries.SymplecticPolarGraph instead.
-        See http://trac.sagemath.org/19136 for details.
+        sage: g = graphs.SymplecticPolarGraph(6,2)
         sage: g.is_strongly_regular(parameters=True)
         (63, 30, 13, 15)
         sage: set(g.spectrum()) == {-5, 3, 30}
@@ -112,8 +110,6 @@ def SymplecticPolarGraph(d, q, algorithm=None):
     G.relabel()
     return G
 
-from sage.misc.superseded import deprecated_function_alias
-SymplecticGraph = deprecated_function_alias(19136, SymplecticPolarGraph)
 
 def AffineOrthogonalPolarGraph(d,q,sign="+"):
     r"""
diff --git a/src/sage/graphs/graph_generators.py b/src/sage/graphs/graph_generators.py
index da142cc7fd2..1c490a9a8ff 100644
--- a/src/sage/graphs/graph_generators.py
+++ b/src/sage/graphs/graph_generators.py
@@ -2044,7 +2044,6 @@ def quadrangulations(self, order, minimum_degree=None, minimum_connectivity=None
     NonisotropicUnitaryPolarGraph = staticmethod(sage.graphs.generators.classical_geometries.NonisotropicUnitaryPolarGraph)
     OrthogonalPolarGraph   = staticmethod(sage.graphs.generators.classical_geometries.OrthogonalPolarGraph)
     SymplecticDualPolarGraph = staticmethod(sage.graphs.generators.classical_geometries.SymplecticDualPolarGraph)
-    SymplecticGraph   = staticmethod(sage.graphs.generators.classical_geometries.SymplecticGraph)
     SymplecticPolarGraph   = staticmethod(sage.graphs.generators.classical_geometries.SymplecticPolarGraph)
     TaylorTwographDescendantSRG = \
              staticmethod(sage.graphs.generators.classical_geometries.TaylorTwographDescendantSRG)

From 907aff6ae458ad83749a1c785763b808d4515457 Mon Sep 17 00:00:00 2001
From: Ralf Stephan <ralf@ark.in-berlin.de>
Date: Tue, 9 Jan 2018 10:17:16 +0100
Subject: [PATCH 051/128] 24497: pkg version/chksum

---
 build/pkgs/pynac/checksums.ini       | 6 +++---
 build/pkgs/pynac/package-version.txt | 2 +-
 2 files changed, 4 insertions(+), 4 deletions(-)

diff --git a/build/pkgs/pynac/checksums.ini b/build/pkgs/pynac/checksums.ini
index e35983b473e..0b2fe41225c 100644
--- a/build/pkgs/pynac/checksums.ini
+++ b/build/pkgs/pynac/checksums.ini
@@ -1,4 +1,4 @@
 tarball=pynac-VERSION.tar.bz2
-sha1=33e2990a1f3a90ced00c2d87709a851682892e7f
-md5=5faf705c049ca4cf09f1de436363c3a3
-cksum=3009897742
+sha1=ec322d219a9c02b95a29789ca221b28c6cca7a14
+md5=10f21726733209ae6f641b5736c4c9fb
+cksum=2341458065
diff --git a/build/pkgs/pynac/package-version.txt b/build/pkgs/pynac/package-version.txt
index a597e4f317c..def4250351c 100644
--- a/build/pkgs/pynac/package-version.txt
+++ b/build/pkgs/pynac/package-version.txt
@@ -1 +1 @@
-0.7.14
+0.7.15

From 9cf556b0a9ad8bdf708ab083f160e0fe674c4569 Mon Sep 17 00:00:00 2001
From: "Erik M. Bray" <erik.bray@lri.fr>
Date: Tue, 9 Jan 2018 12:48:01 +0000
Subject: [PATCH 052/128] Rework str_to_bytes so that it accepts unicode on
 Python 2 and treats it same as str on Python 3.

Also in both cases the default encoding for encoding and decoding is now just
fixed to UTF-8; the locale encoding should be used explicitly if/when
interfacing with other locale-aware software.

Fixes https://trac.sagemath.org/ticket/24475
---
 src/sage/cpython/string.pxd | 56 ++++++++++++++++++++++++++-----------
 1 file changed, 39 insertions(+), 17 deletions(-)

diff --git a/src/sage/cpython/string.pxd b/src/sage/cpython/string.pxd
index d8157669932..5449a9a354d 100644
--- a/src/sage/cpython/string.pxd
+++ b/src/sage/cpython/string.pxd
@@ -19,8 +19,6 @@ IF PY_MAJOR_VERSION >= 3:
     cdef extern from "Python.h":
         # Missing from cpython.unicode in Cython 0.27.3
         char* PyUnicode_AsUTF8(object s)
-        str PyUnicode_DecodeLocale(const char* s, const char* errors)
-        bytes PyUnicode_EncodeLocale(object s, const char* errors)
 
 
 cdef inline str char_to_str(const char* c, encoding=None, errors=None):
@@ -34,7 +32,7 @@ cdef inline str char_to_str(const char* c, encoding=None, errors=None):
             err = PyUnicode_AsUTF8(errors)
 
         if encoding is None:
-            return PyUnicode_DecodeLocale(c, err)
+            encoding = 'utf-8'
 
         return PyUnicode_Decode(c, strlen(c), PyUnicode_AsUTF8(encoding), err)
 
@@ -76,39 +74,63 @@ cpdef inline str_to_bytes(s, encoding=None, errors=None):
     r"""
     Convert ``str`` to ``bytes``.
 
-    On Python 2 this is a no-op since ``str is bytes``.  On Python 3
-    this encodes the given ``str`` to a Python 3 ``bytes`` using the
-    specified encoding.
+    On Python 3 this encodes the given ``str`` to a Python 3 ``bytes`` using
+    the specified encoding.
+
+
+    On Python 2 this is a no-op on ``str`` input since ``str is bytes``.
+    However, this function also accepts Python 2 ``unicode`` objects and treats
+    them the same as Python 3 unicode ``str`` objects.
 
     EXAMPLES::
 
         sage: import six
         sage: from sage.cpython.string import str_to_bytes
         sage: if six.PY2:
-        ....:     b = str_to_bytes('\xcf\x80')
+        ....:     bs = [str_to_bytes('\xcf\x80'), str_to_bytes(u'π')]
         ....: else:
-        ....:     b = str_to_bytes(u'π')
-        sage: b == b'\xcf\x80'
+        ....:     bs = [str_to_bytes(u'π')]
+        sage: all(b == b'\xcf\x80' for b in bs)
         True
         sage: str_to_bytes([])
         Traceback (most recent call last):
         ...
-        TypeError: expected str, list found
+        TypeError: expected str ... list found
     """
-    # Make this check explicit to avoid obscure error message below
-    if not isinstance(s, str):
-        raise TypeError(f"expected str, {type(s).__name__} found")
+
+    cdef char* err
+    cdef char* enc
 
     IF PY_MAJOR_VERSION <= 2:
-        return s
+        # Make this check explicit to avoid obscure error message below
+        if isinstance(s, str):
+            # On Python 2 str is already bytes so this should be a no-op
+            return s
+        elif not isinstance(s, unicode):
+            raise TypeError(
+                    f"expected str or unicode, {type(s).__name__} found")
+
+        if errors is None:
+            err = NULL  # implies "strict"
+        else:
+            err = errors
+
+        if encoding is None:
+            enc = 'utf-8'
+        else:
+            enc = encoding
     ELSE:
-        cdef char* err
+        if not isinstance(s, str):
+            raise TypeError(f"expected str, {type(s).__name__} found")
+
         if errors is None:
             err = NULL  # implies "strict"
         else:
             err = PyUnicode_AsUTF8(errors)
 
         if encoding is None:
-            return PyUnicode_EncodeLocale(s, err)
+            enc = 'utf-8'
+        else:
+            enc = PyUnicode_AsUTF8(encoding)
 
-        return PyUnicode_AsEncodedString(s, PyUnicode_AsUTF8(encoding), err)
+    return PyUnicode_AsEncodedString(s, enc, err)

From a0448a21aea340aa6dc4be2cbca17fc6cf756ab5 Mon Sep 17 00:00:00 2001
From: John Cremona <john.cremona@gmail.com>
Date: Thu, 11 Jan 2018 13:06:22 +0000
Subject: [PATCH 053/128] #10017: fix new example and simplify code in line
 with review comments

---
 src/sage/rings/number_field/number_field.py | 61 ++++++---------------
 1 file changed, 18 insertions(+), 43 deletions(-)

diff --git a/src/sage/rings/number_field/number_field.py b/src/sage/rings/number_field/number_field.py
index a692372458c..5e1a03d0f9a 100644
--- a/src/sage/rings/number_field/number_field.py
+++ b/src/sage/rings/number_field/number_field.py
@@ -1201,7 +1201,7 @@ class NumberField_generic(WithEqualityById, number_field_base.NumberField):
         sage: NumberField(QQ['x'].0^4 + 23, 'a') == NumberField(QQ['y'].0^4 + 23, 'a')
         False
 
-        sage: x = var('x'); y = ZZ['y'].gen()
+        sage: x = polygen(QQ); y = ZZ['y'].gen()
         sage: NumberField(x^3 + x + 5, 'a') == NumberField(y^3 + y + 5, 'a')
         False
         sage: NumberField(x^3 + x + 5, 'a') == NumberField(y^4 + y + 5, 'a')
@@ -5050,7 +5050,7 @@ def extension(self, poly, name=None, names=None, *args, **kwds):
 
             sage: k.<a> = NumberField(x^2 + 1); k
             Number Field in a with defining polynomial x^2 + 1
-            sage: y = var('y')
+            sage: y = polygen(QQ,'y')
             sage: m.<b> = k.extension(y^2 + 2); m
             Number Field in b with defining polynomial y^2 + 2 over its base field
 
@@ -5595,7 +5595,7 @@ def reduced_basis(self, prec=None):
         Check that the bug reported at :trac:`10017` is fixed::
 
             sage: x = polygen(QQ)
-            sage: k = NumberField(x^6 + 2218926655879913714112*x^4 - 32507675650290949030789018433536*x^3 + 4923635504174417014460581055002374467948544*x^2 - 3666074010564497464129951249279114076897746988630016*x + 264187244046129768986806800244258952598300346857154900812365824,'a')
+            sage: k = NumberField(x^6 + 2218926655879913714112*x^4 - 32507675650290949030789018433536*x^3 + 4923635504174417014460581055002374467948544*x^2 - 36066074010564497464129951249279114076897746988630016*x + 264187244046129768986806800244258952598300346857154900812365824,'a')
             sage: new_basis = k.reduced_basis()
             sage: [c.minpoly() for c in new_basis]
             [x - 1,
@@ -5608,45 +5608,21 @@ def reduced_basis(self, prec=None):
             sage: R.discriminant()==k.discriminant()
             True
         """
-        if self.is_totally_real():
-            try:
-                return self.__reduced_basis
-            except AttributeError:
-                pass
-        else:
-            try:
-                if self.__reduced_basis_precision >= prec:
-                    return self.__reduced_basis
-            except AttributeError:
-                pass
-
-        from sage.matrix.constructor import matrix
-
+        ZK = self.integral_basis()
         d = self.absolute_degree()
-        Z_basis = self.integral_basis()
 
-        ## If self is totally real, then we can use (x*y).trace() as
-        ## the inner product on the Minkowski embedding, which is
-        ## faster than computing all the conjugates, etc ...
+        # If self is totally real, then we can use (x*y).trace() as
+        # the inner product on the Minkowski embedding, which is
+        # faster than computing all the conjugates, etc ...
+
         if self.is_totally_real():
-            T = pari(matrix(ZZ, d, d, [[(x*y).trace() for x in Z_basis]
-                                       for y in Z_basis])).qflllgram()
-            self.__reduced_basis = [ sum([ ZZ(T[i][j]) * Z_basis[j]
-                                           for j in range(d)])
-                                     for i in range(d)]
+            from sage.matrix.constructor import matrix
+            T = pari(matrix(ZZ, d, d, [[(x*y).trace() for x in ZK]  for y in ZK])).qflllgram()
         else:
-            M = self.Minkowski_embedding(self.integral_basis(), prec=prec)
-            T = pari(M).qflll().sage()
-            ZK = self.ring_of_integers()
-            self.__reduced_basis = [ ZK(v.list()) for v in T.columns() ]
-            if prec is None:
-                ## this is the default choice for Minkowski_embedding
-                self.__reduced_basis_prec = 53
-            else:
-                self.__reduced_basis_prec = prec
-
-        return self.__reduced_basis
+            M = self.Minkowski_embedding(ZK, prec=prec)
+            T = pari(M).qflll()
 
+        return [ sum([ ZZ(T[i][j]) * ZK[j] for j in range(d)])  for i in range(d)]
 
     def reduced_gram_matrix(self, prec=None):
         r"""
@@ -5703,14 +5679,13 @@ def reduced_gram_matrix(self, prec=None):
 
         ::
 
-            sage: var('x')
-            x
+            sage: x = polygen(QQ)
             sage: F.<alpha> = NumberField(x^4+x^2+712312*x+131001238)
             sage: F.reduced_gram_matrix(prec=128)
-            [   4.0000000000000000000000000000000000000   0.00000000000000000000000000000000000000 -2.1369360000000000000000000000000000000e6 -3.3122478000000000000000000000000000000e7]
-            [  0.00000000000000000000000000000000000000    46721.539331563218381658483353092335550 -2.2467769057394530109094755223395819322e7 -3.4807276041138450473611629088647496430e8]
-            [-2.1369360000000000000000000000000000000e6 -2.2467769057394530109094755223395819322e7 7.0704285924714907491782135494859351061e12 1.1256639928034037006027526953641297995e14]
-            [-3.3122478000000000000000000000000000000e7 -3.4807276041138450473611629088647496430e8 1.1256639928034037006027526953641297995e14 1.7923838231014970520503146603069479547e15]
+            [   4.0000000000000000000000000000000000000   0.00000000000000000000000000000000000000   -1.9999999999999999999999999999999999037  -0.99999999999999999999999999999999383702]
+            [  0.00000000000000000000000000000000000000    46721.539331563218381658483353092335550   -11488.910026551724275122749703614966768   -418.12718083977141198754424579680468382]
+            [  -1.9999999999999999999999999999999999037   -11488.910026551724275122749703614966768  5.5658915310500611768713076521847709187e8  1.4179092271494070050433368847682152174e8]
+            [ -0.99999999999999999999999999999999383702   -418.12718083977141198754424579680468382  1.4179092271494070050433368847682152174e8 1.3665897267919181137884111201405279175e12]
         """
         if self.is_totally_real():
             try:

From 39fc2278ce182b46715ffd4fb2071178a4c11092 Mon Sep 17 00:00:00 2001
From: John Cremona <john.cremona@gmail.com>
Date: Thu, 11 Jan 2018 15:11:07 +0000
Subject: [PATCH 054/128] #10017: small stylistic improvement

---
 src/sage/rings/number_field/order.py | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/src/sage/rings/number_field/order.py b/src/sage/rings/number_field/order.py
index cf20dbf72c0..9295be801f3 100644
--- a/src/sage/rings/number_field/order.py
+++ b/src/sage/rings/number_field/order.py
@@ -1155,7 +1155,7 @@ def _element_constructor_(self, x):
         """
         if is_Element(x) and x.parent() is self:
             return x
-        if isinstance(x,list) or isinstance(x,tuple):
+        if isinstance(x, (tuple, list)):
             x = sum(xi*gi for xi,gi in zip(x,self.gens()))
         if not is_Element(x) or x.parent() is not self._K:
             x = self._K(x)

From 6760db0bc5406c4c36d131dad4d928e31f806008 Mon Sep 17 00:00:00 2001
From: "Erik M. Bray" <erik.bray@lri.fr>
Date: Thu, 11 Jan 2018 15:42:46 +0000
Subject: [PATCH 055/128] Add an additional test for normalize_type_repr

---
 src/sage/doctest/parsing.py | 5 +++++
 1 file changed, 5 insertions(+)

diff --git a/src/sage/doctest/parsing.py b/src/sage/doctest/parsing.py
index b1c615ed98d..02c82711fc1 100644
--- a/src/sage/doctest/parsing.py
+++ b/src/sage/doctest/parsing.py
@@ -145,6 +145,11 @@ def normalize_type_repr(s):
         sage: print(normalize_type_repr(s))
         The desired output was <class 'int'>
         The received output was <class 'int'>
+
+    And should work when types are embedded in other nested expressions::
+
+        sage: normalize_type_repr(repr([Integer, float]))
+        "[<class 'sage.rings.integer.Integer'>, <class 'float'>]"
     """
 
     def subst(m):

From 6bdb52abba96a24a25685a56260f67f0d4a0b2b3 Mon Sep 17 00:00:00 2001
From: Jeroen Demeyer <jdemeyer@cage.ugent.be>
Date: Fri, 12 Jan 2018 10:41:45 +0100
Subject: [PATCH 056/128] Various minor fixes

---
 src/sage/cpython/string.pxd | 46 +++++++++++++++++++------------------
 1 file changed, 24 insertions(+), 22 deletions(-)

diff --git a/src/sage/cpython/string.pxd b/src/sage/cpython/string.pxd
index 5449a9a354d..eefc2d685ea 100644
--- a/src/sage/cpython/string.pxd
+++ b/src/sage/cpython/string.pxd
@@ -15,29 +15,33 @@ from libc.string cimport strlen
 from cpython.bytes cimport PyBytes_AS_STRING, PyBytes_FromString
 from cpython.unicode cimport PyUnicode_Decode, PyUnicode_AsEncodedString
 
-IF PY_MAJOR_VERSION >= 3:
-    cdef extern from "Python.h":
-        # Missing from cpython.unicode in Cython 0.27.3
-        char* PyUnicode_AsUTF8(object s)
+
+cdef extern from "Python.h":
+    # Missing from cpython.unicode in Cython 0.27.3
+    char* PyUnicode_AsUTF8(object s)
 
 
 cdef inline str char_to_str(const char* c, encoding=None, errors=None):
     IF PY_MAJOR_VERSION <= 2:
         return <str>PyBytes_FromString(c)
     ELSE:
-        cdef char* err
+        cdef const char* err
+        cdef const char* enc
+
         if errors is None:
             err = NULL  # implies "strict"
         else:
             err = PyUnicode_AsUTF8(errors)
 
         if encoding is None:
-            encoding = 'utf-8'
+            enc = NULL  # default to utf-8
+        else:
+            enc = PyUnicode_AsUTF8(encoding)
 
-        return PyUnicode_Decode(c, strlen(c), PyUnicode_AsUTF8(encoding), err)
+        return PyUnicode_Decode(c, strlen(c), enc, err)
 
 
-cpdef inline bytes_to_str(b, encoding=None, errors=None):
+cpdef inline str bytes_to_str(b, encoding=None, errors=None):
     r"""
     Convert ``bytes`` to ``str``.
 
@@ -64,23 +68,22 @@ cpdef inline bytes_to_str(b, encoding=None, errors=None):
         raise TypeError(f"expected bytes, {type(b).__name__} found")
 
     IF PY_MAJOR_VERSION <= 2:
-        return b
+        return <str>b
     ELSE:
         return char_to_str(PyBytes_AS_STRING(b), encoding=encoding,
                            errors=errors)
 
 
-cpdef inline str_to_bytes(s, encoding=None, errors=None):
+cpdef inline bytes str_to_bytes(s, encoding=None, errors=None):
     r"""
-    Convert ``str`` to ``bytes``.
-
-    On Python 3 this encodes the given ``str`` to a Python 3 ``bytes`` using
-    the specified encoding.
+    Convert ``str`` or ``unicode`` to ``bytes``.
 
+    On Python 3 this encodes the given ``str`` to a Python 3 ``bytes``
+    using the specified encoding.
 
     On Python 2 this is a no-op on ``str`` input since ``str is bytes``.
-    However, this function also accepts Python 2 ``unicode`` objects and treats
-    them the same as Python 3 unicode ``str`` objects.
+    However, this function also accepts Python 2 ``unicode`` objects and
+    treats them the same as Python 3 unicode ``str`` objects.
 
     EXAMPLES::
 
@@ -97,15 +100,14 @@ cpdef inline str_to_bytes(s, encoding=None, errors=None):
         ...
         TypeError: expected str ... list found
     """
-
-    cdef char* err
-    cdef char* enc
+    cdef const char* err
+    cdef const char* enc
 
     IF PY_MAJOR_VERSION <= 2:
         # Make this check explicit to avoid obscure error message below
         if isinstance(s, str):
             # On Python 2 str is already bytes so this should be a no-op
-            return s
+            return <bytes>s
         elif not isinstance(s, unicode):
             raise TypeError(
                     f"expected str or unicode, {type(s).__name__} found")
@@ -129,8 +131,8 @@ cpdef inline str_to_bytes(s, encoding=None, errors=None):
             err = PyUnicode_AsUTF8(errors)
 
         if encoding is None:
-            enc = 'utf-8'
+            enc = NULL  # default to utf-8
         else:
             enc = PyUnicode_AsUTF8(encoding)
 
-    return PyUnicode_AsEncodedString(s, enc, err)
+    return <bytes>PyUnicode_AsEncodedString(s, enc, err)

From 62c14676ba1e256b6293f210c2678407b01a7885 Mon Sep 17 00:00:00 2001
From: David Coudert <david.coudert@inria.fr>
Date: Fri, 12 Jan 2018 15:49:46 +0100
Subject: [PATCH 057/128] trac #24512: fix issues in WheelGraph and CycleGraph

---
 src/sage/graphs/generators/basic.py    | 64 ++++++++++++++++----------
 src/sage/graphs/generators/families.py | 45 +++++++++---------
 2 files changed, 62 insertions(+), 47 deletions(-)

diff --git a/src/sage/graphs/generators/basic.py b/src/sage/graphs/generators/basic.py
index 8777b95c4be..e108f2d57f9 100644
--- a/src/sage/graphs/generators/basic.py
+++ b/src/sage/graphs/generators/basic.py
@@ -237,24 +237,22 @@ def CycleGraph(n):
     r"""
     Returns a cycle graph with n nodes.
 
-    A cycle graph is a basic structure which is also typically called
-    an n-gon.
+    A cycle graph is a basic structure which is also typically called an
+    `n`-gon.
 
-    PLOTTING: Upon construction, the position dictionary is filled to
-    override the spring-layout algorithm. By convention, each cycle
-    graph will be displayed with the first (0) node at the top, with
-    the rest following in a counterclockwise manner.
+    PLOTTING: Upon construction, the position dictionary is filled to override
+    the spring-layout algorithm. By convention, each cycle graph will be
+    displayed with the first (0) node at the top, with the rest following in a
+    counterclockwise manner.
 
-    The cycle graph is a good opportunity to compare efficiency of
-    filling a position dictionary vs. using the spring-layout algorithm
-    for plotting. Because the cycle graph is very symmetric, the
-    resulting plots should be similar (in cases of small n).
+    The cycle graph is a good opportunity to compare efficiency of filling a
+    position dictionary vs. using the spring-layout algorithm for
+    plotting. Because the cycle graph is very symmetric, the resulting plots
+    should be similar (in cases of small `n`).
 
-    Filling the position dictionary in advance adds O(n) to the
-    constructor.
+    Filling the position dictionary in advance adds `O(n)` to the constructor.
 
-    EXAMPLES: Compare plotting using the predefined layout and
-    networkx::
+    EXAMPLES: Compare plotting using the predefined layout and networkx::
 
         sage: import networkx
         sage: n = networkx.cycle_graph(23)
@@ -263,9 +261,8 @@ def CycleGraph(n):
         sage: spring23.show() # long time
         sage: posdict23.show() # long time
 
-    We next view many cycle graphs as a Sage graphics array. First we
-    use the ``CycleGraph`` constructor, which fills in the
-    position dictionary::
+    We next view many cycle graphs as a Sage graphics array. First we use the
+    ``CycleGraph`` constructor, which fills in the position dictionary::
 
         sage: g = []
         sage: j = []
@@ -295,14 +292,33 @@ def CycleGraph(n):
         ....:     j.append(n)
         sage: G = sage.plot.graphics.GraphicsArray(j)
         sage: G.show() # long time
+
+    TESTS:
+
+    The input parameter must be a positive integer::
+
+        sage: G = graphs.CycleGraph(-1)
+        Traceback (most recent call last):
+        ...
+        ValueError: parameter n must be a positive integer
     """
-    pos_dict = {}
-    for i in range(n):
-        x = float(cos((pi/2) + ((2*pi)/n)*i))
-        y = float(sin((pi/2) + ((2*pi)/n)*i))
-        pos_dict[i] = (x, y)
-    G = graph.Graph(n, pos=pos_dict, name="Cycle graph")
-    G.add_cycle(list(range(n)))
+    if n < 0:
+        raise ValueError("parameter n must be a positive integer")
+
+    G = Graph(n, name="Cycle graph")
+    if n == 1:
+        G.set_pos({0:(0, 0)})
+    elif n == 2:
+        G.add_edge(0, 1)
+        G.set_pos({0:(0, 1), 1:(0, -1)})
+    else:
+        pos_dict = {}
+        for i in range(n):
+            x = float(cos((pi/2) + ((2*pi)/n)*i))
+            y = float(sin((pi/2) + ((2*pi)/n)*i))
+            pos_dict[i] = (x, y)
+        G.set_pos(pos_dict)
+        G.add_cycle(list(range(n)))
     return G
 
 def CompleteGraph(n):
diff --git a/src/sage/graphs/generators/families.py b/src/sage/graphs/generators/families.py
index 103f487933d..131ef8f5028 100644
--- a/src/sage/graphs/generators/families.py
+++ b/src/sage/graphs/generators/families.py
@@ -2478,24 +2478,22 @@ def WheelGraph(n):
     """
     Returns a Wheel graph with n nodes.
 
-    A Wheel graph is a basic structure where one node is connected to
-    all other nodes and those (outer) nodes are connected cyclically.
+    A Wheel graph is a basic structure where one node is connected to all other
+    nodes and those (outer) nodes are connected cyclically.
 
-    This constructor depends on NetworkX numeric labels.
+    PLOTTING: Upon construction, the position dictionary is filled to override
+    the spring-layout algorithm. By convention, each wheel graph will be
+    displayed with the first (0) node in the center, the second node at the top,
+    and the rest following in a counterclockwise manner.
 
-    PLOTTING: Upon construction, the position dictionary is filled to
-    override the spring-layout algorithm. By convention, each wheel
-    graph will be displayed with the first (0) node in the center, the
-    second node at the top, and the rest following in a
-    counterclockwise manner.
+    With the wheel graph, we see that it doesn't take a very large n at all for
+    the spring-layout to give a counter-intuitive display. (See Graphics Array
+    examples below).
 
-    With the wheel graph, we see that it doesn't take a very large n at
-    all for the spring-layout to give a counter-intuitive display. (See
-    Graphics Array examples below).
+    EXAMPLES:
 
-    EXAMPLES: We view many wheel graphs with a Sage Graphics Array,
-    first with this constructor (i.e., the position dictionary
-    filled)::
+    We view many wheel graphs with a Sage Graphics Array, first with this
+    constructor (i.e., the position dictionary filled)::
 
         sage: g = []
         sage: j = []
@@ -2539,15 +2537,16 @@ def WheelGraph(n):
         sage: spring23.show() # long time
         sage: posdict23.show() # long time
     """
-    pos_dict = {}
-    pos_dict[0] = (0,0)
-    for i in range(1,n):
-        x = float(cos((pi/2) + ((2*pi)/(n-1))*(i-1)))
-        y = float(sin((pi/2) + ((2*pi)/(n-1))*(i-1)))
-        pos_dict[i] = (x,y)
-    import networkx
-    G = networkx.wheel_graph(n)
-    return Graph(G, pos=pos_dict, name="Wheel graph")
+    from sage.graphs.generators.basic import CycleGraph
+    if n < 4:
+        G = CycleGraph(n)
+    else:
+        G = CycleGraph(n-1)
+        G.relabel(perm=list(range(1, n)), inplace=True)
+        G.add_edges([(0, i) for i in range(1, n)])
+        G._pos[0] = (0, 0)
+    G.name("Wheel graph")
+    return G
 
 def WindmillGraph(k, n):
     r"""

From 84e3a8a767cee1ced7f76c3c0ac17b5a26776a72 Mon Sep 17 00:00:00 2001
From: Jeroen Demeyer <jdemeyer@cage.ugent.be>
Date: Sat, 9 Dec 2017 20:00:50 +0100
Subject: [PATCH 058/128] Upgrade MPFR, MPC and MPFI

---
 build/pkgs/mpc/checksums.ini                  |   6 +-
 build/pkgs/mpc/package-version.txt            |   2 +-
 build/pkgs/mpc/patches/mpc_mul_faster.patch   | 124 ------------------
 build/pkgs/mpfi/checksums.ini                 |   6 +-
 build/pkgs/mpfi/package-version.txt           |   2 +-
 build/pkgs/mpfr/checksums.ini                 |   6 +-
 build/pkgs/mpfr/package-version.txt           |   2 +-
 .../pkgs/mpfr/patches/clang_workaround.patch  |  20 ---
 8 files changed, 12 insertions(+), 156 deletions(-)
 delete mode 100644 build/pkgs/mpc/patches/mpc_mul_faster.patch
 delete mode 100644 build/pkgs/mpfr/patches/clang_workaround.patch

diff --git a/build/pkgs/mpc/checksums.ini b/build/pkgs/mpc/checksums.ini
index c97e6b75889..70fbea4b5be 100644
--- a/build/pkgs/mpc/checksums.ini
+++ b/build/pkgs/mpc/checksums.ini
@@ -1,4 +1,4 @@
 tarball=mpc-VERSION.tar.gz
-sha1=b8be66396c726fdc36ebb0f692ed8a8cca3bcc66
-md5=d6a1d5f8ddea3abd2cc3e98f58352d26
-cksum=1941630434
+sha1=b019d9e1d27ec5fb99497159d43a3164995de2d0
+md5=4125404e41e482ec68282a2e687f6c73
+cksum=3987925640
diff --git a/build/pkgs/mpc/package-version.txt b/build/pkgs/mpc/package-version.txt
index 3b69baff860..9084fa2f716 100644
--- a/build/pkgs/mpc/package-version.txt
+++ b/build/pkgs/mpc/package-version.txt
@@ -1 +1 @@
-1.0.3.p1
+1.1.0
diff --git a/build/pkgs/mpc/patches/mpc_mul_faster.patch b/build/pkgs/mpc/patches/mpc_mul_faster.patch
deleted file mode 100644
index 5fc59a1bffc..00000000000
--- a/build/pkgs/mpc/patches/mpc_mul_faster.patch
+++ /dev/null
@@ -1,124 +0,0 @@
-diff -ru src/src/mul.c b/src/mul.c
---- src/src/mul.c	2012-07-22 17:40:22.000000000 +0200
-+++ b/src/mul.c	2014-01-27 15:12:37.449617411 +0100
-@@ -170,6 +170,10 @@
-    return MPC_INEX (inex_re, inex_im);
- }
- 
-+#define MPFR_MANT(x)      ((x)->_mpfr_d)
-+#define MPFR_PREC(x)      ((x)->_mpfr_prec)
-+#define MPFR_EXP(x)       ((x)->_mpfr_exp)
-+#define MPFR_LIMB_SIZE(x) ((MPFR_PREC (x) - 1) / GMP_NUMB_BITS + 1)
- 
- static int
- mpfr_fmma (mpfr_ptr z, mpfr_srcptr a, mpfr_srcptr b, mpfr_srcptr c,
-@@ -183,33 +187,68 @@
- 
-    int inex;
-    mpfr_t u, v;
-+   mp_size_t an, bn, cn, dn;
- 
-    /* u=a*b, v=sign*c*d exactly */
--   mpfr_init2 (u, mpfr_get_prec (a) + mpfr_get_prec (b));
--   mpfr_init2 (v, mpfr_get_prec (c) + mpfr_get_prec (d));
--   mpfr_mul (u, a, b, GMP_RNDN);
--   mpfr_mul (v, c, d, GMP_RNDN);
--   if (sign < 0)
--      mpfr_neg (v, v, GMP_RNDN);
-+   an = MPFR_LIMB_SIZE(a);
-+   bn = MPFR_LIMB_SIZE(b);
-+   cn = MPFR_LIMB_SIZE(c);
-+   dn = MPFR_LIMB_SIZE(d);
-+   MPFR_MANT(u) = malloc ((an + bn) * sizeof (mp_limb_t));
-+   MPFR_MANT(v) = malloc ((cn + dn) * sizeof (mp_limb_t));
-+   if (an >= bn)
-+     mpn_mul (MPFR_MANT(u), MPFR_MANT(a), an, MPFR_MANT(b), bn);
-+   else
-+     mpn_mul (MPFR_MANT(u), MPFR_MANT(b), bn, MPFR_MANT(a), an);
-+   if ((MPFR_MANT(u)[an + bn - 1] >> (GMP_NUMB_BITS - 1)) == 0)
-+     {
-+       mpn_lshift (MPFR_MANT(u), MPFR_MANT(u), an + bn, 1);
-+       MPFR_EXP(u) = MPFR_EXP(a) + MPFR_EXP(b) - 1;
-+     }
-+   else
-+     MPFR_EXP(u) = MPFR_EXP(a) + MPFR_EXP(b);
-+   if (cn >= dn)
-+     mpn_mul (MPFR_MANT(v), MPFR_MANT(c), cn, MPFR_MANT(d), dn);
-+   else
-+     mpn_mul (MPFR_MANT(v), MPFR_MANT(d), dn, MPFR_MANT(c), cn);
-+   if ((MPFR_MANT(v)[cn + dn - 1] >> (GMP_NUMB_BITS - 1)) == 0)
-+     {
-+       mpn_lshift (MPFR_MANT(v), MPFR_MANT(v), cn + dn, 1);
-+       MPFR_EXP(v) = MPFR_EXP(c) + MPFR_EXP(d) - 1;
-+     }
-+   else
-+     MPFR_EXP(v) = MPFR_EXP(c) + MPFR_EXP(d);
-+   MPFR_PREC(u) = (an + bn) * GMP_NUMB_BITS;
-+   MPFR_PREC(v) = (cn + dn) * GMP_NUMB_BITS;
-+   MPFR_SIGN(u) = MPFR_SIGN(a) * MPFR_SIGN(b);
-+   if (sign > 0)
-+     MPFR_SIGN(v) = MPFR_SIGN(c) * MPFR_SIGN(d);
-+   else
-+     MPFR_SIGN(v) = -MPFR_SIGN(c) * MPFR_SIGN(d);
-+
-+   mpfr_check_range (u, 0, GMP_RNDN);
-+   mpfr_check_range (v, 0, GMP_RNDN);
- 
-    /* tentatively compute z as u+v; here we need z to be distinct
-       from a, b, c, d to not lose the latter */
-    inex = mpfr_add (z, u, v, rnd);
--
--   if (mpfr_inf_p (z)) {
--      /* replace by "correctly rounded overflow" */
--      mpfr_set_si (z, (mpfr_signbit (z) ? -1 : 1), GMP_RNDN);
--      inex = mpfr_mul_2ui (z, z, mpfr_get_emax (), rnd);
--   }
--   else if (mpfr_zero_p (u) && !mpfr_zero_p (v)) {
--      /* exactly u underflowed, determine inexact flag */
--      inex = (mpfr_signbit (u) ? 1 : -1);
--   }
--   else if (mpfr_zero_p (v) && !mpfr_zero_p (u)) {
--      /* exactly v underflowed, determine inexact flag */
--      inex = (mpfr_signbit (v) ? 1 : -1);
--   }
--   else if (mpfr_nan_p (z) || (mpfr_zero_p (u) && mpfr_zero_p (v))) {
-+   
-+   if (!mpfr_regular_p(z) || !mpfr_regular_p(u) || !mpfr_regular_p(v))
-+     {
-+       if (mpfr_inf_p (z)) {
-+         /* replace by "correctly rounded overflow" */
-+         mpfr_set_si (z, (mpfr_signbit (z) ? -1 : 1), GMP_RNDN);
-+         inex = mpfr_mul_2ui (z, z, mpfr_get_emax (), rnd);
-+       }
-+       else if (mpfr_zero_p (u) && !mpfr_zero_p (v)) {
-+         /* exactly u underflowed, determine inexact flag */
-+         inex = (mpfr_signbit (u) ? 1 : -1);
-+       }
-+       else if (mpfr_zero_p (v) && !mpfr_zero_p (u)) {
-+         /* exactly v underflowed, determine inexact flag */
-+         inex = (mpfr_signbit (v) ? 1 : -1);
-+       }
-+       else if (mpfr_nan_p (z) || (mpfr_zero_p (u) && mpfr_zero_p (v))) {
-       /* In the first case, u and v are infinities with opposite signs.
-          In the second case, u and v are zeroes; their sum may be 0 or the
-          least representable number, with a sign to be determined.
-@@ -312,15 +351,14 @@
-       mpfr_set_exp ((mpfr_ptr) c, ec);
-       mpfr_set_exp ((mpfr_ptr) d, ed);
-          /* works also when some of a, b, c, d are not all distinct */
--   }
--
--   mpfr_clear (u);
--   mpfr_clear (v);
-+       }
-+     }
- 
-+   free (MPFR_MANT(u));
-+   free (MPFR_MANT(v));
-    return inex;
- }
- 
--
- int
- mpc_mul_naive (mpc_ptr z, mpc_srcptr x, mpc_srcptr y, mpc_rnd_t rnd)
- {
diff --git a/build/pkgs/mpfi/checksums.ini b/build/pkgs/mpfi/checksums.ini
index 108e255e173..6d6940e0237 100644
--- a/build/pkgs/mpfi/checksums.ini
+++ b/build/pkgs/mpfi/checksums.ini
@@ -1,4 +1,4 @@
 tarball=mpfi-VERSION.tar.bz2
-sha1=68773ce05e89e0f968687dd82d402f80ccc4c31f
-md5=50d05e9d6f20a07c043b3b038927a456
-cksum=2405993671
+sha1=6a44e59f69fa72b4fe1c67b9c9ccf678f321ef80
+md5=1c233f3646bfb8a363aee0cc653c8baa
+cksum=4291278873
diff --git a/build/pkgs/mpfi/package-version.txt b/build/pkgs/mpfi/package-version.txt
index 343372e95da..4cda8f19edc 100644
--- a/build/pkgs/mpfi/package-version.txt
+++ b/build/pkgs/mpfi/package-version.txt
@@ -1 +1 @@
-1.5.1.p0
+1.5.2
diff --git a/build/pkgs/mpfr/checksums.ini b/build/pkgs/mpfr/checksums.ini
index cd5a5a629d9..2728dda9c04 100644
--- a/build/pkgs/mpfr/checksums.ini
+++ b/build/pkgs/mpfr/checksums.ini
@@ -1,4 +1,4 @@
 tarball=mpfr-VERSION.tar.bz2
-sha1=874e84bb5959fd5a19c032cfb5d673dded4b5cff
-md5=b1d23a55588e3b2a13e3be66bc69fd8d
-cksum=3347469031
+sha1=799245347044c8f0da9e513f86bb5e4c07974931
+md5=ef619f3bb68039e35c4a219e06be72d0
+cksum=3469661192
diff --git a/build/pkgs/mpfr/package-version.txt b/build/pkgs/mpfr/package-version.txt
index fc261c4280b..fcdb2e109f6 100644
--- a/build/pkgs/mpfr/package-version.txt
+++ b/build/pkgs/mpfr/package-version.txt
@@ -1 +1 @@
-3.1.5.p0
+4.0.0
diff --git a/build/pkgs/mpfr/patches/clang_workaround.patch b/build/pkgs/mpfr/patches/clang_workaround.patch
deleted file mode 100644
index 845ee1accef..00000000000
--- a/build/pkgs/mpfr/patches/clang_workaround.patch
+++ /dev/null
@@ -1,20 +0,0 @@
-diff --git a/src/set_d.c b/src/set_d.c
-index c076ccf..5fc9548 100644
---- a/src/set_d.c
-+++ b/src/set_d.c
-@@ -118,8 +118,15 @@ __gmpfr_extract_double (mpfr_limb_ptr rp, double d)
- 
-     d *= MP_BASE_AS_DOUBLE;
- #if GMP_NUMB_BITS >= 64
-+#ifndef __clang__
-     manl = d;
- #else
-+    /* clang produces an invalid exception when d >= 2^63,
-+       see https://bugs.llvm.org//show_bug.cgi?id=17686.
-+       Since this is always the case, here, we use the following patch. */
-+    manl = 0x8000000000000000 + (mp_limb_t) (d - 0x8000000000000000);
-+#endif /* __clang__ */
-+#else
-     manh = (mp_limb_t) d;
-     manl = (mp_limb_t) ((d - manh) * MP_BASE_AS_DOUBLE);
- #endif

From 3c089ff224e709cc6ad647a123b8e06fe35d152a Mon Sep 17 00:00:00 2001
From: Jeroen Demeyer <jdemeyer@cage.ugent.be>
Date: Tue, 9 Jan 2018 09:30:44 +0100
Subject: [PATCH 059/128] Minor fixes for MPFR-4; support MPFR_RNDF

---
 src/sage/libs/mpfr/__init__.pxd   |  1 +
 src/sage/rings/complex_mpc.pyx    |  2 +-
 src/sage/rings/complex_number.pyx |  2 +-
 src/sage/rings/real_mpfr.pyx      | 26 ++++++++++++++++----------
 4 files changed, 19 insertions(+), 12 deletions(-)

diff --git a/src/sage/libs/mpfr/__init__.pxd b/src/sage/libs/mpfr/__init__.pxd
index 12c7a655864..facac9aa6c7 100644
--- a/src/sage/libs/mpfr/__init__.pxd
+++ b/src/sage/libs/mpfr/__init__.pxd
@@ -96,6 +96,7 @@ cdef extern from "mpfr.h":
     int mpfr_sqrt(mpfr_t rop, mpfr_t op, mpfr_rnd_t rnd)
     int mpfr_sqrt_ui(mpfr_t rop, unsigned long int op, mpfr_rnd_t rnd)
     int mpfr_cbrt(mpfr_t rop, mpfr_t op, mpfr_rnd_t rnd)
+    int mpfr_rootn_ui(mpfr_t rop, mpfr_t op, unsigned long int k, mpfr_rnd_t rnd)
     int mpfr_root(mpfr_t rop, mpfr_t op, unsigned long int k, mpfr_rnd_t rnd)
     int mpfr_pow(mpfr_t rop, mpfr_t op1, mpfr_t op2, mpfr_rnd_t rnd)
     int mpfr_pow_ui(mpfr_t rop, mpfr_t op1, unsigned long int op2, mpfr_rnd_t rnd)
diff --git a/src/sage/rings/complex_mpc.pyx b/src/sage/rings/complex_mpc.pyx
index 824fe55a382..6c9dcaae908 100644
--- a/src/sage/rings/complex_mpc.pyx
+++ b/src/sage/rings/complex_mpc.pyx
@@ -2142,7 +2142,7 @@ cdef class MPComplexNumber(sage.structure.element.FieldElement):
         cdef RealNumber a,r
         a = self.argument()/n
         r = self.abs()
-        mpfr_root(r.value, r.value, n, rrnd)
+        mpfr_rootn_ui(r.value, r.value, n, rrnd)
 
         cdef MPComplexNumber z
         z = self._new()
diff --git a/src/sage/rings/complex_number.pyx b/src/sage/rings/complex_number.pyx
index 16604510037..6df884420a0 100644
--- a/src/sage/rings/complex_number.pyx
+++ b/src/sage/rings/complex_number.pyx
@@ -2217,7 +2217,7 @@ cdef class ComplexNumber(sage.structure.element.FieldElement):
         rho = abs(self)
         arg = self.argument() / n
         mpfr_init2(r, self._prec)
-        mpfr_root(r, rho.value, n, rnd)
+        mpfr_rootn_ui(r, rho.value, n, rnd)
 
         mpfr_sin_cos(z.__im, z.__re, arg.value, rnd)
         mpfr_mul(z.__re, z.__re, r, rnd)
diff --git a/src/sage/rings/real_mpfr.pyx b/src/sage/rings/real_mpfr.pyx
index df9d736c5a4..d892c0985aa 100644
--- a/src/sage/rings/real_mpfr.pyx
+++ b/src/sage/rings/real_mpfr.pyx
@@ -190,16 +190,16 @@ def mpfr_prec_min():
 
         sage: from sage.rings.real_mpfr import mpfr_prec_min
         sage: mpfr_prec_min()
-        2
+        1
         sage: R = RealField(2)
         sage: R(2) + R(1)
         3.0
         sage: R(4) + R(1)
         4.0
-        sage: R = RealField(1)
+        sage: R = RealField(0)
         Traceback (most recent call last):
         ...
-        ValueError: prec (=1) must be >= 2 and <= 2147483391
+        ValueError: prec (=0) must be >= 1 and <= 2147483391
     """
     return MPFR_PREC_MIN
 
@@ -218,7 +218,7 @@ def mpfr_prec_max():
         sage: R = RealField(2^31-256)
         Traceback (most recent call last):
         ...
-        ValueError: prec (=2147483392) must be >= 2 and <= 2147483391
+        ValueError: prec (=2147483392) must be >= 1 and <= 2147483391
     """
     global MY_MPFR_PREC_MAX
     return MY_MPFR_PREC_MAX
@@ -353,7 +353,7 @@ mpfr_set_exp_max(mpfr_get_emax_max())
 
 from sage.arith.long cimport pyobject_to_long
 cdef dict rounding_modes = dict(RNDN=MPFR_RNDN, RNDZ=MPFR_RNDZ,
-        RNDD=MPFR_RNDD, RNDU=MPFR_RNDU, RNDA=MPFR_RNDA)
+        RNDD=MPFR_RNDD, RNDU=MPFR_RNDU, RNDA=MPFR_RNDA, RNDF=MPFR_RNDF)
 
 cdef double LOG_TEN_TWO_PLUS_EPSILON = 3.321928094887363 # a small overestimate of log(10,2)
 
@@ -384,6 +384,8 @@ cpdef RealField(int prec=53, int sci_not=0, rnd=MPFR_RNDN):
       - ``'RNDZ'`` -- round towards zero
       - ``'RNDU'`` -- round towards plus infinity
       - ``'RNDA'`` -- round away from zero
+      - ``'RNDF'`` -- faithful rounding (currently experimental; not
+                      guaranteed correct for every operation)
       - for specialized applications, the rounding mode can also be
         given as an integer value of type ``mpfr_rnd_t``. However, the
         exact values are unspecified.
@@ -472,6 +474,8 @@ cdef class RealField_class(sage.rings.ring.Field):
             Real Field with 100 bits of precision and rounding RNDD
             sage: RealField(100, rnd="RNDA")
             Real Field with 100 bits of precision and rounding RNDA
+            sage: RealField(100, rnd="RNDF")
+            Real Field with 100 bits of precision and rounding RNDF
             sage: RealField(100, rnd=0)
             Real Field with 100 bits of precision
             sage: RealField(100, rnd=1)
@@ -482,14 +486,16 @@ cdef class RealField_class(sage.rings.ring.Field):
             Real Field with 100 bits of precision and rounding RNDD
             sage: RealField(100, rnd=4)
             Real Field with 100 bits of precision and rounding RNDA
+            sage: RealField(100, rnd=5)
+            Real Field with 100 bits of precision and rounding RNDF
             sage: RealField(100, rnd=3.14)
             Traceback (most recent call last):
             ...
-            ValueError: rounding mode (=3.14000000000000) must be one of ['RNDA', 'RNDZ', 'RNDD', 'RNDU', 'RNDN']
-            sage: RealField(100, rnd=5)
+            ValueError: rounding mode (=3.14000000000000) must be one of ['RNDA', 'RNDD', 'RNDF', 'RNDN', 'RNDU', 'RNDZ']
+            sage: RealField(100, rnd=6)
             Traceback (most recent call last):
             ...
-            ValueError: unknown rounding mode 5
+            ValueError: unknown rounding mode 6
             sage: RealField(100, rnd=10^100)
             Traceback (most recent call last):
             ...
@@ -4419,7 +4425,7 @@ cdef class RealNumber(sage.structure.element.RingElement):
 
             sage: r = -1.0
             sage: r.eint()
-            NaN
+            -0.219383934395520
         """
         cdef RealNumber x = self._new()
         if (<RealField_class>self._parent).__prec > SIG_PREC_THRESHOLD: sig_on()
@@ -5275,7 +5281,7 @@ cdef class RealNumber(sage.structure.element.RingElement):
         if algorithm == 1:
             x = self._new()
             sig_on()
-            mpfr_root(x.value, self.value, n, (<RealField_class>self._parent).rnd)
+            mpfr_rootn_ui(x.value, self.value, n, (<RealField_class>self._parent).rnd)
             sig_off()
             return x
 

From 22746f8e5bd59a1f1f53189dc8e8281cc83933c4 Mon Sep 17 00:00:00 2001
From: John Cremona <john.cremona@gmail.com>
Date: Fri, 12 Jan 2018 17:12:52 +0000
Subject: [PATCH 060/128] #10017: adjust doctest for 32-bit

---
 src/sage/rings/number_field/number_field.py | 14 +++++++-------
 1 file changed, 7 insertions(+), 7 deletions(-)

diff --git a/src/sage/rings/number_field/number_field.py b/src/sage/rings/number_field/number_field.py
index 5e1a03d0f9a..b4df31bc4e3 100644
--- a/src/sage/rings/number_field/number_field.py
+++ b/src/sage/rings/number_field/number_field.py
@@ -5595,15 +5595,15 @@ def reduced_basis(self, prec=None):
         Check that the bug reported at :trac:`10017` is fixed::
 
             sage: x = polygen(QQ)
-            sage: k = NumberField(x^6 + 2218926655879913714112*x^4 - 32507675650290949030789018433536*x^3 + 4923635504174417014460581055002374467948544*x^2 - 36066074010564497464129951249279114076897746988630016*x + 264187244046129768986806800244258952598300346857154900812365824,'a')
-            sage: new_basis = k.reduced_basis()
+            sage: k.<a> = NumberField(x^6 + 2218926655879913714112*x^4 - 32507675650290949030789018433536*x^3 + 4923635504174417014460581055002374467948544*x^2 - 36066074010564497464129951249279114076897746988630016*x + 264187244046129768986806800244258952598300346857154900812365824)
+            sage: new_basis = k.reduced_basis(prec=120)
             sage: [c.minpoly() for c in new_basis]
             [x - 1,
-             x^6 + 3*x^5 + 258*x^4 + 511*x^3 + 3564*x^2 + 3309*x + 2347,
-             x^6 - 24*x^5 + 6126*x^4 - 312664*x^3 + 5407566*x^2 - 33643572*x + 95921443,
-             x^6 + 18*x^5 + 3366*x^4 + 82008*x^3 + 886962*x^2 - 840726*x + 5521647,
-             x^6 + 27*x^5 + 9579*x^4 + 623358*x^3 + 5060091*x^2 - 139224285*x + 880944177,
-             x^6 - 72*x^5 + 65286*x^4 - 10762768*x^3 + 473072922*x^2 - 2502686322*x + 54227921641]
+             x^2 - x + 1,
+             x^6 + 3*x^5 - 102*x^4 - 103*x^3 + 10572*x^2 - 59919*x + 127657,
+             x^6 - 3*x^5 - 102*x^4 + 315*x^3 + 10254*x^2 - 80955*x + 198147,
+             x^3 - 171*x + 848,
+             x^6 + 171*x^4 + 1696*x^3 + 29241*x^2 + 145008*x + 719104]
             sage: R = k.order(new_basis)
             sage: R.discriminant()==k.discriminant()
             True

From cee3cb8a7090d9f145de65296849e4860746c28f Mon Sep 17 00:00:00 2001
From: Jeroen Demeyer <jdemeyer@cage.ugent.be>
Date: Wed, 31 May 2017 13:49:32 +0200
Subject: [PATCH 061/128] New function richcmp_item

---
 src/sage/structure/richcmp.pxd |   2 +
 src/sage/structure/richcmp.pyx | 149 +++++++++++++++++++++++++++++++++
 2 files changed, 151 insertions(+)

diff --git a/src/sage/structure/richcmp.pxd b/src/sage/structure/richcmp.pxd
index aa6115a1d37..a5730ebbeea 100644
--- a/src/sage/structure/richcmp.pxd
+++ b/src/sage/structure/richcmp.pxd
@@ -3,6 +3,8 @@ from cpython.object cimport Py_LT, Py_LE, Py_EQ, Py_NE, Py_GT, Py_GE
 from cpython.object cimport PyObject_RichCompare as richcmp
 
 
+cpdef richcmp_item(x, y, int op)
+
 cpdef inline richcmp_not_equal(x, y, int op):
     """
     Like ``richcmp(x, y, op)`` but assuming that `x` is not equal to `y`.
diff --git a/src/sage/structure/richcmp.pyx b/src/sage/structure/richcmp.pyx
index 083f09e606e..4db20de5151 100644
--- a/src/sage/structure/richcmp.pyx
+++ b/src/sage/structure/richcmp.pyx
@@ -105,6 +105,155 @@ def richcmp(x, y, int op):
     return PyObject_RichCompare(x, y, op)
 
 
+cpdef richcmp_item(x, y, int op):
+    """
+    This function is meant to implement lexicographic rich comparison
+    of list-like objects. The inputs ``x`` and ``y`` are items of such
+    lists which should compared.
+
+    INPUT:
+
+    - ``x``, ``y`` -- arbitrary Python objects
+
+    - ``op`` -- comparison operator (one of ``op_LT`, ``op_LE``,
+      ``op_EQ``, ``op_NE``, ``op_GT``, ``op_GE``)
+
+    OUTPUT:
+
+    - if the comparison could not be decided (i.e. we should compare
+      the next items in the list): return ``NotImplemented``
+
+    - otherwise, the result of the comparison of the lists containing
+      ``x`` and ``y``
+
+    The semantics of the comparison is different from Python lists or
+    tuples in the case that the order is not total. Assume that ``A``
+    and ``B`` are lists whose rich comparison is implemented using
+    ``richcmp_item`` (as in EXAMPLES below). Then
+
+    - ``A == B`` iff ``A[i] == B[i]`` for all indices `i`.
+
+    - ``A != B`` iff ``A[i] != B[i]`` for some index `i`.
+
+    - ``A < B`` iff ``A[i] < B[i]`` for some index `i` and
+      for all `j < i`, ``A[j] <= B[j]``.
+
+    - ``A <= B`` iff ``A < B`` or ``A[i] <= B[i]`` for all `i`.
+
+    - ``A > B`` iff ``A[i] > B[i]`` for some index `i` and
+      for all `j < i`, ``A[j] >= B[j]``.
+
+    - ``A >= B`` iff ``A > B`` or ``A[i] >= B[i]`` for all `i`.
+
+    EXAMPLES::
+
+        sage: from sage.structure.richcmp import *
+        sage: @richcmp_method
+        ....: class Listcmp(list):
+        ....:     def __richcmp__(self, other, op):
+        ....:         for i in range(len(self)):  # Assume equal lengths
+        ....:             res = richcmp_item(self[i], other[i], op)
+        ....:             if res is not NotImplemented:
+        ....:                 return res
+        ....:         return rich_to_bool(op, 0)  # Consider the lists to be equal
+        sage: a = Listcmp([0, 1, 3])
+        sage: b = Listcmp([0, 2, 1])
+        sage: a == a
+        True
+        sage: a != a
+        False
+        sage: a < a
+        False
+        sage: a <= a
+        True
+        sage: a > a
+        False
+        sage: a >= a
+        True
+        sage: a == b, b == a
+        (False, False)
+        sage: a != b, b != a
+        (True, True)
+        sage: a < b, b > a
+        (True, True)
+        sage: a <= b, b >= a
+        (True, True)
+        sage: a > b, b < a
+        (False, False)
+        sage: a >= b, b <= a
+        (False, False)
+
+    The above tests used a list of integers, where the result of
+    comparisons are the same as for Python lists.
+
+    If we want to see the difference, we need more general entries in
+    the list. The comparison rules are made to be consistent with
+    setwise operations. If `A` and `B` are sets, we define ``A {op} B``
+    to be true if ``a {op} B`` is true for every `a` in `A` and
+    `b` in `B`. Interval comparisons are a special case of this. For
+    lists of non-empty(!) sets, we want that ``[A1, A2] {op} [B1, B2]``
+    is true if and only if ``[a1, a2] {op} [b1, b2]`` is true for all
+    elements. We verify this::
+
+        sage: @richcmp_method
+        ....: class Setcmp(tuple):
+        ....:     def __richcmp__(self, other, op):
+        ....:         return all(richcmp(x, y, op) for x in self for y in other)
+        sage: sym = {op_EQ: "==", op_NE: "!=", op_LT: "<", op_GT: ">", op_LE: "<=", op_GE: ">="}
+        sage: for A1 in Set(range(4)).subsets():  # long time
+        ....:     if not A1: continue
+        ....:     for B1 in Set(range(4)).subsets():
+        ....:         if not B1: continue
+        ....:         for A2 in Set(range(4)).subsets():
+        ....:             if not A2: continue
+        ....:             for B2 in Set(range(3)).subsets():
+        ....:                 if not B2: continue
+        ....:                 L1 = Listcmp([Setcmp(A1), Setcmp(A2)])
+        ....:                 L2 = Listcmp([Setcmp(B1), Setcmp(B2)])
+        ....:                 for op in range(6):
+        ....:                     reslist = richcmp(L1, L2, op)
+        ....:                     reselt = all(richcmp([a1, a2], [b1, b2], op) for a1 in A1 for a2 in A2 for b1 in B1 for b2 in B2)
+        ....:                     assert reslist is reselt
+    """
+    if op == Py_NE:
+        res = (x != y)
+        if not res:
+            return NotImplemented
+        else:
+            return res  # (x != y)  --> True
+
+    # If x and y are equal, we cannot decide
+    res = (x == y)
+    if res:
+        return NotImplemented
+    if op == Py_EQ:
+        return res  # not (x == y)  --> False
+
+    res = PyObject_RichCompare(x, y, op)
+    cdef bint bres = res
+    if bres != (op & 1):
+        # If we are asked to compute (x < y) and (x < y) is true, return true.
+        # If we are asked to compute (x <= y) and (x <= y) is false, return false.
+        return res
+
+    # Finally, check the inequality with the other strictness
+    # (< becomes <= and vice versa). This check is redundant in the
+    # typical case that (x <= y) is equivalent to (x < y or x == y).
+    # Since (x == y) returned false, we expect this
+    # PyObject_RichCompare() call to return the same result as the
+    # previous one.
+    cdef bint xres = PyObject_RichCompare(x, y, op ^ 1)
+    if xres == bres:  # As expected
+        return res
+
+    # OK, we are in a special case now. Assuming that the op stands
+    # for < or for <=, we know that
+    # (x == y) is false, that (x < y) is false but (x <= y) is true.
+    # Since we want to give more importance to the < and <= results than
+    # the == result, we treat this case as equality.
+    return NotImplemented
+
+
 cdef slot_tp_richcompare(self, other, int op):
     """
     Function to put in the ``tp_richcompare`` slot.

From e7975db3891d2429747ae14003bbb118c23de75a Mon Sep 17 00:00:00 2001
From: Jeroen Demeyer <jdemeyer@cage.ugent.be>
Date: Thu, 1 Jun 2017 10:57:40 +0200
Subject: [PATCH 062/128] Implement comparison for polynomials using
 richcmp_item

---
 .../rings/polynomial/polynomial_element.pyx   | 49 ++++++++++++++++---
 .../polynomial/polynomial_element_generic.py  |  7 +--
 2 files changed, 47 insertions(+), 9 deletions(-)

diff --git a/src/sage/rings/polynomial/polynomial_element.pyx b/src/sage/rings/polynomial/polynomial_element.pyx
index 9c05876d926..7c77b8e7c86 100644
--- a/src/sage/rings/polynomial/polynomial_element.pyx
+++ b/src/sage/rings/polynomial/polynomial_element.pyx
@@ -73,7 +73,7 @@ from sage.misc.abstract_method import abstract_method
 from sage.misc.latex import latex
 from sage.arith.long cimport pyobject_to_long
 from sage.structure.factorization import Factorization
-from sage.structure.richcmp cimport (richcmp, richcmp_not_equal,
+from sage.structure.richcmp cimport (richcmp, richcmp_item,
         rich_to_bool, rich_to_bool_sgn)
 
 from sage.interfaces.singular import singular as singular_default, is_SingularElement
@@ -964,13 +964,49 @@ cdef class Polynomial(CommutativeAlgebraElement):
             False
             sage: R(0) == R(0)
             True
+
+        TESTS::
+
+        Test that comparisons are consistent when using interval
+        coefficients::
+
+            sage: R.<x> = RIF[]
+            sage: a = RIF(0,1) * x
+            sage: b = RIF(1,2) * x
+            sage: a == a
+            False
+            sage: a != a
+            False
+            sage: a == b
+            False
+            sage: a < b
+            False
+            sage: a > b
+            False
+            sage: a <= b
+            True
+            sage: a >= b
+            False
+            sage: a != b
+            False
+
+        For ``RBF``, identical elements are considered equal::
+
+            sage: R.<x> = RBF[]
+            sage: pol = RBF(1.0, 0.1)
+            sage: pol == pol
+            True
+            sage: pol == copy(pol)
+            False
         """
+        cdef Polynomial pol = <Polynomial?>other
+
         cdef Py_ssize_t d1 = self.degree()
-        cdef Py_ssize_t d2 = other.degree()
+        cdef Py_ssize_t d2 = pol.degree()
 
         # Special case constant polynomials
         if d1 <= 0 and d2 <= 0:
-            return richcmp(self[0], other[0], op)
+            return richcmp(self[0], pol[0], op)
 
         # For different degrees, compare the degree
         if d1 != d2:
@@ -979,9 +1015,10 @@ cdef class Polynomial(CommutativeAlgebraElement):
         cdef Py_ssize_t i
         for i in reversed(range(d1+1)):
             x = self.get_unsafe(i)
-            y = other[i]
-            if x != y:
-                return richcmp_not_equal(x, y, op)
+            y = pol.get_unsafe(i)
+            res = richcmp_item(x, y, op)
+            if res is not NotImplemented:
+                return res
         return rich_to_bool(op, 0)
 
     def __nonzero__(self):
diff --git a/src/sage/rings/polynomial/polynomial_element_generic.py b/src/sage/rings/polynomial/polynomial_element_generic.py
index a5e76ea7f10..e71d85309ca 100644
--- a/src/sage/rings/polynomial/polynomial_element_generic.py
+++ b/src/sage/rings/polynomial/polynomial_element_generic.py
@@ -39,7 +39,7 @@
 from sage.rings.polynomial.polynomial_singular_interface import Polynomial_singular_repr
 
 from sage.libs.pari.all import pari_gen
-from sage.structure.richcmp import richcmp, richcmp_not_equal, rich_to_bool, rich_to_bool_sgn
+from sage.structure.richcmp import richcmp, richcmp_item, rich_to_bool, rich_to_bool_sgn
 from sage.structure.element import coerce_binop
 
 from sage.rings.infinity import infinity, Infinity
@@ -687,8 +687,9 @@ def _richcmp_(self, other, op):
         for i in sorted(degs, reverse=True):
             x = self[i]
             y = other[i]
-            if x != y:
-                return richcmp_not_equal(x, y, op)
+            res = richcmp_item(x, y, op)
+            if res is not NotImplemented:
+                return res
         return rich_to_bool(op, 0)
 
     def shift(self, n):

From 73fbd0571a629071bceb1300d699f0b826e983c1 Mon Sep 17 00:00:00 2001
From: Mark <mark00bell@googlemail.com>
Date: Sat, 13 Jan 2018 22:25:01 +0000
Subject: [PATCH 063/128] Added # optional - latte_int markers to doctests that
 require latte-int.

---
 src/sage/geometry/polyhedron/base.py | 8 ++++----
 1 file changed, 4 insertions(+), 4 deletions(-)

diff --git a/src/sage/geometry/polyhedron/base.py b/src/sage/geometry/polyhedron/base.py
index 09ac396f7c9..23187a56ee9 100644
--- a/src/sage/geometry/polyhedron/base.py
+++ b/src/sage/geometry/polyhedron/base.py
@@ -5337,9 +5337,9 @@ def get_integral_point(self, index, **kwds):
             sage: Q = Polyhedron([(1,3), (2, 7), (9, 77)])
             sage: [Q.get_integral_point(i) for i in range(Q.integral_points_count())] == sorted(Q.integral_points())
             True
-            sage: Q.get_integral_point(0, explicit_enumeration_threshold=0, triangulation='cddlib')
+            sage: Q.get_integral_point(0, explicit_enumeration_threshold=0, triangulation='cddlib')  # optional - latte_int
             (1, 3)
-            sage: Q.get_integral_point(0, explicit_enumeration_threshold=0, triangulation='cddlib', foo=True)
+            sage: Q.get_integral_point(0, explicit_enumeration_threshold=0, triangulation='cddlib', foo=True)  # optional - latte_int
             Traceback (most recent call last):
             ...
             RuntimeError: ...
@@ -5411,9 +5411,9 @@ def random_integral_point(self, **kwds):
             (0, 0)
             sage: P.random_integral_point() in P.integral_points()
             True
-            sage: P.random_integral_point(explicit_enumeration_threshold=0, triangulation='cddlib')  # random
+            sage: P.random_integral_point(explicit_enumeration_threshold=0, triangulation='cddlib')  # random, optional - latte_int
             (1, 1)
-            sage: P.random_integral_point(explicit_enumeration_threshold=0, triangulation='cddlib', foo=7)
+            sage: P.random_integral_point(explicit_enumeration_threshold=0, triangulation='cddlib', foo=7)  # optional - latte_int
             Traceback (most recent call last):
             ...
             RuntimeError: ...

From 66ef74d5cafe931a0da4abdfd099b54d1ff18fff Mon Sep 17 00:00:00 2001
From: Clemens Heuberger <clemens.heuberger@aau.at>
Date: Sun, 14 Jan 2018 12:18:55 +0100
Subject: [PATCH 064/128] Trac #24539: fix missing format

---
 src/sage/rings/fraction_field.py | 24 ++++++++++++++++++------
 1 file changed, 18 insertions(+), 6 deletions(-)

diff --git a/src/sage/rings/fraction_field.py b/src/sage/rings/fraction_field.py
index 6df2ae78629..9619636c96f 100644
--- a/src/sage/rings/fraction_field.py
+++ b/src/sage/rings/fraction_field.py
@@ -569,6 +569,18 @@ def _element_constructor_(self, x, y=None, coerce=True):
             sage: R.<x> = PolynomialRing(B,'x')
             sage: (a*d*x^2+a+e+1).resultant(-4*c^2*x+1)
             a*d + 16*c^4*e + 16*a*c^4 + 16*c^4
+
+        Check that :trac:`24539` is fixed::
+
+            sage: var('tau')
+            tau
+            sage: R = PolynomialRing(CyclotomicField(2), 'tau').fraction_field()(
+            ....:     tau/(1+tau))
+            Traceback (most recent call last):
+            ...
+            TypeError: cannot convert tau/(tau + 1)/1 to an element of Fraction
+            Field of Univariate Polynomial Ring in tau over Cyclotomic Field of
+            order 2 and degree 1
         """
         if y is None:
             if isinstance(x, Element) and x.parent() is self:
@@ -614,8 +626,8 @@ def _element_constructor_(self, x, y=None, coerce=True):
                 x = x0.numerator()*y0.denominator()
                 y = y0.numerator()*x0.denominator()
             except AttributeError:
-                raise TypeError("cannot convert {!r}/{!r} to an element of {}",
-                                x0, y0, self)
+                raise TypeError("cannot convert {!r}/{!r} to an element of {}".format(
+                                x0, y0, self))
             try:
                 return self._element_class(self, x, y, coerce=coerce)
             except TypeError:
@@ -928,7 +940,7 @@ class FractionFieldEmbedding(DefaultConvertMap_unique):
         Coercion map:
           From: Univariate Polynomial Ring in x over Rational Field
           To:   Fraction Field of Univariate Polynomial Ring in x over Rational Field
- 
+
     TESTS::
 
         sage: from sage.rings.fraction_field import FractionFieldEmbedding
@@ -1003,7 +1015,7 @@ def _richcmp_(self, other, op):
             sage: f = R.fraction_field().coerce_map_from(R)
             sage: S.<y> = GF(2)[]
             sage: g = S.fraction_field().coerce_map_from(S)
- 
+
             sage: f == g # indirect doctest
             False
             sage: f == f
@@ -1040,7 +1052,7 @@ class FractionFieldEmbeddingSection(Section):
         Section map:
           From: Fraction Field of Univariate Polynomial Ring in x over Rational Field
           To:   Univariate Polynomial Ring in x over Rational Field
- 
+
     TESTS::
 
         sage: from sage.rings.fraction_field import FractionFieldEmbeddingSection
@@ -1118,7 +1130,7 @@ def _richcmp_(self, other, op):
             sage: f = R.fraction_field().coerce_map_from(R).section()
             sage: S.<y> = GF(2)[]
             sage: g = S.fraction_field().coerce_map_from(S).section()
- 
+
             sage: f == g # indirect doctest
             False
             sage: f == f

From 4e52b82ad495851e64071f7dff2b2bc53349a2ab Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?Fr=C3=A9d=C3=A9ric=20Chapoton?=
 <chapoton@math.univ-lyon1.fr>
Date: Sun, 14 Jan 2018 14:34:48 +0100
Subject: [PATCH 065/128] add q-Stirling numbers of first type

---
 src/sage/combinat/q_analogues.py | 77 +++++++++++++++++++++++++++-----
 1 file changed, 65 insertions(+), 12 deletions(-)

diff --git a/src/sage/combinat/q_analogues.py b/src/sage/combinat/q_analogues.py
index f15a58caba1..90e85255293 100644
--- a/src/sage/combinat/q_analogues.py
+++ b/src/sage/combinat/q_analogues.py
@@ -2,7 +2,7 @@
 r"""
 `q`-Analogues
 """
-#*****************************************************************************
+# ****************************************************************************
 #       Copyright (C) 2007 Mike Hansen <mhansen@gmail.com>,
 #
 #  Distributed under the terms of the GNU General Public License (GPL)
@@ -15,7 +15,7 @@
 #  The full text of the GPL is available at:
 #
 #                  http://www.gnu.org/licenses/
-#*****************************************************************************
+# ****************************************************************************
 # python3
 from __future__ import division
 
@@ -69,7 +69,7 @@ def q_int(n, q=None):
         sage: q_int(0).parent()
         Univariate Polynomial Ring in q over Integer Ring
     """
-    if not n in ZZ:
+    if n not in ZZ:
         raise ValueError('%s must be an integer' % n)
 
     if q is None:
@@ -80,6 +80,7 @@ def q_int(n, q=None):
         return sum(q**i for i in range(n))
     return -q**n*sum(q**i for i in range(-n))
 
+
 def q_factorial(n, q=None):
     """
     Returns the `q`-analogue of the factorial `n!`.
@@ -105,9 +106,10 @@ def q_factorial(n, q=None):
         ValueError: Argument (-2) must be a nonnegative integer.
     """
     if n in ZZ and n >= 0:
-        return prod([q_int(i, q) for i in range(1, n+1)])
+        return prod(q_int(i, q) for i in range(1, n + 1))
     else:
-        raise ValueError("Argument (%s) must be a nonnegative integer." %n)
+        raise ValueError("Argument (%s) must be a nonnegative integer." % n)
+
 
 def q_binomial(n, k, q=None, algorithm='auto'):
     r"""
@@ -297,7 +299,7 @@ def q_binomial(n, k, q=None, algorithm='auto'):
     if not(0 <= k and k <= n):
         return zero
 
-    k = min(n-k,k) # Pick the smallest k
+    k = min(n - k, k)  # Pick the smallest k
 
     # heuristic choice of the fastest algorithm
     if algorithm == 'auto':
@@ -322,7 +324,7 @@ def q_binomial(n, k, q=None, algorithm='auto'):
     # the algorithms
     if algorithm == 'naive':
         denom = prod(one - q**i for i in range(1, k+1))
-        if not denom: # q is a root of unity, use the cyclotomic algorithm
+        if not denom:  # q is a root of unity, use the cyclotomic algorithm
             from sage.rings.polynomial.cyclotomic import cyclotomic_value
             return cyclotomic_value(n, k, q, algorithm='cyclotomic')
         else:
@@ -359,6 +361,7 @@ def gaussian_binomial(n, k, q=None, algorithm='auto'):
     """
     return q_binomial(n, k, q, algorithm)
 
+
 def q_multinomial(seq, q=None, binomial_algorithm='auto'):
     r"""
     Return the `q`-multinomial coefficient.
@@ -485,11 +488,12 @@ def qt_catalan_number(n):
         ZZqt = ZZ['q','t']
         d = {}
         for dw in DyckWords(n):
-            tup = (dw.area(),dw.bounce())
-            d[tup] = d.get(tup,0)+1
+            tup = (dw.area(), dw.bounce())
+            d[tup] = d.get(tup, 0) + 1
         return ZZqt(d)
     else:
-        raise ValueError("Argument (%s) must be a nonnegative integer." %n)
+        raise ValueError("Argument (%s) must be a nonnegative integer." % n)
+
 
 def q_pochhammer(n, a, q=None):
     r"""
@@ -556,6 +560,7 @@ def q_pochhammer(n, a, q=None):
         return R.prod(one / (one - a/q**-k) for k in range(1,-n+1))
     return R.prod((one - a*q**k) for k in range(n))
 
+
 @cached_function
 def q_jordan(t, q):
     r"""
@@ -614,7 +619,6 @@ def q_jordan(t, q):
 
     - Xavier Caruso (2012-06-29)
     """
-
     if q == 1:
         raise ValueError("q must not be equal to 1")
 
@@ -631,6 +635,7 @@ def q_jordan(t, q):
             tj = ti
     return res
 
+
 def q_subgroups_of_abelian_group(la, mu, q=None, algorithm='birkhoff'):
     r"""
     Return the `q`-number of subgroups of type ``mu`` in a finite abelian
@@ -756,7 +761,7 @@ def q_subgroups_of_abelian_group(la, mu, q=None, algorithm='birkhoff'):
     - Tomer Bauer (2013-09-26): Implemented the Birkhoff algorithm
     """
     if q is None:
-        q = ZZ['q'].gens()[0]
+        q = ZZ['q'].gen()
     la_c = Partition(la).conjugate()
     mu_c = Partition(mu).conjugate()
     k = mu_c.length()
@@ -780,3 +785,51 @@ def F(args):
 
     raise ValueError("invalid algorithm choice")
 
+
+@cached_function
+def q_stirling_number1(n, k, q=None):
+    r"""
+    Return the `q`-Stirling number of the first kind.
+
+    This is a `q`-analogue of :func:`sage.combinat.combinat.stirling_number1` .
+
+    INPUT:
+
+    - `n`, `k` -- integers with `1 \leq k \leg n`
+
+    - ``q`` -- optional variable (default `q`)
+
+    OUTPUT: a polynomial in the variable `q`
+
+    EXAMPLES::
+
+        sage: from sage.combinat.q_analogues import q_stirling_number1
+        sage: q_stirling_number1(4,2)
+        q^3 + 3*q^2 + 4*q + 3
+
+        sage: all(stirling_number1(6,k) == q_stirling_number1(6,k)(1)
+        ....:     for k in range(1,7))
+        True
+
+        sage: x = polygen(QQ['q'],'x')
+        sage: S = sum(q_stirling_number1(5,k)*x**k for k in range(1, 6))
+        sage: factor(S)
+        x * (x + 1) * (x + q + 1) * (x + q^2 + q + 1) * (x + q^3 + q^2 + q + 1)
+
+    REFERENCES:
+
+    - [Ca1948]_
+
+    - [Ca1954]_
+    """
+    if q is None:
+        q = ZZ['q'].gen()
+    A = q.parent()
+    if n < 0:
+        raise ValueError('q-stirling numbers are not defined for n < 0')
+    if n == 0 == k:
+        return A.one()
+    if k > n or k < 1:
+        return A.zero()
+    return (q_stirling_number1(n - 1, k - 1, q=q) +
+            q_int(n - 1) * q_stirling_number1(n - 1, k, q=q))

From bca2e329a878e099459517894fd854b60e131f9b Mon Sep 17 00:00:00 2001
From: Jeroen Demeyer <jdemeyer@cage.ugent.be>
Date: Sat, 13 Jan 2018 20:57:24 +0100
Subject: [PATCH 066/128] More documentation for richcmp_item

---
 src/sage/structure/richcmp.pyx | 91 ++++++++++++++++++++++++++--------
 1 file changed, 70 insertions(+), 21 deletions(-)

diff --git a/src/sage/structure/richcmp.pyx b/src/sage/structure/richcmp.pyx
index 4db20de5151..bc6f020024c 100644
--- a/src/sage/structure/richcmp.pyx
+++ b/src/sage/structure/richcmp.pyx
@@ -108,23 +108,34 @@ def richcmp(x, y, int op):
 cpdef richcmp_item(x, y, int op):
     """
     This function is meant to implement lexicographic rich comparison
-    of list-like objects. The inputs ``x`` and ``y`` are items of such
-    lists which should compared.
+    of sequences (lists, vectors, polynomials, ...).
+    The inputs ``x`` and ``y`` are corresponding items of such lists
+    which should compared.
 
     INPUT:
 
-    - ``x``, ``y`` -- arbitrary Python objects
+    - ``x``, ``y`` -- arbitrary Python objects. Typically, these are
+      ``X[i]`` and ``Y[i]`` for sequences ``X`` and ``Y``.
 
     - ``op`` -- comparison operator (one of ``op_LT`, ``op_LE``,
       ``op_EQ``, ``op_NE``, ``op_GT``, ``op_GE``)
 
     OUTPUT:
 
-    - if the comparison could not be decided (i.e. we should compare
-      the next items in the list): return ``NotImplemented``
+    Assuming that ``x = X[i]`` and ``y = Y[i]``:
+
+    - if the comparison ``X {op} Y`` (where ``op`` is the given
+      operation) could not be decided yet (i.e. we should compare the
+      next items in the list): return ``NotImplemented``
+
+    - otherwise, if the comparison ``X {op} Y`` could be decided:
+      return ``x {op} y``, which should then also be the result for
+      ``X {op} Y``.
+
+    .. NOTE::
 
-    - otherwise, the result of the comparison of the lists containing
-      ``x`` and ``y``
+        Since ``x {op} y`` cannot return ``NotImplemented``, the two
+        cases above are mutually exclusive.
 
     The semantics of the comparison is different from Python lists or
     tuples in the case that the order is not total. Assume that ``A``
@@ -145,6 +156,9 @@ cpdef richcmp_item(x, y, int op):
 
     - ``A >= B`` iff ``A > B`` or ``A[i] >= B[i]`` for all `i`.
 
+    See below for a detailed description of the exact semantics of
+    ``richcmp_item`` in general.
+
     EXAMPLES::
 
         sage: from sage.structure.richcmp import *
@@ -214,43 +228,78 @@ cpdef richcmp_item(x, y, int op):
         ....:                     reslist = richcmp(L1, L2, op)
         ....:                     reselt = all(richcmp([a1, a2], [b1, b2], op) for a1 in A1 for a2 in A2 for b1 in B1 for b2 in B2)
         ....:                     assert reslist is reselt
+
+    EXACT SEMANTICS:
+
+    Above, we only described how ``richcmp_item`` behaves when it is
+    used to compare sequences. Here, we specify the exact semantics.
+    First of all, recall that the result of ``richcmp_item(x, y, op)``
+    is either ``NotImplemented`` or ``x {op} y``.
+
+    - if ``op`` is ``==``: return ``NotImplemented`` if ``x == y``.
+      If ``x == y`` is false, then return ``x == y``.
+
+    - if ``op`` is ``!=``: return ``NotImplemented`` if not ``x != y``.
+      If ``x != y`` is true, then return ``x != y``.
+
+    - if ``op`` is ``<``: return ``NotImplemented`` if ``x == y``.
+      If ``x < y`` or not ``x <= y``, return ``x < y``.
+      Otherwise (if both ``x == y`` and ``x < y`` are false but
+      ``x <= y`` is true), return ``NotImplemented``.
+
+    - if ``op`` is ``<=``: return ``NotImplemented`` if ``x == y``.
+      If ``x < y`` or not ``x <= y``, return ``x <= y``.
+      Otherwise (if both ``x == y`` and ``x < y`` are false but
+      ``x <= y`` is true), return ``NotImplemented``.
+
+    - the ``>`` and ``>=`` operators are analogous to ``<`` and ``<=``.
     """
     if op == Py_NE:
         res = (x != y)
         if not res:
             return NotImplemented
-        else:
-            return res  # (x != y)  --> True
+        return res  # (x != y)  --> True
 
     # If x and y are equal, we cannot decide
     res = (x == y)
     if res:
         return NotImplemented
+
     if op == Py_EQ:
         return res  # not (x == y)  --> False
 
+    # At this point, {op} is < or <= or > or >=. In the comments below,
+    # we always refer to < and <= but > and >= are obviously analogous.
+
+    # Compute x {op} y and convert to boolean (0 or 1)
     res = PyObject_RichCompare(x, y, op)
     cdef bint bres = res
-    if bres != (op & 1):
-        # If we are asked to compute (x < y) and (x < y) is true, return true.
-        # If we are asked to compute (x <= y) and (x <= y) is false, return false.
+
+    # true (1) for <= and >= and false (0) for < and >
+    cdef bint op_is_not_strict = op & 1
+
+    if bres != op_is_not_strict:
+        # If we are asked to compute (x < y) and (x < y) is true,
+        # return (x < y) which is true.
+        # If we are asked to compute (x <= y) and (x <= y) is false,
+        # return (x <= y) which is false.
         return res
 
     # Finally, check the inequality with the other strictness
-    # (< becomes <= and vice versa). This check is redundant in the
-    # typical case that (x <= y) is equivalent to (x < y or x == y).
-    # Since (x == y) returned false, we expect this
-    # PyObject_RichCompare() call to return the same result as the
-    # previous one.
+    # (< becomes <= and vice versa; this corresponds to replacing op by
+    # op ^ 1). This check is redundant in the typical case that (x <= y)
+    # is equivalent to (x < y or x == y): since (x == y) returned false,
+    # we expect that this PyObject_RichCompare() call returns the same
+    # boolean result as the previous one.
     cdef bint xres = PyObject_RichCompare(x, y, op ^ 1)
     if xres == bres:  # As expected
         return res
 
-    # OK, we are in a special case now. Assuming that the op stands
-    # for < or for <=, we know that
-    # (x == y) is false, that (x < y) is false but (x <= y) is true.
+    # OK, we are in a special case now. We checked that (x == y) is
+    # false, that (x < y) is false but (x <= y) is true.
     # Since we want to give more importance to the < and <= results than
-    # the == result, we treat this case as equality.
+    # the == result, we treat this case as equality. Therefore, we
+    # cannot decide.
     return NotImplemented
 
 

From 0d26272b81d7768c26650a6693d705449ec7e102 Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?Fr=C3=A9d=C3=A9ric=20Chapoton?=
 <chapoton@math.univ-lyon1.fr>
Date: Sun, 14 Jan 2018 16:40:29 +0100
Subject: [PATCH 067/128] trac 3313 fix doc

---
 src/doc/en/reference/references/index.rst | 4 ++--
 1 file changed, 2 insertions(+), 2 deletions(-)

diff --git a/src/doc/en/reference/references/index.rst b/src/doc/en/reference/references/index.rst
index 4ab4f9e6a12..0e6f2a0c868 100644
--- a/src/doc/en/reference/references/index.rst
+++ b/src/doc/en/reference/references/index.rst
@@ -2053,8 +2053,8 @@ REFERENCES:
             Volume 921, 1995, pp 1-12.
 
 .. [Shi1971] Goro Shimura, *Introduction to the arithmetic theory of
-            automorphic functions*. Publications of the Mathematical
-             Society of Japan and Princeton University Press, 1971. 
+             automorphic functions*. Publications of the Mathematical
+             Society of Japan and Princeton University Press, 1971.
 
 .. [Shr2004] \S. Shreve, *Stochastic Calculus for Finance II:
              Continuous-Time Models*.  New York: Springer, 2004

From 68a78ac0358406783825685f823aa1122e883db2 Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?Fr=C3=A9d=C3=A9ric=20Chapoton?=
 <chapoton@math.univ-lyon1.fr>
Date: Sun, 14 Jan 2018 20:36:28 +0100
Subject: [PATCH 068/128] trac 24540 more doc

---
 src/sage/combinat/q_analogues.py | 19 ++++++++++++++++---
 1 file changed, 16 insertions(+), 3 deletions(-)

diff --git a/src/sage/combinat/q_analogues.py b/src/sage/combinat/q_analogues.py
index 90e85255293..5610576bbe1 100644
--- a/src/sage/combinat/q_analogues.py
+++ b/src/sage/combinat/q_analogues.py
@@ -789,18 +789,24 @@ def F(args):
 @cached_function
 def q_stirling_number1(n, k, q=None):
     r"""
-    Return the `q`-Stirling number of the first kind.
+    Return the (unsigned) `q`-Stirling number of the first kind.
 
     This is a `q`-analogue of :func:`sage.combinat.combinat.stirling_number1` .
 
     INPUT:
 
-    - `n`, `k` -- integers with `1 \leq k \leg n`
+    - ``n``, ``k`` -- integers with ``1 <= k <= n``
 
     - ``q`` -- optional variable (default `q`)
 
     OUTPUT: a polynomial in the variable `q`
 
+    These polynomials satisfy the recurrence
+
+    .. MATH::
+
+         s_{n,k} = s_{n-1,k-1} + [n-1]_q s_{n-1, k}.
+
     EXAMPLES::
 
         sage: from sage.combinat.q_analogues import q_stirling_number1
@@ -816,6 +822,13 @@ def q_stirling_number1(n, k, q=None):
         sage: factor(S)
         x * (x + 1) * (x + q + 1) * (x + q^2 + q + 1) * (x + q^3 + q^2 + q + 1)
 
+    TESTS::
+
+        sage: q_stirling_number1(-1,2)
+        Traceback (most recent call last):
+        ...
+        ValueError: q-Stirling numbers are not defined for n < 0
+
     REFERENCES:
 
     - [Ca1948]_
@@ -826,7 +839,7 @@ def q_stirling_number1(n, k, q=None):
         q = ZZ['q'].gen()
     A = q.parent()
     if n < 0:
-        raise ValueError('q-stirling numbers are not defined for n < 0')
+        raise ValueError('q-Stirling numbers are not defined for n < 0')
     if n == 0 == k:
         return A.one()
     if k > n or k < 1:

From ce7e0a44383eb38ba1d746616d758ae1e12737e2 Mon Sep 17 00:00:00 2001
From: "Erik M. Bray" <erik.bray@lri.fr>
Date: Wed, 25 Oct 2017 14:36:56 +0000
Subject: [PATCH 069/128] Add the ability to temporarily install to an
 alternate installation root (referred to often as the DESTDIR convention,
 which is supported by most automake packages).  From the temporary install
 root files are then copied into the real install root.  This is called a
 "staged installation".

This has a number of uses, such as being able to build a binary archive
containing just the files installed for that package.  Here we use it also
to generate a manifest of files installed/owned by a given package.  This
can be used, for example, to implement more careful package uninstallation.

In particular, this supports passing a SAGE_DESTDIR variable to spkg build
scripts.  In the case of packages installed with `make install`, this is
passed to `make` as `DESTDIR=$SAGE_DESTDIR`.  Not all packages that use
make support this (but most do).  For those that don't this is a no-op.

The same could be done for Python packages by having `sdh_pip_install` add
`--root=${SAGE_DESTDIR}`, but currently that breaks a tiny set of Python
packages whose build scripts do not fully support this kind of staged
installation, so their case will be addressed separately.
---
 build/bin/sage-spkg       | 60 ++++++++++++++++++++++++++++++++++-----
 src/bin/sage-dist-helpers |  7 +++--
 2 files changed, 57 insertions(+), 10 deletions(-)

diff --git a/build/bin/sage-spkg b/build/bin/sage-spkg
index 80f6370a8ec..7a4941f57fb 100755
--- a/build/bin/sage-spkg
+++ b/build/bin/sage-spkg
@@ -21,6 +21,7 @@
 #      SAGE_ROOT      -- root directory of sage install
 #      SAGE_LOCAL     -- $SAGE_ROOT/local
 #      SAGE_DISTFILES -- directory that stores upstream tarballs
+#      SAGE_DESTDIR   -- temporary root the package will be installed to
 #      PKG_BASE       -- the base name of the package itself (e.g. 'patch')
 #      PKG_VER        -- the version number of the package
 #      PKG_NAME       -- $PKG_BASE-$PKG_VER
@@ -804,6 +805,10 @@ export rsync_proxy=$http_proxy
 # Actually install
 ##################################################################
 
+# Set the $SAGE_DESTDIR variable to be passed to the spkg-install
+# script (the script itself could set this, but better to standardize
+# this in one place)
+export SAGE_DESTDIR="$(pwd)/inst"
 
 if [ -f spkg-build ]; then
     # Package has both spkg-build and spkg-install; execute the latter with SAGE_SUDO
@@ -826,6 +831,42 @@ else
     fi
 fi
 
+# All spkgs should eventually support this, but fall back on old behavior in
+# case DESTDIR=$SAGE_DESTDIR installation was not used
+echo "Copying package files from temporary location $SAGE_DESTDIR to $SAGE_LOCAL"
+if [ -d "$SAGE_DESTDIR" ]; then
+    PREFIX="${SAGE_DESTDIR}${SAGE_LOCAL%/}/"
+
+    rm -f "$PREFIX"lib/*.la
+    if [ $? -ne 0 ]; then
+        error_msg "Error deleting unnecessary libtool archive files"
+        exit 1
+    fi
+
+    # Generate installed filed list
+    FILE_LIST=""
+    FIRST=1
+    IFS=$'\n'
+    for filename in $(find "$PREFIX" -type f -o -type l | sort); do
+        filename="${filename#$PREFIX}"
+        if [ $FIRST -eq 1 ]; then
+            FILE_LIST="\"$filename\""
+            FIRST=0
+        else
+            FILE_LIST="${FILE_LIST},"$'\n        '"\"${filename}\""
+        fi
+        # Copy file from the temp install path into $SAGE_LOCAL
+        if [ ! -d "$SAGE_LOCAL/$(dirname "$filename")" ]; then
+            mkdir -p "$SAGE_LOCAL/$(dirname "$filename")"
+        fi
+        cp -a "$PREFIX$filename" "${SAGE_LOCAL%/}/$filename"
+        if [ $? -ne 0 ]; then
+            error_msg "Error copying files for $PKG_BASE."
+            exit 1
+        fi
+    done
+fi
+
 if [ "$UNAME" = "CYGWIN" ]; then
     # Rebase after installing each package--in case any packages load this
     # package at build time we need to ensure during the build that no binaries
@@ -834,7 +875,11 @@ if [ "$UNAME" = "CYGWIN" ]; then
         sage-rebase.sh "$SAGE_LOCAL" 2>/dev/null
 fi
 
-echo "Successfully installed $PKG_NAME"
+
+# Note: spkg-check tests are run after the package has been copied into
+# SAGE_LOCAL.  It might make more sense to run the tests before, but the
+# spkg-check scripts were written before use of DESTDIR installs, and so
+# fail in many cases.  This might be good to change later.
 
 if [ "$SAGE_CHECK" = "yes" ]; then
     if [ -f spkg-check ]; then
@@ -851,11 +896,6 @@ if [ "$SAGE_CHECK" = "yes" ]; then
     fi
 fi
 
-rm -f "$SAGE_LOCAL"/lib/*.la
-if [ $? -ne 0 ]; then
-    error_msg "Error deleting unnecessary libtool archive files"
-    exit 1
-fi
 
 # Mark that the new package has been installed (and tested, if
 # applicable).
@@ -867,11 +907,17 @@ cat > "$PKG_NAME_INSTALLED" << __EOF__
     "install_date": "$(date)",
     "system_uname": "$(uname -a)",
     "sage_version": "$(cat "${SAGE_ROOT}/VERSION.txt")",
-    "test_result": "$TEST_SUITE_RESULT"
+    "test_result": "$TEST_SUITE_RESULT",
+    "files": [
+        $FILE_LIST
+    ]
 }
 __EOF__
 
 
+echo "Successfully installed $PKG_NAME"
+
+
 ##################################################################
 # Delete the temporary build directory if required
 ##################################################################
diff --git a/src/bin/sage-dist-helpers b/src/bin/sage-dist-helpers
index 30a56e639e6..0708ebec909 100644
--- a/src/bin/sage-dist-helpers
+++ b/src/bin/sage-dist-helpers
@@ -45,8 +45,9 @@
 #
 # - sdh_make_install [...]
 #
-#    Runs `$SAGE_SUDO $MAKE install`.  Additional arguments to `make` may be
-#    given as arguments.
+#    Runs `$SAGE_SUDO $MAKE install` with DESTDIR correctly set to a temporary
+#    install directory, for staged installations.  Additional arguments to
+#    `make` may be given as arguments.
 #
 # - sdh_pip_install [...]
 #
@@ -131,7 +132,7 @@ sdh_make() {
 
 sdh_make_install() {
     echo "Installing $PKG_NAME"
-    $SAGE_SUDO ${MAKE:-make} install "$@" || \
+    $SAGE_SUDO ${MAKE:-make} install DESTDIR="$SAGE_DESTDIR" "$@" || \
         sdh_die "Error installing $PKG_NAME"
 }
 

From c0cb165d227eee2c2c7bd4014acee542a2865051 Mon Sep 17 00:00:00 2001
From: "Erik M. Bray" <erik.bray@lri.fr>
Date: Wed, 25 Oct 2017 15:20:17 +0000
Subject: [PATCH 070/128] Fix typo in comment

---
 build/bin/sage-spkg | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/build/bin/sage-spkg b/build/bin/sage-spkg
index 7a4941f57fb..77fff5d9bf2 100755
--- a/build/bin/sage-spkg
+++ b/build/bin/sage-spkg
@@ -843,7 +843,7 @@ if [ -d "$SAGE_DESTDIR" ]; then
         exit 1
     fi
 
-    # Generate installed filed list
+    # Generate installed file manifest
     FILE_LIST=""
     FIRST=1
     IFS=$'\n'

From d085587a0f4319f03a830c39eb5b3d83836f18dd Mon Sep 17 00:00:00 2001
From: Ralf Stephan <ralf@ark.in-berlin.de>
Date: Mon, 15 Jan 2018 15:03:05 +0100
Subject: [PATCH 071/128] 24497: doctest fixes

---
 src/sage/functions/transcendental.py                          | 2 +-
 src/sage/modular/modform_hecketriangle/graded_ring_element.py | 4 ++--
 src/sage/symbolic/series.pyx                                  | 4 ++--
 3 files changed, 5 insertions(+), 5 deletions(-)

diff --git a/src/sage/functions/transcendental.py b/src/sage/functions/transcendental.py
index 769651f8af9..69ce413ed46 100644
--- a/src/sage/functions/transcendental.py
+++ b/src/sage/functions/transcendental.py
@@ -86,7 +86,7 @@ def __init__(self):
 
             sage: s = SR('s')
             sage: zeta(s).series(s==1, 2)
-            1*(s - 1)^(-1) + (euler_gamma) + (-stieltjes(1))*(s - 1) + Order((s - 1)^2)
+            1*(s - 1)^(-1) + euler_gamma + (-stieltjes(1))*(s - 1) + Order((s - 1)^2)
 
         Generally, the Stieltjes constants occur in the Laurent
         expansion of `\zeta`-type singularities::
diff --git a/src/sage/modular/modform_hecketriangle/graded_ring_element.py b/src/sage/modular/modform_hecketriangle/graded_ring_element.py
index a23d922460f..ca15bf9e13a 100644
--- a/src/sage/modular/modform_hecketriangle/graded_ring_element.py
+++ b/src/sage/modular/modform_hecketriangle/graded_ring_element.py
@@ -1944,8 +1944,8 @@ def evaluate(self, tau, prec = None, num_prec = None, check=False):
             2.525...e-10 - 3.884...e-6*I
             sage: f_i(i)
             0
-            sage: f_i(i + 1e-1000)
-            -6.084...e-14 - 4.101...e-1000*I
+            sage: f_i(i + 1e-1000)  # rel tol 5e-2
+            -6.08402217494586e-14 - 4.10147008296517e-1000*I
             sage: f_inf(infinity)
             0
 
diff --git a/src/sage/symbolic/series.pyx b/src/sage/symbolic/series.pyx
index 6ebc12357f7..a0a5a510d3a 100644
--- a/src/sage/symbolic/series.pyx
+++ b/src/sage/symbolic/series.pyx
@@ -88,7 +88,7 @@ TESTS:
 Check that :trac:`20088` is fixed::
 
     sage: ((1+x).series(x)^pi).series(x,3)
-    1 + (pi)*x + (-1/2*pi + 1/2*pi^2)*x^2 + Order(x^3)
+    1 + pi*x + (-1/2*pi + 1/2*pi^2)*x^2 + Order(x^3)
 
 Check that :trac:`14878` is fixed, this should take only microseconds::
 
@@ -281,7 +281,7 @@ cdef class SymbolicSeries(Expression):
         EXAMPLES::
 
             sage: ex=(gamma(1-x)).series(x,3); ex
-            1 + (euler_gamma)*x + (1/2*euler_gamma^2 + 1/12*pi^2)*x^2 + Order(x^3)
+            1 + euler_gamma*x + (1/2*euler_gamma^2 + 1/12*pi^2)*x^2 + Order(x^3)
             sage: g=ex.power_series(SR); g
             1 + euler_gamma*x + (1/2*euler_gamma^2 + 1/12*pi^2)*x^2 + O(x^3)
             sage: g.parent()

From 6bc73324b370910856165b7dc3673c227d83db2d Mon Sep 17 00:00:00 2001
From: "Erik M. Bray" <erik.bray@lri.fr>
Date: Mon, 15 Jan 2018 15:17:39 +0000
Subject: [PATCH 072/128] Make $SAGE_DESTDIR explicitly relative to
 $SAGE_BUILD_DIR, and not whatever $(pwd) happens to be.

---
 build/bin/sage-spkg | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/build/bin/sage-spkg b/build/bin/sage-spkg
index 77fff5d9bf2..8f077a6d7ee 100755
--- a/build/bin/sage-spkg
+++ b/build/bin/sage-spkg
@@ -808,7 +808,7 @@ export rsync_proxy=$http_proxy
 # Set the $SAGE_DESTDIR variable to be passed to the spkg-install
 # script (the script itself could set this, but better to standardize
 # this in one place)
-export SAGE_DESTDIR="$(pwd)/inst"
+export SAGE_DESTDIR="${SAGE_BUILD_DIR}/${PKG_NAME}/inst"
 
 if [ -f spkg-build ]; then
     # Package has both spkg-build and spkg-install; execute the latter with SAGE_SUDO

From ed0194852aa8925e32b31d83b8ec4d34441f121c Mon Sep 17 00:00:00 2001
From: Jeroen Demeyer <jdemeyer@cage.ugent.be>
Date: Mon, 15 Jan 2018 15:33:16 +0100
Subject: [PATCH 073/128] lazy_import in lfunctions

---
 src/sage/lfunctions/all.py | 13 +++++--------
 1 file changed, 5 insertions(+), 8 deletions(-)

diff --git a/src/sage/lfunctions/all.py b/src/sage/lfunctions/all.py
index d7d4d065841..9281f97ebbe 100644
--- a/src/sage/lfunctions/all.py
+++ b/src/sage/lfunctions/all.py
@@ -1,9 +1,6 @@
-from __future__ import absolute_import
+from sage.misc.lazy_import import lazy_import as _lazy_import_
 
-from .dokchitser import Dokchitser
-
-from .lcalc import lcalc
-
-from .sympow import sympow
-
-from .zero_sums import LFunctionZeroSum
+_lazy_import_("sage.lfunctions.dokchitser", "Dokchitser")
+_lazy_import_("sage.lfunctions.sympow", "sympow")
+_lazy_import_("sage.lfunctions.zero_sums", "LFunctionZeroSum")
+_lazy_import_("sage.lfunctions.lcalc", "lcalc")

From 2fdd3e46baa3ac120646c86d0edbdc4701ad8c6f Mon Sep 17 00:00:00 2001
From: Travis Scrimshaw <tcscrims at gmail.com>
Date: Mon, 15 Jan 2018 10:48:44 -0600
Subject: [PATCH 074/128] Use next() and typo fixes.

---
 src/sage/algebras/lie_algebras/virasoro.py | 6 +++---
 1 file changed, 3 insertions(+), 3 deletions(-)

diff --git a/src/sage/algebras/lie_algebras/virasoro.py b/src/sage/algebras/lie_algebras/virasoro.py
index 4b1c8ffc527..eb19dcaf8d8 100644
--- a/src/sage/algebras/lie_algebras/virasoro.py
+++ b/src/sage/algebras/lie_algebras/virasoro.py
@@ -584,14 +584,14 @@ class ChargelessRepresentation(CombinatorialFreeModule):
 
     We construct the reducible `V_{0,2}` and the trivial
     subrepresentation given by the span of `v_2`. We verify
-    this for `\{d_i \mid -10 \leq i < 10\}::
+    this for `\{d_i \mid -10 \leq i < 10\}`::
 
         sage: M = L.chargeless_representation(0, 2)
         sage: v = M.basis()
         sage: all(d[i] * v[2] == M.zero() for i in range(-10, 10))
         True
 
-    REFERNCES::
+    REFERENCES::
 
     - [Mat1992]_
     - [IK2010]_
@@ -997,7 +997,7 @@ def _acted_upon_(self, scalar, self_on_left=False):
                 13/4*v
 
                 sage: it = iter(M.basis())
-                sage: B = [it.next() for _ in range(10)]
+                sage: B = [next(it) for _ in range(10)]
                 sage: all(d[i]*(d[j]*v) - d[j]*(d[i]*v) == d[i].bracket(d[j])*v
                 ....:     for i in range(-5, 5) for j in range(-5, 5) for v in B)
                 True

From ed41210d578b395009e76a50e38b1987c0e0fa2d Mon Sep 17 00:00:00 2001
From: "Erik M. Bray" <erik.bray@lri.fr>
Date: Mon, 15 Jan 2018 16:56:45 +0000
Subject: [PATCH 075/128] Move files from SAGE_DESTDIR into SAGE_LOCAL instead
 of copying.

Remove SAGE_DESTDIR once we're done installing.
---
 build/bin/sage-spkg | 8 ++++++--
 1 file changed, 6 insertions(+), 2 deletions(-)

diff --git a/build/bin/sage-spkg b/build/bin/sage-spkg
index 8f077a6d7ee..b86336cdc35 100755
--- a/build/bin/sage-spkg
+++ b/build/bin/sage-spkg
@@ -859,12 +859,16 @@ if [ -d "$SAGE_DESTDIR" ]; then
         if [ ! -d "$SAGE_LOCAL/$(dirname "$filename")" ]; then
             mkdir -p "$SAGE_LOCAL/$(dirname "$filename")"
         fi
-        cp -a "$PREFIX$filename" "${SAGE_LOCAL%/}/$filename"
+        mv "$PREFIX$filename" "${SAGE_LOCAL%/}/$filename"
         if [ $? -ne 0 ]; then
-            error_msg "Error copying files for $PKG_BASE."
+            error_msg "Error moving files for $PKG_BASE."
             exit 1
         fi
     done
+
+    # Remove the $SAGE_DESTDIR entirely once all files have been moved to their
+    # final location.
+    rm -rf "$SAGE_DESTDIR"
 fi
 
 if [ "$UNAME" = "CYGWIN" ]; then

From 91dfc131ed8d0b98a87d50c10d16f05cd0df8b1d Mon Sep 17 00:00:00 2001
From: "Erik M. Bray" <erik.bray@lri.fr>
Date: Mon, 15 Jan 2018 16:57:30 +0000
Subject: [PATCH 076/128] ecl: create post-build links in SAGE_DESTDIR instead
 of directly in SAGE_LOCAL

---
 build/pkgs/ecl/spkg-install | 4 ++--
 1 file changed, 2 insertions(+), 2 deletions(-)

diff --git a/build/pkgs/ecl/spkg-install b/build/pkgs/ecl/spkg-install
index 226af5333e8..7ee84ec5bd8 100644
--- a/build/pkgs/ecl/spkg-install
+++ b/build/pkgs/ecl/spkg-install
@@ -81,13 +81,13 @@ sdh_make_install
 # Create symbolic link to lib/ecl-version directory.
 # Also create a symbolic link lib/ecl/ecl -> include/ecl.
 # This is important when the Sage install is moved, see Trac #14662.
-cd "$SAGE_LOCAL/lib/" && rm -f ecl && ln -s ecl-* ecl
+cd "$SAGE_DESTDIR$SAGE_LOCAL/lib/" && rm -f ecl && ln -s ecl-* ecl
 if [ $? -ne 0 ]; then
     echo >&2 "Error - Failed to create symbolic link to ECL library"
     echo >&2 "directory ... exiting"
     exit 1
 fi
-cd "$SAGE_LOCAL/lib/ecl" && rm -f ecl && ln -s ../../include/ecl ecl
+cd "$SAGE_DESTDIR$SAGE_LOCAL/lib/ecl" && rm -f ecl && ln -s ../../include/ecl ecl
 if [ $? -ne 0 ]; then
     echo >&2 "Error - Failed to create symbolic link to ECL include"
     echo >&2 "directory ... exiting"

From 4b9ef9413c64d2c081977d1266b24e451d7d5aa7 Mon Sep 17 00:00:00 2001
From: Travis Scrimshaw <tcscrims at gmail.com>
Date: Mon, 15 Jan 2018 20:47:08 -0600
Subject: [PATCH 077/128] No double colon on references.

---
 src/sage/algebras/lie_algebras/virasoro.py | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/src/sage/algebras/lie_algebras/virasoro.py b/src/sage/algebras/lie_algebras/virasoro.py
index eb19dcaf8d8..9ba8c71a79d 100644
--- a/src/sage/algebras/lie_algebras/virasoro.py
+++ b/src/sage/algebras/lie_algebras/virasoro.py
@@ -591,7 +591,7 @@ class ChargelessRepresentation(CombinatorialFreeModule):
         sage: all(d[i] * v[2] == M.zero() for i in range(-10, 10))
         True
 
-    REFERENCES::
+    REFERENCES:
 
     - [Mat1992]_
     - [IK2010]_

From 5f6401d8d4add1cbd1c0c7c85b75e8e414f349aa Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?Fr=C3=A9d=C3=A9ric=20Chapoton?=
 <chapoton@math.univ-lyon1.fr>
Date: Tue, 16 Jan 2018 08:58:40 +0100
Subject: [PATCH 078/128] trac 24514 deprecate __hex__

---
 src/sage/libs/ntl/ntl_GF2X.pyx | 120 +++++++++++++++++++++------------
 1 file changed, 77 insertions(+), 43 deletions(-)

diff --git a/src/sage/libs/ntl/ntl_GF2X.pyx b/src/sage/libs/ntl/ntl_GF2X.pyx
index 5c3fc79d689..03b5a6436bf 100644
--- a/src/sage/libs/ntl/ntl_GF2X.pyx
+++ b/src/sage/libs/ntl/ntl_GF2X.pyx
@@ -24,6 +24,7 @@ include 'decl.pxi'
 
 from cpython.object cimport Py_EQ, Py_NE
 from sage.rings.integer cimport Integer
+from sage.misc.superseded import deprecated_function_alias
 
 from .ntl_ZZ import unpickle_class_value
 from .ntl_GF2 cimport ntl_GF2
@@ -52,7 +53,8 @@ def GF2XHexOutput(have_hex=None):
     INPUT:
         have_hex if True hex representation will be used
 
-    EXAMPLES:
+    EXAMPLES::
+
         sage: m = ntl.GF2EContext(ntl.GF2X([1,1,0,1,1,0,0,0,1]))
         sage: x = ntl.GF2E([1,0,1,0,1], m) ; x
         [1 0 1 0 1]
@@ -100,7 +102,8 @@ cdef class ntl_GF2X(object):
         OUTPUT:
             a new ntl.GF2X element
 
-        EXAMPLES:
+        EXAMPLES::
+
             sage: ntl.GF2X(ntl.ZZ_pX([1,1,3],2))
             [1 1 1]
             sage: ntl.GF2X('0x1c')
@@ -148,7 +151,7 @@ cdef class ntl_GF2X(object):
             x = x.list() # this is slow but cimport leads to circular imports
         elif isinstance(x, FiniteField):
             if x.characteristic() == 2:
-                x= list(x.modulus())
+                x = list(x.modulus())
         elif isinstance(x, FiniteField_givaroElement):
             x = "0x"+hex(x.integer_representation())[2:][::-1]
         elif isinstance(x, FiniteField_ntl_gf2eElement):
@@ -159,7 +162,8 @@ cdef class ntl_GF2X(object):
 
     def __reduce__(self):
         """
-        EXAMPLES:
+        EXAMPLES::
+
             sage: f = ntl.GF2X(ntl.ZZ_pX([1,1,3],2))
             sage: loads(dumps(f)) == f
             True
@@ -167,13 +171,14 @@ cdef class ntl_GF2X(object):
             sage: loads(dumps(f)) == f
             True
         """
-        return unpickle_class_value, (ntl_GF2X, hex(self))
+        return unpickle_class_value, (ntl_GF2X, self.hex())
 
     def __repr__(self):
         """
         Return the string representation of self.
 
-        EXAMPLES:
+        EXAMPLES::
+
             sage: ntl.GF2X(ntl.ZZ_pX([1,1,3],2)).__repr__()
             '[1 1 1]'
         """
@@ -181,7 +186,8 @@ cdef class ntl_GF2X(object):
 
     def __mul__(ntl_GF2X self, other):
         """
-        EXAMPLES:
+        EXAMPLES::
+
             sage: f = ntl.GF2X([1,0,1,1]) ; g = ntl.GF2X([0,1])
             sage: f*g ## indirect doctest
             [0 1 0 1 1]
@@ -194,7 +200,8 @@ cdef class ntl_GF2X(object):
 
     def __truediv__(ntl_GF2X self, b):
         """
-        EXAMPLES:
+        EXAMPLES::
+
             sage: a = ntl.GF2X(4)
             sage: a / ntl.GF2X(2)
             [0 1]
@@ -219,7 +226,8 @@ cdef class ntl_GF2X(object):
 
     def DivRem(ntl_GF2X self, b):
         """
-        EXAMPLES:
+        EXAMPLES::
+
             sage: a = ntl.GF2X(4)
             sage: a.DivRem( ntl.GF2X(2) )
             ([0 1], [])
@@ -237,7 +245,8 @@ cdef class ntl_GF2X(object):
 
     def __floordiv__(ntl_GF2X self, b):
         """
-        EXAMPLES:
+        EXAMPLES::
+
             sage: a = ntl.GF2X(4)
             sage: a // ntl.GF2X(2)
             [0 1]
@@ -254,7 +263,8 @@ cdef class ntl_GF2X(object):
 
     def __mod__(ntl_GF2X self, b):
         """
-        EXAMPLES:
+        EXAMPLES::
+
             sage: a = ntl.GF2X(4)
             sage: a % ntl.GF2X(2)
             []
@@ -271,7 +281,8 @@ cdef class ntl_GF2X(object):
 
     def __sub__(ntl_GF2X self, other):
         """
-        EXAMPLES:
+        EXAMPLES::
+
             sage: f = ntl.GF2X([1,0,1,1]) ; g = ntl.GF2X([0,1])
             sage: f - g ## indirect doctest
             [1 1 1 1]
@@ -286,7 +297,8 @@ cdef class ntl_GF2X(object):
 
     def __add__(ntl_GF2X self, other):
         """
-        EXAMPLES:
+        EXAMPLES::
+
             sage: f = ntl.GF2X([1,0,1,1]) ; g = ntl.GF2X([0,1,0])
             sage: f + g ## indirect doctest
             [1 1 1 1]
@@ -299,7 +311,8 @@ cdef class ntl_GF2X(object):
 
     def __neg__(ntl_GF2X self):
         """
-        EXAMPLES:
+        EXAMPLES::
+
             sage: f = ntl.GF2X([1,0,1,1])
             sage: -f ## indirect doctest
             [1 0 1 1]
@@ -312,7 +325,8 @@ cdef class ntl_GF2X(object):
 
     def __pow__(ntl_GF2X self, long e, ignored):
         """
-        EXAMPLES:
+        EXAMPLES::
+
             sage: f = ntl.GF2X([1,0,1,1]) ; g = ntl.GF2X([0,1,0])
             sage: f**3 ## indirect doctest
             [1 0 1 1 1 0 0 1 1 1]
@@ -355,7 +369,8 @@ cdef class ntl_GF2X(object):
         INPUT:
             i -- offset/power of X
 
-        EXAMPLES:
+        EXAMPLES::
+
             sage: a = ntl.GF2X(4); a
             [0 0 1]
             sage: a << 2
@@ -373,7 +388,8 @@ cdef class ntl_GF2X(object):
         INPUT:
             i -- offset/power of X
 
-        EXAMPLES:
+        EXAMPLES::
+
             sage: a = ntl.GF2X(4); a
             [0 0 1]
             sage: a >> 1
@@ -390,7 +406,8 @@ cdef class ntl_GF2X(object):
         INPUT:
             other -- ntl.GF2X
 
-        EXAMPLES:
+        EXAMPLES::
+
             sage: a = ntl.GF2X(10)
             sage: b = ntl.GF2X(4)
             sage: a.GCD(b)
@@ -413,7 +430,8 @@ cdef class ntl_GF2X(object):
         INPUT:
             other -- ntl.GF2X
 
-        EXAMPLES:
+        EXAMPLES::
+
             sage: a = ntl.GF2X(10)
             sage: b = ntl.GF2X(4)
             sage: r,s,t = a.XGCD(b)
@@ -435,7 +453,8 @@ cdef class ntl_GF2X(object):
         """
         Returns the degree of this polynomial
 
-        EXAMPLES:
+        EXAMPLES::
+
             sage: ntl.GF2X([1,0,1,1]).deg()
             3
         """
@@ -445,7 +464,8 @@ cdef class ntl_GF2X(object):
         """
         Represents this element as a list of binary digits.
 
-        EXAMPLES:
+        EXAMPLES::
+
              sage: e=ntl.GF2X([0,1,1])
              sage: e.list()
              [0, 1, 1]
@@ -467,7 +487,8 @@ cdef class ntl_GF2X(object):
         faster and preserves the HexOutput state as opposed to
         the above code.
 
-        EXAMPLES:
+        EXAMPLES::
+
              sage: e=ntl.GF2X([1,1,0,1,1,1,0,0,1])
              sage: e.bin()
              '[1 1 0 1 1 1 0 0 1]'
@@ -481,22 +502,24 @@ cdef class ntl_GF2X(object):
         GF2XHexOutput_c[0] = _hex
         return s
 
-    def __hex__(ntl_GF2X self):
+    def hex(ntl_GF2X self):
         """
-        Returns hexadecimal representation of this element. It is
-        the same as setting \code{ntl.GF2XHexOutput(True)} and
-        representing this element afterwards. However it should be
-        faster and preserves the HexOutput state as opposed to
-        the above code.
+        Return an hexadecimal representation of this element.
 
-        EXAMPLES:
-             sage: e=ntl.GF2X([1,1,0,1,1,1,0,0,1])
-             sage: hex(e)
-             '0xb31'
+        It is the same as setting \code{ntl.GF2XHexOutput(True)} and
+        representing this element afterwards. However it should be
+        faster and preserves the HexOutput state as opposed to the
+        above code.
 
         OUTPUT:
-            string representing this element in hexadecimal
 
+        string representing this element in hexadecimal
+
+        EXAMPLES::
+
+             sage: e = ntl.GF2X([1,1,0,1,1,1,0,0,1])
+             sage: e.hex()
+             '0xb31'
         """
         cdef long _hex = GF2XHexOutput_c[0]
         GF2XHexOutput_c[0] = 1
@@ -504,8 +527,10 @@ cdef class ntl_GF2X(object):
         GF2XHexOutput_c[0] = _hex
         return s
 
+    __hex__ = deprecated_function_alias(24514, hex)
+
     def __hash__(self):
-        return hash(hex(self))
+        return hash(self.hex())
 
     def _sage_(ntl_GF2X self, R=None):
         """
@@ -521,7 +546,8 @@ cdef class ntl_GF2X(object):
         OUTPUT:
             polynomial in R
 
-        EXAMPLES:
+        EXAMPLES::
+
             sage: f = ntl.GF2X([1,0,1,1,0,1])
             sage: f._sage_()
             x^5 + x^3 + x^2 + 1
@@ -542,7 +568,8 @@ cdef class ntl_GF2X(object):
         INPUT:
             i -- degree of X
 
-        EXAMPLES:
+        EXAMPLES::
+
             sage: e = ntl.GF2X([0,1,0,1])
             sage: e.coeff(0)
             0
@@ -570,7 +597,8 @@ cdef class ntl_GF2X(object):
         Return the leading coefficient of self. This is always 1
         except when self == 0.
 
-        EXAMPLES:
+        EXAMPLES::
+
             sage: e = ntl.GF2X([0,1])
             sage: e.LeadCoeff()
             1
@@ -586,7 +614,8 @@ cdef class ntl_GF2X(object):
         """
         Return the constant term of self.
 
-        EXAMPLES:
+        EXAMPLES::
+
             sage: e = ntl.GF2X([1,0,1])
             sage: e.ConstTerm()
             1
@@ -602,7 +631,8 @@ cdef class ntl_GF2X(object):
         """
         Return the constant term of self.
 
-        EXAMPLES:
+        EXAMPLES::
+
             sage: e = ntl.GF2X([1,0,1]); e
             [1 0 1]
             sage: e.SetCoeff(1,1)
@@ -643,7 +673,8 @@ cdef class ntl_GF2X(object):
         INPUT:
             hi -- bit position until which reverse is requested
 
-        EXAMPLES:
+        EXAMPLES::
+
             sage: e = ntl.GF2X([1,0,1,1,0])
             sage: e.reverse()
             [1 1 0 1]
@@ -658,7 +689,8 @@ cdef class ntl_GF2X(object):
         """
         Return the number of nonzero coefficients in self.
 
-        EXAMPLES:
+        EXAMPLES::
+
             sage: e = ntl.GF2X([1,0,1,1,0])
             sage: e.weight()
             3
@@ -685,7 +717,8 @@ cdef class ntl_GF2X(object):
         """
         returns number of bits of self, i.e., deg(self) + 1.
 
-        EXAMPLES:
+        EXAMPLES::
+
             sage: e = ntl.GF2X([1,0,1,1,0])
             sage: e.NumBits()
             4
@@ -704,7 +737,8 @@ cdef class ntl_GF2X(object):
         """
         Returns number of bytes of self, i.e., floor((NumBits(self)+7)/8)
 
-        EXAMPLES:
+        EXAMPLES::
+
             sage: e = ntl.GF2X([1,0,1,1,0,0,0,0,1,1,1,0,0,1,1,0,1,1])
             sage: e.NumBytes()
             3

From 8dfb361968ed8d631bdd8f5ede5387e7fb7a1500 Mon Sep 17 00:00:00 2001
From: Travis Scrimshaw <tcscrims at gmail.com>
Date: Tue, 16 Jan 2018 02:09:09 -0600
Subject: [PATCH 079/128] Tweak documentation.

---
 src/sage/algebras/lie_algebras/virasoro.py | 27 +++++++++++-----------
 1 file changed, 14 insertions(+), 13 deletions(-)

diff --git a/src/sage/algebras/lie_algebras/virasoro.py b/src/sage/algebras/lie_algebras/virasoro.py
index 9ba8c71a79d..21b74defae9 100644
--- a/src/sage/algebras/lie_algebras/virasoro.py
+++ b/src/sage/algebras/lie_algebras/virasoro.py
@@ -527,9 +527,9 @@ class ChargelessRepresentation(CombinatorialFreeModule):
     r"""
     A chargeless representation of the Virasoro algebra.
 
-    Let `L` be the Virasoro algebra over the field `F` of characteristic
-    `0`. For `\alpha, \beta \in R`, we denote `V_{a,b}` as the
-    `(a, b)`-*chargeless representation* of `L`, which is the
+    Let `L` be the Virasoro algebra over the field `F` of
+    characteristic `0`. For `\alpha, \beta \in R`, we denote `V_{a,b}`
+    as the `(a, b)`-*chargeless representation* of `L`, which is the
     `F`-span of `\{v_k \mid k \in \ZZ\}` with `L` action
 
     .. MATH::
@@ -539,13 +539,14 @@ class ChargelessRepresentation(CombinatorialFreeModule):
         \\ c \cdot v_k & = 0,
         \end{aligned}
 
-    This comes from the action of `d_n = -t^{n+1} \frac{d}{dt}`
-    on `F[t, t^{-1}]` (recall that `V` is the central extension
-    of the algebra of derivations of `F[t, t^{-1}]`), where
+    This comes from the action of `d_n = -t^{n+1} \frac{d}{dt}` on
+    `F[t, t^{-1}]` (recall that `L` is the central extension of the
+    :class:`algebra of derivations <LieAlgebraRegularVectorFields>`
+    of `F[t, t^{-1}]`), where
 
     .. MATH::
 
-        V_{a,b} = F[t, t^{-1}] t^(a-b) (dt)^{-a}
+        V_{a,b} = F[t, t^{-1}] t^{a-b} (dt)^{-a}
 
     and `v_k = t^{a-b+k} (dz)^{-a}`.
 
@@ -559,12 +560,12 @@ class ChargelessRepresentation(CombinatorialFreeModule):
     `a \neq 0, -1` or `b \notin \ZZ`. When `a = 0` and `b \in \ZZ`,
     then there exists a subrepresentation isomorphic to the trivial
     representation. If `a = -1` and `b \in \ZZ`, then there exists
-    a subrepresentation `V` such that `V_{a,b} / V` is isomorphic to
-    `K \frac{dt}{t}` and `V` is irreducible.
+    a subrepresentation `V` such that `V_{a,b} / V` is isomorphic
+    to `K \frac{dt}{t}` and `V` is irreducible.
 
-    In characteristic `p`, the non-trivial simple subquotient is
-    isomorphic to `F[t, t^{-1}] / F[t^p, t^{-p}]`. For `p \neq 2,3`,
-    then the action is given as above.
+    In characteristic `p`, the non-trivial simple subquotient
+    is isomorphic to `F[t, t^{-1}] / F[t^p, t^{-p}]`. For
+    `p \neq 2,3`, then the action is given as above.
 
     EXAMPLES:
 
@@ -689,7 +690,7 @@ class VermaModule(CombinatorialFreeModule):
     """
     A Verma module of the Virasoro algebra.
 
-    The Virasoro algebra admits a triangle decomposition of
+    The Virasoro algebra admits a trianglar decomposition of
 
     .. MATH::
 

From c418d07ca298ef6059eedd01528e59a264f3a94e Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?Fr=C3=A9d=C3=A9ric=20Chapoton?=
 <chapoton@math.univ-lyon1.fr>
Date: Tue, 16 Jan 2018 10:17:30 +0100
Subject: [PATCH 080/128] trac 24514 test the deprecation

---
 src/sage/libs/ntl/ntl_GF2X.pyx | 20 +++++++++++++++-----
 1 file changed, 15 insertions(+), 5 deletions(-)

diff --git a/src/sage/libs/ntl/ntl_GF2X.pyx b/src/sage/libs/ntl/ntl_GF2X.pyx
index 03b5a6436bf..3b4892a132f 100644
--- a/src/sage/libs/ntl/ntl_GF2X.pyx
+++ b/src/sage/libs/ntl/ntl_GF2X.pyx
@@ -24,7 +24,7 @@ include 'decl.pxi'
 
 from cpython.object cimport Py_EQ, Py_NE
 from sage.rings.integer cimport Integer
-from sage.misc.superseded import deprecated_function_alias
+from sage.misc.superseded import deprecation
 
 from .ntl_ZZ import unpickle_class_value
 from .ntl_GF2 cimport ntl_GF2
@@ -517,9 +517,17 @@ cdef class ntl_GF2X(object):
 
         EXAMPLES::
 
-             sage: e = ntl.GF2X([1,1,0,1,1,1,0,0,1])
-             sage: e.hex()
-             '0xb31'
+            sage: e = ntl.GF2X([1,1,0,1,1,1,0,0,1])
+            sage: e.hex()
+            '0xb31'
+
+        TESTS::
+
+            sage: hex(e)
+            doctest:warning...:
+            DeprecationWarning: use the method .hex instead
+            See http://trac.sagemath.org/24514 for details.
+            '0xb31'
         """
         cdef long _hex = GF2XHexOutput_c[0]
         GF2XHexOutput_c[0] = 1
@@ -527,7 +535,9 @@ cdef class ntl_GF2X(object):
         GF2XHexOutput_c[0] = _hex
         return s
 
-    __hex__ = deprecated_function_alias(24514, hex)
+    def __hex__(self):
+        deprecation(24514, 'use the method .hex instead')
+        return self.hex()
 
     def __hash__(self):
         return hash(self.hex())

From 514ed9369f12f760b6e714468f45b3ce6c7b20a9 Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?Fr=C3=A9d=C3=A9ric=20Chapoton?=
 <chapoton@math.univ-lyon1.fr>
Date: Tue, 16 Jan 2018 10:37:53 +0100
Subject: [PATCH 081/128] trac 24258 make doc build

---
 src/sage/doctest/parsing.py | 14 +++++++-------
 1 file changed, 7 insertions(+), 7 deletions(-)

diff --git a/src/sage/doctest/parsing.py b/src/sage/doctest/parsing.py
index 02c82711fc1..79cac3f136f 100644
--- a/src/sage/doctest/parsing.py
+++ b/src/sage/doctest/parsing.py
@@ -116,13 +116,13 @@ def remove_unicode_u(string):
 _type_repr_re = re.compile(r"<type '(?P<name>[^']+)'>")
 
 def normalize_type_repr(s):
-    """
-    Converts the repr of type objects (e.g. ``int``, ``float``) from their
+    r"""
+    Convert the repr of type objects (e.g. ``int``, ``float``) from their
     Python 2 representation to their Python 3 representation.
 
-    In Python 2, the repr of built-in types like ``int`` is like ``<type
-    'int'>``, whereas user-defined pure Python classes are displayed as
-    ``<class 'classname'>``.  On Python 3 this was normalized so that
+    In Python 2, the repr of built-in types like ``int`` is like
+    ``<type 'int'>``, whereas user-defined pure Python classes are displayed
+    as ``<class 'classname'>``.  On Python 3 this was normalized so that
     built-in types are represented the same as user-defined classes (e.g.
     ``<class 'int'>``.
 
@@ -140,8 +140,8 @@ def normalize_type_repr(s):
 
     This can work on multi-line output as well::
 
-        sage: s = "The desired output was <class 'int'>\n" \
-        ....:     "The received output was <type 'int'>"
+        sage: s = "The desired output was <class 'int'>\n"
+        sage: s += "The received output was <type 'int'>"
         sage: print(normalize_type_repr(s))
         The desired output was <class 'int'>
         The received output was <class 'int'>

From 1cb2d9430150691bd189483a81a3bb31d9f66d26 Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?Fr=C3=A9d=C3=A9ric=20Chapoton?=
 <chapoton@math.univ-lyon1.fr>
Date: Tue, 16 Jan 2018 11:39:17 +0100
Subject: [PATCH 082/128] get rid of some builtins imports (in doc and in pyx
 code)

---
 src/sage/combinat/species/series.py             |  3 +--
 src/sage/combinat/tutorial.py                   | 17 ++++-------------
 src/sage/graphs/strongly_regular_db.pyx         |  6 +++---
 .../groups/perm_gps/symgp_conjugacy_class.py    |  7 +++----
 src/sage/rings/polynomial/pbori.pyx             |  1 -
 5 files changed, 11 insertions(+), 23 deletions(-)

diff --git a/src/sage/combinat/species/series.py b/src/sage/combinat/species/series.py
index bdad43ef40f..e16f9857f1d 100644
--- a/src/sage/combinat/species/series.py
+++ b/src/sage/combinat/species/series.py
@@ -406,10 +406,9 @@ def _product_generator_gen(self, g):
         """
         EXAMPLES::
 
-            sage: from builtins import map
             sage: from sage.combinat.species.stream import _integers_from
             sage: L = LazyPowerSeriesRing(QQ)
-            sage: g = map(lambda i: L([1]+[0]*i+[1]), _integers_from(0))
+            sage: g = (L([1]+[0]*i+[1]) for i in _integers_from(0))
             sage: g2 = L._product_generator_gen(g)
             sage: [next(g2) for i in range(10)]
             [1, 1, 2, 4, 7, 12, 20, 33, 53, 84]
diff --git a/src/sage/combinat/tutorial.py b/src/sage/combinat/tutorial.py
index 95f07084e97..cf479065cfd 100644
--- a/src/sage/combinat/tutorial.py
+++ b/src/sage/combinat/tutorial.py
@@ -1270,27 +1270,18 @@
 
     sage: from builtins import map, filter
 
+but they should rather be avoided, using list comprehension instead.
+
 To apply a function to all the elements, one can do::
 
-    sage: from builtins import map
-    sage: list(map(lambda z: z.cycle_type(), Permutations(3)))
+    sage: list(z.cycle_type() for z in Permutations(3))
     [[1, 1, 1], [2, 1], [2, 1], [3], [3], [2, 1]]
 
 and similarly to select the elements satisfying a certain condition::
 
-    sage: from builtins import filter
-    sage: list(filter(lambda z: z.has_pattern([1,2]), Permutations(3)))
+    sage: list(z for z in Permutations(3) if z.has_pattern([1,2]))
     [[1, 2, 3], [1, 3, 2], [2, 1, 3], [2, 3, 1], [3, 1, 2]]
 
-In all these situations, ``attrcall`` can be an advantageous alternative
-to creating an anonymous function::
-
-    sage: from builtins import map
-    sage: list(map(lambda z: z.cycle_type(), Permutations(3)))
-    [[1, 1, 1], [2, 1], [2, 1], [3], [3], [2, 1]]
-    sage: list(map(attrcall("cycle_type"), Permutations(3)))
-    [[1, 1, 1], [2, 1], [2, 1], [3], [3], [2, 1]]
-
 Implementation of new iterators
 ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
 
diff --git a/src/sage/graphs/strongly_regular_db.pyx b/src/sage/graphs/strongly_regular_db.pyx
index c88215bdca6..b438abb466c 100644
--- a/src/sage/graphs/strongly_regular_db.pyx
+++ b/src/sage/graphs/strongly_regular_db.pyx
@@ -1649,9 +1649,8 @@ def is_switch_OA_srg(int v, int k, int l, int mu):
         not orthogonal_array(c+1,n,existence=True,resolvable=True)):
         return None
 
-    def switch_OA_srg(c,n):
-        from builtins import zip
-        OA = map(tuple,orthogonal_array(c+1,n,resolvable=True))
+    def switch_OA_srg(c, n):
+        OA = map(tuple, orthogonal_array(c+1, n, resolvable=True))
         g = Graph([OA, lambda x,y: any(xx==yy for xx,yy in zip(x,y))],
                   loops=False)
         g.add_vertex(0)
@@ -1660,6 +1659,7 @@ def is_switch_OA_srg(int v, int k, int l, int mu):
 
     return (switch_OA_srg,c,n)
 
+
 def is_nowhere0_twoweight(int v, int k, int l, int mu):
     r"""
     Test whether some graph of nowhere 0 words is `(v,k,\lambda,\mu)`-strongly regular.
diff --git a/src/sage/groups/perm_gps/symgp_conjugacy_class.py b/src/sage/groups/perm_gps/symgp_conjugacy_class.py
index 7bd1a42e0f4..3b55bcf178b 100644
--- a/src/sage/groups/perm_gps/symgp_conjugacy_class.py
+++ b/src/sage/groups/perm_gps/symgp_conjugacy_class.py
@@ -292,6 +292,7 @@ def default_representative(part, G):
     #   once SymmetricGroup is a proper parent.
     return PermutationGroupElement(cycles, G, check=False)
 
+
 def conjugacy_class_iterator(part, S=None):
     r"""
     Return an iterator over the conjugacy class associated to
@@ -319,12 +320,10 @@ def conjugacy_class_iterator(part, S=None):
         [(1, 3), (2, 4)]
         [(1, 4), (2, 3)]
 
-    In order to get permutations, one can use ``map``
-    from the Python module ``builtins`` (works with Python 2 and Python 3)::
+    In order to get permutations, one just has to wrap::
 
-        sage: from builtins import map
         sage: S = SymmetricGroup(5)
-        sage: for p in map(S, conjugacy_class_iterator([3,2])): print(p)
+        sage: for p in conjugacy_class_iterator([3,2]): print(S(p))
         (1,2)(3,4,5)
         (1,2)(3,5,4)
         (1,3)(2,4,5)
diff --git a/src/sage/rings/polynomial/pbori.pyx b/src/sage/rings/polynomial/pbori.pyx
index 318ff62af75..59ac764b4bb 100644
--- a/src/sage/rings/polynomial/pbori.pyx
+++ b/src/sage/rings/polynomial/pbori.pyx
@@ -3144,7 +3144,6 @@ cdef class BooleanPolynomial(MPolynomial):
             sage: x != False
             True
         """
-        from builtins import zip
         for lm, rm in zip(left, right):
             if lm != rm:
                 return richcmp_not_equal(lm, rm, op)

From edf5898ef0ca0d40e6d44a6fa613f3f51c330a8b Mon Sep 17 00:00:00 2001
From: "Erik M. Bray" <erik.bray@lri.fr>
Date: Tue, 16 Jan 2018 12:34:13 +0000
Subject: [PATCH 083/128] mpfi: perform this sanity check relative to
 $SAGE_DESTDIR

---
 build/pkgs/mpfi/spkg-install | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/build/pkgs/mpfi/spkg-install b/build/pkgs/mpfi/spkg-install
index 7c5aaf3ac45..fad7f89a9eb 100644
--- a/build/pkgs/mpfi/spkg-install
+++ b/build/pkgs/mpfi/spkg-install
@@ -19,7 +19,7 @@ sdh_configure --with-mpfr="$SAGE_LOCAL" --with-gmp="$SAGE_LOCAL"
 sdh_make
 sdh_make_install
 
-if ! [ $? -eq 0 -a -f $SAGE_LOCAL/include/mpfi.h ]; then
+if ! [ $? -eq 0 -a -f $SAGE_DESTDIR$SAGE_LOCAL/include/mpfi.h ]; then
     echo "An error occurred while building MPFI."
     exit 1
 fi

From 1398d1dc63059066819d31491d0335aa1550827c Mon Sep 17 00:00:00 2001
From: "Erik M. Bray" <erik.bray@lri.fr>
Date: Tue, 16 Jan 2018 12:44:46 +0000
Subject: [PATCH 084/128] patch: On Cygwin, ensure the .manifest file is
 installed relative to $SAGE_DESTDIR

Remove the 'sanity check' that the installed patch is the correct one.
Alternatively we could run the patch installed in $SAGE_DESTDIR.  It seems
unnecessary though--if patch were installed incorrectly there would be
bigger problems already.  That said, if we really wanted to keep this it
would make sense to move to a post-install script.
---
 build/pkgs/patch/spkg-install | 9 +--------
 1 file changed, 1 insertion(+), 8 deletions(-)

diff --git a/build/pkgs/patch/spkg-install b/build/pkgs/patch/spkg-install
index f5d5a6e92da..d9de2282753 100644
--- a/build/pkgs/patch/spkg-install
+++ b/build/pkgs/patch/spkg-install
@@ -31,12 +31,5 @@ sdh_make
 sdh_make_install
 
 if [ "$UNAME" = "CYGWIN" ] ; then
-    cp ../patch.exe.manifest "$SAGE_LOCAL/bin/"
-fi
-
-# Sanity check that we have the correct version of patch
-# in our PATH.
-if ! patch --version | grep >/dev/null 'patch 2\.7\.5'; then
-    echo >&2 "Cannot find the patch program we just installed"
-    exit 1
+    cp ../patch.exe.manifest "$SAGE_DESTDIR$SAGE_LOCAL/bin/"
 fi

From 97ebe8e6bdeb6ed2db9fd0d2374107b7b5fd8039 Mon Sep 17 00:00:00 2001
From: "Erik M. Bray" <erik.bray@lri.fr>
Date: Tue, 16 Jan 2018 12:50:23 +0000
Subject: [PATCH 085/128] readline: these post-build steps should be performed
 relative to $SAGE_DESTDIR

---
 build/pkgs/readline/spkg-install | 6 +++---
 1 file changed, 3 insertions(+), 3 deletions(-)

diff --git a/build/pkgs/readline/spkg-install b/build/pkgs/readline/spkg-install
index b8c2663871e..e17b66fdcff 100644
--- a/build/pkgs/readline/spkg-install
+++ b/build/pkgs/readline/spkg-install
@@ -69,10 +69,10 @@ esac
 
 # Make sure that the install worked, despite whatever the
 # exit code of 'make' or 'make install' was:
-if [[ -f "$SAGE_LOCAL/lib/$DYLIB_NAME" ]]; then
+if [[ -f "$SAGE_DESTDIR$SAGE_LOCAL/lib/$DYLIB_NAME" ]]; then
     echo "Fixing permissions of libraries..."
-    chmod 755 "$SAGE_LOCAL"/lib/libreadline.*
-    chmod 755 "$SAGE_LOCAL"/lib/libhistory.*
+    chmod 755 "$SAGE_DESTDIR$SAGE_LOCAL"/lib/libreadline.*
+    chmod 755 "$SAGE_DESTDIR$SAGE_LOCAL"/lib/libhistory.*
 else
     # One or both of the readline libraries are missing, i.e.
     # haven't been installed.

From 691e9de0f194e5928a41c750891b5ebd1d0d7007 Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?Fr=C3=A9d=C3=A9ric=20Chapoton?=
 <chapoton@math.univ-lyon1.fr>
Date: Tue, 16 Jan 2018 14:24:42 +0100
Subject: [PATCH 086/128] py#; various fixes, mostly about division

---
 .../algebraic_combinatorics/rsk.rst           |  2 +-
 .../steenrod/steenrod_algebra_bases.py        | 22 +++++++++----------
 src/sage/combinat/free_module.py              | 15 +++++++++++++
 src/sage/combinat/root_system/cartan_type.py  | 10 ++++-----
 src/sage/geometry/newton_polygon.py           |  6 +++--
 src/sage/graphs/digraph_generators.py         |  6 ++---
 src/sage/graphs/graph_generators.py           |  4 ++--
 .../modular/btquotients/pautomorphicform.py   | 14 ++++++------
 src/sage/modular/hecke/module.py              |  2 +-
 src/sage/modular/modform/element.py           |  6 ++---
 src/sage/numerical/sdp.pyx                    |  3 +--
 src/sage/rings/asymptotic/growth_group.py     |  3 ---
 src/sage/rings/power_series_pari.pyx          |  4 ++--
 13 files changed, 55 insertions(+), 42 deletions(-)

diff --git a/src/doc/en/thematic_tutorials/algebraic_combinatorics/rsk.rst b/src/doc/en/thematic_tutorials/algebraic_combinatorics/rsk.rst
index cbc10938634..cbbf6a1d89a 100644
--- a/src/doc/en/thematic_tutorials/algebraic_combinatorics/rsk.rst
+++ b/src/doc/en/thematic_tutorials/algebraic_combinatorics/rsk.rst
@@ -88,7 +88,7 @@ We can also check this against the hook length formula (Theorem 8.1)::
 
     sage: def hook_length_formula(p):
     ....:     n = p.size()
-    ....:     return factorial(n) / prod(p.hook_length(*c) for c in p.cells())
+    ....:     return factorial(n) // prod(p.hook_length(*c) for c in p.cells())
 
     sage: for la in u.support():
     ....:     assert u[la] == hook_length_formula(la)
diff --git a/src/sage/algebras/steenrod/steenrod_algebra_bases.py b/src/sage/algebras/steenrod/steenrod_algebra_bases.py
index bf04407ada0..8b59bee8d3b 100644
--- a/src/sage/algebras/steenrod/steenrod_algebra_bases.py
+++ b/src/sage/algebras/steenrod/steenrod_algebra_bases.py
@@ -105,7 +105,7 @@
 <sage.algebras.steenrod.steenrod_algebra.SteenrodAlgebra_generic>` in
 :file:`steenrod_algebra.py`.
 """
-from __future__ import absolute_import
+from __future__ import absolute_import, division
 
 #*****************************************************************************
 #  Copyright (C) 2008-2010 John H. Palmieri <palmieri@math.washington.edu>
@@ -484,12 +484,12 @@ def xi_degrees(n,p=2, reverse=True):
         [307, 18, 1]
     """
     from sage.rings.all import Integer
-    if n <= 0: return []
+    if n <= 0:
+        return []
     N = Integer(n*(p-1) + 1)
-    l = [int((p**d-1)/(p-1)) for d in range(1,N.exact_log(p)+1)]
-    if not reverse:
-        return l
-    l.reverse()
+    l = [(p**d-1)//(p-1) for d in range(1, N.exact_log(p)+1)]
+    if reverse:
+        l.reverse()
     return l
 
 ########################################################
@@ -609,7 +609,7 @@ def milnor_basis(n, p=2, **kwds):
         # first find the P part of each basis element.
         # in this part of the code (the P part), all dimensions are
         # divided by 2(p-1).
-        for dim in range(n/(2*(p-1)) + 1):
+        for dim in range(n//(2*(p-1)) + 1):
             if dim == 0:
                 P_result = [[0]]
             else:
@@ -625,7 +625,7 @@ def milnor_basis(n, p=2, **kwds):
             for p_mono in P_result:
                 deg = n - 2*dim*(p-1)
                 q_degrees = [1+2*(p-1)*d for d in
-                             xi_degrees(int((deg - 1)/(2*(p-1))), p)] + [1]
+                             xi_degrees(int((deg - 1)//(2*(p-1))), p)] + [1]
                 q_degrees_decrease = q_degrees
                 q_degrees.reverse()
                 if deg % (2*(p-1)) <= len(q_degrees):
@@ -721,8 +721,8 @@ def serre_cartan_basis(n, p=2, bound=1, **kwds):
                     new = vec + (last,)
                     result.append(new)
         else: # p odd
-            if n % (2 * (p-1)) == 0 and n/(2 * (p-1)) >= bound:
-                result = [(0, int(n/(2 * (p-1))), 0)]
+            if n % (2 * (p-1)) == 0 and n//(2 * (p-1)) >= bound:
+                result = [(0, int(n//(2 * (p-1))), 0)]
             elif n == 1:
                 result = [(1,)]
             else:
@@ -1041,7 +1041,7 @@ def sorting_pair(s,t,basis):   # pair used for sorting the basis
     trunc = kwds.get("truncation_type", 0)
 
     result = []
-    for dim in range(n/(2*p-2) + 1):
+    for dim in range(n//(2*p-2) + 1):
         P_result = []
         for v in WeightedIntegerVectors(dim, xi_degrees(dim, p=p, reverse=False)):
             mono = []
diff --git a/src/sage/combinat/free_module.py b/src/sage/combinat/free_module.py
index 447da288ae1..a7579527bf2 100644
--- a/src/sage/combinat/free_module.py
+++ b/src/sage/combinat/free_module.py
@@ -31,9 +31,11 @@
 import sage.data_structures.blas_dict as blas
 from sage.typeset.ascii_art import AsciiArt
 from sage.typeset.unicode_art import UnicodeArt
+from sage.misc.superseded import deprecation
 
 import six
 
+
 class CombinatorialFreeModule(UniqueRepresentation, Module, IndexedGenerators):
     r"""
     Class for free modules with a named basis
@@ -851,10 +853,16 @@ def get_order_cmp(self):
         Return a comparison function on the basis indices that is
         compatible with the current term order.
 
+        DEPRECATED by :trac:`24548`.
+
         EXAMPLES::
 
             sage: A = FiniteDimensionalAlgebrasWithBasis(QQ).example()
             sage: Acmp = A.get_order_cmp()
+            doctest:warning...:
+            DeprecationWarning: comparison should use keys
+            See http://trac.sagemath.org/24548 for details.
+
             sage: sorted(A.basis().keys(), Acmp)
             ['x', 'y', 'a', 'b']
             sage: A.set_order(list(reversed(A.basis().keys())))
@@ -862,6 +870,7 @@ def get_order_cmp(self):
             sage: sorted(A.basis().keys(), Acmp)
             ['b', 'a', 'y', 'x']
         """
+        deprecation(24548, 'comparison should use keys')
         self.get_order()
         return self._order_cmp
 
@@ -869,6 +878,8 @@ def _order_cmp(self, x, y):
         """
         Compare `x` and `y` w.r.t. the term order.
 
+        DEPRECATED by :trac:`24548`.
+
         INPUT:
 
         - ``x``, ``y`` -- indices of the basis of ``self``
@@ -883,12 +894,16 @@ def _order_cmp(self, x, y):
             sage: A = CombinatorialFreeModule(QQ, ['x','y','a','b'])
             sage: A.set_order(['x', 'y', 'a', 'b'])
             sage: A._order_cmp('x', 'y')
+            doctest:warning...:
+            DeprecationWarning: comparison should use keys
+            See http://trac.sagemath.org/24548 for details.
             -1
             sage: A._order_cmp('y', 'y')
             0
             sage: A._order_cmp('a', 'y')
             1
         """
+        deprecation(24548, 'comparison should use keys')
         ix = self._rank_basis(x)
         iy = self._rank_basis(y)
         if ix < iy:
diff --git a/src/sage/combinat/root_system/cartan_type.py b/src/sage/combinat/root_system/cartan_type.py
index c4231a6af0a..f3515a39f1e 100644
--- a/src/sage/combinat/root_system/cartan_type.py
+++ b/src/sage/combinat/root_system/cartan_type.py
@@ -473,7 +473,7 @@
 # (at your option) any later version.
 #                  http://www.gnu.org/licenses/
 #*****************************************************************************
-from __future__ import print_function, absolute_import
+from __future__ import print_function, absolute_import, division
 
 from six.moves import range
 from six.moves.builtins import sorted
@@ -708,17 +708,17 @@ def __call__(self, *args):
                             from . import type_BC_affine
                             return type_BC_affine.CartanType(n)
                     if letter == "A" and t[2] == 2:
-                        if n%2 == 0: # Kac' A_2n^(2)
-                            return CartanType(["BC", ZZ(n/2), 2])
+                        if n % 2 == 0: # Kac' A_2n^(2)
+                            return CartanType(["BC", ZZ(n//2), 2])
                         else:        # Kac' A_2n-1^(2)
-                            return CartanType(["B", ZZ((n+1)/2), 1]).dual()
+                            return CartanType(["B", ZZ((n+1)//2), 1]).dual()
                     if letter == "D" and t[2] == 2:
                         return CartanType(["C", n-1, 1]).dual()
                     if letter == "D" and t[2] == 3 and n == 4:
                         return CartanType(["G", 2, 1]).dual().relabel([0,2,1])
                     if letter == "E" and t[2] == 2 and n == 6:
                         return CartanType(["F", 4, 1]).dual()
-            raise ValueError("%s is not a valid Cartan type"%t)
+            raise ValueError("%s is not a valid Cartan type" % t)
 
         if isinstance(t[0], string_types) and isinstance(t[1], (list, tuple)):
             letter, n = t[0], t[1]
diff --git a/src/sage/geometry/newton_polygon.py b/src/sage/geometry/newton_polygon.py
index 795692b10bf..b613982aab6 100644
--- a/src/sage/geometry/newton_polygon.py
+++ b/src/sage/geometry/newton_polygon.py
@@ -13,6 +13,7 @@
 #
 #                  http://www.gnu.org/licenses/
 #############################################################################
+from __future__ import division
 
 from sage.structure.unique_representation import UniqueRepresentation
 from sage.structure.parent import Parent
@@ -368,9 +369,10 @@ def __call__(self, x):
             return vertices[-1][1]
         if x > vertices[-1][0]:
             return vertices[-1][1] + lastslope * (x - vertices[-1][0])
-        a = 0; b = len(vertices)
+        a = 0
+        b = len(vertices)
         while b - a > 1:
-            c = floor((a+b)/2)
+            c = (a + b) // 2
             if vertices[c][0] < x:
                 a = c
             else:
diff --git a/src/sage/graphs/digraph_generators.py b/src/sage/graphs/digraph_generators.py
index 8689b1b9600..8941978aaff 100644
--- a/src/sage/graphs/digraph_generators.py
+++ b/src/sage/graphs/digraph_generators.py
@@ -60,7 +60,7 @@
 # Distributed  under  the  terms  of  the  GNU  General  Public  License (GPL)
 #                         http://www.gnu.org/licenses/
 ################################################################################
-from __future__ import print_function
+from __future__ import print_function, division
 from six.moves import range
 
 from   math import sin, cos, pi
@@ -1289,14 +1289,14 @@ def RandomDirectedGNM(self, n, m, loops = False):
         if loops:
             if m > n*n:
                 good_input = False
-            elif m > n*n/2:
+            elif 2*m > n*n:
                 is_dense = True
                 m = n*n - m
 
         else:
             if m > n*(n-1):
                 good_input = False
-            elif m > n*(n-1)/2:
+            elif m > (n * (n - 1)) // 2:
                 is_dense = True
                 m = n*(n-1) - m
 
diff --git a/src/sage/graphs/graph_generators.py b/src/sage/graphs/graph_generators.py
index da142cc7fd2..c10a2e1e234 100644
--- a/src/sage/graphs/graph_generators.py
+++ b/src/sage/graphs/graph_generators.py
@@ -15,7 +15,7 @@
 More interestingly, one can get the list of all graphs that Sage knows how to
 build by typing ``graphs.`` in Sage and then hitting tab.
 """
-from __future__ import print_function, absolute_import
+from __future__ import print_function, absolute_import, division
 from six.moves import range
 
 # This method appends a list of methods to the doc as a 3xN table.
@@ -2229,7 +2229,7 @@ def canaug_traverse_vert(g, aut_gens, max_verts, property, dig=False, loops=Fals
             edges = []
             if dig:
                 index = 0
-                while index < possibilities/2:
+                while 2 * index < possibilities:
                     if (1 << index)&i:
                         edges.append((index,n))
                     index += 1
diff --git a/src/sage/modular/btquotients/pautomorphicform.py b/src/sage/modular/btquotients/pautomorphicform.py
index 98ccf4ddc18..9daf1e3f49c 100644
--- a/src/sage/modular/btquotients/pautomorphicform.py
+++ b/src/sage/modular/btquotients/pautomorphicform.py
@@ -45,7 +45,7 @@
    Cameron Franc
    Ph.D. thesis, McGill University, 2011.
 """
-from __future__ import print_function
+from __future__ import print_function, division
 
 from builtins import zip
 
@@ -751,7 +751,7 @@ def __init__(self, X, k, prec=None, basis_matrix=None, base_field=None):
 
         self._U = Symk(self._k - 2, base=self._R, act_on_left=True,
                        adjuster=_btquot_adjuster(),
-                       dettwist=-ZZ((self._k - 2) / 2), act_padic=True)
+                       dettwist=-ZZ((self._k - 2) // 2), act_padic=True)
 
         if basis_matrix is None:
             self.__rank = self._X.dimension_harmonic_cocycles(self._k)
@@ -1302,9 +1302,9 @@ def __apply_hecke_operator(self, l, f):
         """
         HeckeData, alpha = self._X._get_hecke_data(l)
         if self.level() % l == 0:
-            factor = QQ(l ** (Integer((self._k - 2) / 2)) / (l + 1))
+            factor = QQ(l ** (Integer((self._k - 2) // 2)) / (l + 1))
         else:
-            factor = QQ(l ** (Integer((self._k - 2) / 2)))
+            factor = QQ(l ** (Integer((self._k - 2) // 2)))
         p = self._X._p
         alphamat = self.embed_quaternion(alpha)
         tmp = [self._U(0) for jj in range(len(self._E))]
@@ -1925,7 +1925,7 @@ def integrate(self, f, center=1, level=0, method='moments'):
                 delta = e.determinant()
                 verbose('%s' % (R2([e[0, 1], e[0, 0]])
                                 / R2([e[1, 1], e[1, 0]])))
-                tmp = ((c * x + d) ** n * delta ** -ZZ(n / 2)) * f((a * x + b) / (c * x + d))
+                tmp = ((c * x + d) ** n * delta ** -ZZ(n // 2)) * f((a * x + b) / (c * x + d))
                 exp = R1(tmp.numerator()) / R1(tmp.denominator())
                 new = eval_dist_at_powseries(self.evaluate(e), exp)
 
@@ -2283,12 +2283,12 @@ def __init__(self, domain, U, prec=None, t=None, R=None,
                                         prec_cap=U - 1 + t,
                                         act_on_left=True,
                                         adjuster=_btquot_adjuster(),
-                                        dettwist=-ZZ((U - 2) / 2),
+                                        dettwist=-ZZ((U - 2) // 2),
                                         act_padic=True)
             else:
                 self._U = Symk(U - 2, base=self._R, act_on_left=True,
                                adjuster=_btquot_adjuster(),
-                               dettwist=-ZZ((U - 2) / 2),
+                               dettwist=-ZZ((U - 2) // 2),
                                act_padic=True)
         else:
             self._U = U
diff --git a/src/sage/modular/hecke/module.py b/src/sage/modular/hecke/module.py
index 98231db856d..113b5e19fed 100644
--- a/src/sage/modular/hecke/module.py
+++ b/src/sage/modular/hecke/module.py
@@ -154,7 +154,7 @@ def _compute_hecke_matrix_prime_power(self, p, r, **kwds):
         if eps is None:
             raise NotImplementedError("either character or _compute_hecke_matrix_prime_power must be overloaded in a derived class")
         k = self.weight()
-        Tpr2 = self._hecke_matrices[pow/p]
+        Tpr2 = self._hecke_matrices[pow // p]
         return Tp*Tpr1 - eps(p)*(p**(k-1)) * Tpr2
 
     def _compute_hecke_matrix_general_product(self, F, **kwds):
diff --git a/src/sage/modular/modform/element.py b/src/sage/modular/modform/element.py
index 67aa2e90c46..0d103f49d64 100644
--- a/src/sage/modular/modform/element.py
+++ b/src/sage/modular/modform/element.py
@@ -24,7 +24,7 @@
 # (at your option) any later version.
 #                  http://www.gnu.org/licenses/
 #*****************************************************************************
-from __future__ import absolute_import
+from __future__ import absolute_import, division
 from six.moves import range
 
 import sage.modular.hecke.element as element
@@ -2661,8 +2661,8 @@ def __compute_weight2_trivial_character(self, X):
                 v.append(F(t-1)/F(24))
             else:
                 an = sigma(n,1)
-                if n%t == 0:
-                    an -= t * sigma(n/t,1)
+                if n % t == 0:
+                    an -= t * sigma(n//t,1)
                 v.append(an)
         return v
 
diff --git a/src/sage/numerical/sdp.pyx b/src/sage/numerical/sdp.pyx
index 9075d9bbf19..30b40d3081a 100644
--- a/src/sage/numerical/sdp.pyx
+++ b/src/sage/numerical/sdp.pyx
@@ -740,8 +740,7 @@ cdef class SemidefiniteProgram(SageObject):
         for l in lists:
             if isinstance(l, SDPVariable):
                     c = {}
-                    for (k,v) in l.items():
-                        #c[k] = self._values[v] if self._values.has_key(v) else None
+                    for k, v in l.items():
                         c[k] = self._backend.get_variable_value(self._variables[v])
                     val.append(c)
             elif isinstance(l, list):
diff --git a/src/sage/rings/asymptotic/growth_group.py b/src/sage/rings/asymptotic/growth_group.py
index acddb7a7e60..44ab16e2d1a 100644
--- a/src/sage/rings/asymptotic/growth_group.py
+++ b/src/sage/rings/asymptotic/growth_group.py
@@ -1463,9 +1463,6 @@ def __classcall__(cls, base, var=None, category=None, ignore_variables=None):
             sage: P3 = MonomialGrowthGroup(ZZ, SR.var('x'))
             sage: P1 is P2 and P2 is P3
             True
-            sage: P4 = MonomialGrowthGroup(ZZ, buffer('xylophone', 0, 1))
-            sage: P1 is P4
-            True
             sage: P5 = MonomialGrowthGroup(ZZ, 'x ')
             sage: P1 is P5
             True
diff --git a/src/sage/rings/power_series_pari.pyx b/src/sage/rings/power_series_pari.pyx
index f16aee88201..e4ea4bec250 100644
--- a/src/sage/rings/power_series_pari.pyx
+++ b/src/sage/rings/power_series_pari.pyx
@@ -400,8 +400,8 @@ cdef class PowerSeries_pari(PowerSeries):
         """
         if len(kwds) >= 1:
             name = self._parent.variable_name()
-            if kwds.has_key(name):  # the series variable is specified by a keyword
-                if len(x) > 0:
+            if name in kwds:  # the series variable is specified by a keyword
+                if len(x):
                     raise ValueError("must not specify %s keyword and positional argument" % name)
                 x = [kwds[name]]
                 del kwds[name]

From 847df2c99cbce5f35f4c7c15da1ecb26843f5324 Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?Fr=C3=A9d=C3=A9ric=20Chapoton?=
 <chapoton@math.univ-lyon1.fr>
Date: Mon, 21 Aug 2017 16:13:07 +0200
Subject: [PATCH 087/128] modify scripts towards python3 compatibility

---
 src/bin/sage-eval           | 2 +-
 src/bin/sage-fixdoctests    | 2 +-
 src/bin/sage-ipython        | 2 +-
 src/bin/sage-list-packages  | 2 +-
 src/bin/sage-preparse       | 2 +-
 src/bin/sage-run-cython     | 2 +-
 src/bin/sage-runtests       | 6 ++++--
 src/sage/misc/gperftools.py | 2 +-
 8 files changed, 11 insertions(+), 9 deletions(-)

diff --git a/src/bin/sage-eval b/src/bin/sage-eval
index 3011bff7b6e..781c36150f8 100755
--- a/src/bin/sage-eval
+++ b/src/bin/sage-eval
@@ -1,4 +1,4 @@
-#!/usr/bin/env python
+#!/usr/bin/env sage-python23
 
 import sys
 from sage.all import *
diff --git a/src/bin/sage-fixdoctests b/src/bin/sage-fixdoctests
index 92d6cebd748..0debd28d544 100755
--- a/src/bin/sage-fixdoctests
+++ b/src/bin/sage-fixdoctests
@@ -1,4 +1,4 @@
-#!/usr/bin/env python
+#!/usr/bin/env sage-python23
 
 """
 Given the output of doctest and a file, adjust the doctests so they won't fail.
diff --git a/src/bin/sage-ipython b/src/bin/sage-ipython
index d83ba020be8..d2ca96b1a87 100755
--- a/src/bin/sage-ipython
+++ b/src/bin/sage-ipython
@@ -1,4 +1,4 @@
-#!/usr/bin/env python
+#!/usr/bin/env sage-python23
 # -*- coding: utf-8 -*-
 """
 Sage IPython startup script.
diff --git a/src/bin/sage-list-packages b/src/bin/sage-list-packages
index 1988cb86aec..bf35f8d8df9 100755
--- a/src/bin/sage-list-packages
+++ b/src/bin/sage-list-packages
@@ -1,4 +1,4 @@
-#!/usr/bin/env python
+#!/usr/bin/env sage-python23
 r"""
 Script to list the Sage packages
 
diff --git a/src/bin/sage-preparse b/src/bin/sage-preparse
index 58a26eb7d47..2d87e73dca7 100755
--- a/src/bin/sage-preparse
+++ b/src/bin/sage-preparse
@@ -1,4 +1,4 @@
-#!/usr/bin/env python
+#!/usr/bin/env sage-python23
 """
 Preparse .sage files and save the result to .sage.py files.
 
diff --git a/src/bin/sage-run-cython b/src/bin/sage-run-cython
index feb91fff1b3..c6dbe00e9f5 100755
--- a/src/bin/sage-run-cython
+++ b/src/bin/sage-run-cython
@@ -1,4 +1,4 @@
-#!/usr/bin/env python
+#!/usr/bin/env sage-python23
 
 import sys
 from sage.repl.load import load_cython
diff --git a/src/bin/sage-runtests b/src/bin/sage-runtests
index 405c3f637d4..754081f3015 100755
--- a/src/bin/sage-runtests
+++ b/src/bin/sage-runtests
@@ -1,6 +1,8 @@
-#!/usr/bin/env python
+#!/usr/bin/env sage-python23
 
-import optparse, os, sys
+import optparse
+import os
+import sys
 
 # Note: the DOT_SAGE and SAGE_STARTUP_FILE environment variables have already been set by sage-env
 DOT_SAGE = os.environ['DOT_SAGE']
diff --git a/src/sage/misc/gperftools.py b/src/sage/misc/gperftools.py
index 142308c24d2..36cd36f1c39 100644
--- a/src/sage/misc/gperftools.py
+++ b/src/sage/misc/gperftools.py
@@ -242,7 +242,7 @@ def _executable(self):
             sage: from sage.misc.gperftools import Profiler
             sage: prof = Profiler()
             sage: prof._executable()
-            '.../python'
+            '.../python...'
         """
         import sys
         return sys.executable

From b1047cce75651690fda2ee0a64d59b56110634b3 Mon Sep 17 00:00:00 2001
From: Jeroen Demeyer <jdemeyer@cage.ugent.be>
Date: Tue, 16 Jan 2018 16:02:58 +0100
Subject: [PATCH 088/128] Clean up MPC declarations

---
 src/module_list.py             |   3 +-
 src/sage/libs/mpc.pxd          | 133 ---------------------------------
 src/sage/libs/mpc/__init__.pxd | 113 ++++++++++++++++++++++++++++
 src/sage/libs/mpc/types.pxd    |  27 +++++++
 src/sage/rings/complex_mpc.pxd |   2 +-
 5 files changed, 142 insertions(+), 136 deletions(-)
 delete mode 100644 src/sage/libs/mpc.pxd
 create mode 100644 src/sage/libs/mpc/__init__.pxd
 create mode 100644 src/sage/libs/mpc/types.pxd

diff --git a/src/module_list.py b/src/module_list.py
index a066fca2391..911d598ecfd 100644
--- a/src/module_list.py
+++ b/src/module_list.py
@@ -1154,8 +1154,7 @@ def uname_specific(name, value, alternative):
               sources = ['sage/rings/morphism.pyx']),
 
     Extension('sage.rings.complex_mpc',
-              sources = ['sage/rings/complex_mpc.pyx'],
-              libraries = ['mpc']),
+              sources = ['sage/rings/complex_mpc.pyx']),
 
     Extension('sage.rings.noncommutative_ideals',
               sources = ['sage/rings/noncommutative_ideals.pyx']),
diff --git a/src/sage/libs/mpc.pxd b/src/sage/libs/mpc.pxd
deleted file mode 100644
index 24fb0f82816..00000000000
--- a/src/sage/libs/mpc.pxd
+++ /dev/null
@@ -1,133 +0,0 @@
-from sage.libs.gmp.types cimport *
-from sage.libs.mpfr.types cimport *
-
-cdef extern from "mpc.h":
-    ctypedef struct __mpc_struct:
-        mpfr_t re
-        mpfr_t im
-    ctypedef __mpc_struct mpc_t[1]
-    ctypedef __mpc_struct* mpc_ptr
-    ctypedef __mpc_struct* mpc_srcptr
-
-    ctypedef enum mpc_rnd_t:
-        MPC_RNDNN = 0
-        MPC_RNDZN = 1
-        MPC_RNDUN = 2
-        MPC_RNDDN = 3
-        MPC_RNDNZ = 16
-        MPC_RNDZZ = 17
-        MPC_RNDUZ = 18
-        MPC_RNDDZ = 19
-        MPC_RNDNU = 32
-        MPC_RNDZU = 33
-        MPC_RNDUU = 34
-        MPC_RNDDU = 35
-        MPC_RNDND = 48
-        MPC_RNDZD = 49
-        MPC_RNDUD = 50
-        MPC_RNDDD = 51
-
-    # Memory management
-    void mpc_init (mpc_t)
-    void mpc_init2 (mpc_t, mpfr_prec_t)
-    void mpc_clear (mpc_t)
-
-    # Precision accessors
-    mpfr_prec_t mpc_get_prec (mpc_t)
-    void mpc_set_prec (mpc_t, mpfr_prec_t)
-
-    # Set real part to given value and imaginary part to +0
-    int  mpc_set_ui (mpc_t, unsigned long int, mpc_rnd_t)
-    int  mpc_set_si (mpc_t, long int, mpc_rnd_t)
-    int  mpc_set_z (mpc_t, mpz_t, mpc_rnd_t)
-    int  mpc_set_d (mpc_t, double, mpc_rnd_t)
-    int  mpc_set_fr (mpc_t, mpfr_t, mpc_rnd_t)
-    # Set value
-    int  mpc_set (mpc_t, mpc_t, mpc_rnd_t)
-    int  mpc_set_ui_ui (mpc_t, unsigned long int, unsigned long int, mpc_rnd_t)
-    int  mpc_set_si_si (mpc_t, long int, long int, mpc_rnd_t)
-    int  mpc_set_d_d (mpc_t, double, double, mpc_rnd_t)
-    int  mpc_set_fr_fr (mpc_t, mpfr_t, mpfr_t, mpc_rnd_t)
-    void mpc_set_nan(mpc_t)
-    void mpc_swap(mpc_t, mpc_t)
-
-    # Comparisons
-    int  mpc_cmp (mpc_t, mpc_t)
-    int  mpc_cmp_si_si (mpc_t, long int, long int)
-    int  mpc_cmp_si (mpc_t, long int)
-
-    # Projection
-    int mpc_real (mpfr_t rop, mpc_t op, mpfr_rnd_t rnd)
-    int mpc_imag (mpfr_t rop, mpc_t op, mpfr_rnd_t rnd)
-    mpfr_t mpc_realref (mpc_t op)
-    mpfr_t mpc_imagref (mpc_t op)
-    int mpc_arg (mpfr_t rop, mpc_t op, mpfr_rnd_t rnd)
-    int mpc_proj (mpc_t rop, mpc_t op, mpc_rnd_t rnd)
-
-    # Arithmetic
-    int  mpc_neg (mpc_t, mpc_t, mpc_rnd_t)
-    int  mpc_conj (mpc_t, mpc_t, mpc_rnd_t)
-
-    int  mpc_add (mpc_t, mpc_t, mpc_t, mpc_rnd_t)
-    int  mpc_sub (mpc_t, mpc_t, mpc_t, mpc_rnd_t)
-    int  mpc_mul (mpc_t, mpc_t, mpc_t, mpc_rnd_t)
-    int  mpc_div (mpc_t, mpc_t, mpc_t, mpc_rnd_t)
-    int  mpc_sqr (mpc_t, mpc_t, mpc_rnd_t)
-
-    int  mpc_add_fr (mpc_t, mpc_t, mpfr_t, mpc_rnd_t)
-    int  mpc_add_ui (mpc_t, mpc_t, unsigned long int, mpc_rnd_t)
-    int  mpc_add_si (mpc_t, mpc_t, unsigned long, mpc_rnd_t)
-    int  mpc_sub_fr (mpc_t, mpc_t, mpfr_t, mpc_rnd_t)
-    int  mpc_fr_sub (mpc_t, mpfr_t, mpc_t, mpc_rnd_t)
-    int  mpc_sub_ui (mpc_t, mpc_t, unsigned long int, mpc_rnd_t)
-    int  mpc_ui_sub (mpc_t, unsigned long int, mpc_t, mpc_rnd_t)
-    int  mpc_ui_ui_sub (mpc_t, unsigned long int, unsigned long int, mpc_t, mpc_rnd_t)
-    int  mpc_mul_fr (mpc_t, mpc_t, mpfr_t, mpc_rnd_t)
-    int  mpc_mul_ui (mpc_t, mpc_t, unsigned long int, mpc_rnd_t)
-    int  mpc_mul_si (mpc_t, mpc_t, long int, mpc_rnd_t)
-    int  mpc_mul_i  (mpc_t, mpc_t, int, mpc_rnd_t)
-    int  mpc_ui_div (mpc_t, unsigned long int, mpc_t, mpc_rnd_t)
-    int  mpc_div_fr (mpc_t, mpc_t, mpfr_t, mpc_rnd_t)
-    int  mpc_fr_div (mpc_t, mpfr_t, mpc_t, mpc_rnd_t)
-    int  mpc_div_ui (mpc_t, mpc_t, unsigned long int, mpc_rnd_t)
-    int  mpc_ui_div (mpc_t, unsigned long int, mpc_t, mpc_rnd_t)
-    int  mpc_div_2ui (mpc_t, mpc_t, unsigned long int, mpc_rnd_t)
-    int  mpc_div_2si (mpc_t, mpc_t, long int, mpc_rnd_t)
-    int  mpc_mul_2ui (mpc_t, mpc_t, unsigned long int, mpc_rnd_t)
-    int  mpc_mul_2si (mpc_t, mpc_t, long int, mpc_rnd_t)
-    #
-    int  mpc_abs (mpfr_t, mpc_t, mpfr_rnd_t)
-    int  mpc_norm (mpfr_t, mpc_t, mpfr_rnd_t)
-
-
-    # Power functions and logarithm
-    int mpc_sqrt (mpc_t, mpc_t, mpc_rnd_t)
-    int mpc_exp (mpc_t, mpc_t, mpc_rnd_t)
-    int mpc_log (mpc_t, mpc_t, mpc_rnd_t)
-    int mpc_pow (mpc_t rop, mpc_t op1, mpc_t op2, mpc_rnd_t rnd)
-    int mpc_pow_si (mpc_t rop, mpc_t op1, long op2, mpc_rnd_t rnd)
-    int mpc_pow_ui (mpc_t rop, mpc_t op1, unsigned long op2, mpc_rnd_t rnd)
-    int mpc_pow_z (mpc_t rop, mpc_t op1, mpz_t, mpc_rnd_t rnd)
-    int mpc_pow_d (mpc_t rop, mpc_t op1, double, mpc_rnd_t rnd)
-    int mpc_pow_fr (mpc_t rop, mpc_t op1, mpfr_t op2, mpc_rnd_t rnd)
-
-    # Trigonometric functions
-    void mpc_sin (mpc_t, mpc_t, mpc_rnd_t)
-    void mpc_cos (mpc_t, mpc_t, mpc_rnd_t)
-    void mpc_tan (mpc_t, mpc_t, mpc_rnd_t)
-    void mpc_sinh (mpc_t, mpc_t, mpc_rnd_t)
-    void mpc_cosh (mpc_t, mpc_t, mpc_rnd_t)
-    void mpc_tanh (mpc_t, mpc_t, mpc_rnd_t)
-    void mpc_asin (mpc_t, mpc_t, mpc_rnd_t)
-    void mpc_acos (mpc_t, mpc_t, mpc_rnd_t)
-    void mpc_atan (mpc_t, mpc_t, mpc_rnd_t)
-    void mpc_asinh (mpc_t, mpc_t, mpc_rnd_t)
-    void mpc_acosh (mpc_t, mpc_t, mpc_rnd_t)
-    void mpc_atanh (mpc_t, mpc_t, mpc_rnd_t)
-
-    # Random Function
-    int  mpc_urandom (mpc_t, gmp_randstate_t)
-
-    # utility
-    int MPC_INEX_RE(int)
-    int MPC_INEX_IM(int)
diff --git a/src/sage/libs/mpc/__init__.pxd b/src/sage/libs/mpc/__init__.pxd
new file mode 100644
index 00000000000..4930a636c41
--- /dev/null
+++ b/src/sage/libs/mpc/__init__.pxd
@@ -0,0 +1,113 @@
+# distutils: libraries = gmp mpfr mpc
+
+from sage.libs.gmp.types cimport *
+from sage.libs.mpfr.types cimport *
+from sage.libs.mpc.types cimport *
+
+cdef extern from "mpc.h":
+    int  mpc_add(mpc_ptr, mpc_srcptr, mpc_srcptr, mpc_rnd_t)
+    int  mpc_add_fr(mpc_ptr, mpc_srcptr, mpfr_srcptr, mpc_rnd_t)
+    int  mpc_add_si(mpc_ptr, mpc_srcptr, long int, mpc_rnd_t)
+    int  mpc_add_ui(mpc_ptr, mpc_srcptr, unsigned long int, mpc_rnd_t)
+    int  mpc_sub(mpc_ptr, mpc_srcptr, mpc_srcptr, mpc_rnd_t)
+    int  mpc_sub_fr(mpc_ptr, mpc_srcptr, mpfr_srcptr, mpc_rnd_t)
+    int  mpc_fr_sub(mpc_ptr, mpfr_srcptr, mpc_srcptr, mpc_rnd_t)
+    int  mpc_sub_ui(mpc_ptr, mpc_srcptr, unsigned long int, mpc_rnd_t)
+    int  mpc_ui_sub(mpc_ptr, unsigned long int, mpc_srcptr, mpc_rnd_t)
+    int  mpc_ui_ui_sub(mpc_ptr, unsigned long int, unsigned long int, mpc_srcptr, mpc_rnd_t)
+    int  mpc_mul(mpc_ptr, mpc_srcptr, mpc_srcptr, mpc_rnd_t)
+    int  mpc_mul_fr(mpc_ptr, mpc_srcptr, mpfr_srcptr, mpc_rnd_t)
+    int  mpc_mul_ui(mpc_ptr, mpc_srcptr, unsigned long int, mpc_rnd_t)
+    int  mpc_mul_si(mpc_ptr, mpc_srcptr, long int, mpc_rnd_t)
+    int  mpc_mul_i(mpc_ptr, mpc_srcptr, int, mpc_rnd_t)
+    int  mpc_sqr(mpc_ptr, mpc_srcptr, mpc_rnd_t)
+    int  mpc_div(mpc_ptr, mpc_srcptr, mpc_srcptr, mpc_rnd_t)
+    int  mpc_pow(mpc_ptr, mpc_srcptr, mpc_srcptr, mpc_rnd_t)
+    int  mpc_pow_fr(mpc_ptr, mpc_srcptr, mpfr_srcptr, mpc_rnd_t)
+    int  mpc_pow_ld(mpc_ptr, mpc_srcptr, long double, mpc_rnd_t)
+    int  mpc_pow_d(mpc_ptr, mpc_srcptr, double, mpc_rnd_t)
+    int  mpc_pow_si(mpc_ptr, mpc_srcptr, long, mpc_rnd_t)
+    int  mpc_pow_ui(mpc_ptr, mpc_srcptr, unsigned long, mpc_rnd_t)
+    int  mpc_pow_z(mpc_ptr, mpc_srcptr, mpz_srcptr, mpc_rnd_t)
+    int  mpc_div_fr(mpc_ptr, mpc_srcptr, mpfr_srcptr, mpc_rnd_t)
+    int  mpc_fr_div(mpc_ptr, mpfr_srcptr, mpc_srcptr, mpc_rnd_t)
+    int  mpc_div_ui(mpc_ptr, mpc_srcptr, unsigned long int, mpc_rnd_t)
+    int  mpc_ui_div(mpc_ptr, unsigned long int, mpc_srcptr, mpc_rnd_t)
+    int  mpc_div_2ui(mpc_ptr, mpc_srcptr, unsigned long int, mpc_rnd_t)
+    int  mpc_mul_2ui(mpc_ptr, mpc_srcptr, unsigned long int, mpc_rnd_t)
+    int  mpc_div_2si(mpc_ptr, mpc_srcptr, long int, mpc_rnd_t)
+    int  mpc_mul_2si(mpc_ptr, mpc_srcptr, long int, mpc_rnd_t)
+    int  mpc_conj(mpc_ptr, mpc_srcptr, mpc_rnd_t)
+    int  mpc_neg(mpc_ptr, mpc_srcptr, mpc_rnd_t)
+    int  mpc_norm(mpfr_ptr, mpc_srcptr, mpfr_rnd_t)
+    int  mpc_abs(mpfr_ptr, mpc_srcptr, mpfr_rnd_t)
+    int  mpc_sqrt(mpc_ptr, mpc_srcptr, mpc_rnd_t)
+    int  mpc_set(mpc_ptr, mpc_srcptr, mpc_rnd_t)
+    int  mpc_set_d(mpc_ptr, double, mpc_rnd_t)
+    int  mpc_set_d_d(mpc_ptr, double, double, mpc_rnd_t)
+    int  mpc_set_ld(mpc_ptr, long double, mpc_rnd_t)
+    int  mpc_set_ld_ld(mpc_ptr, long double, long double, mpc_rnd_t)
+    int  mpc_set_f(mpc_ptr, mpf_srcptr, mpc_rnd_t)
+    int  mpc_set_f_f(mpc_ptr, mpf_srcptr, mpf_srcptr, mpc_rnd_t)
+    int  mpc_set_fr(mpc_ptr, mpfr_srcptr, mpc_rnd_t)
+    int  mpc_set_fr_fr(mpc_ptr, mpfr_srcptr, mpfr_srcptr, mpc_rnd_t)
+    int  mpc_set_q(mpc_ptr, mpq_srcptr, mpc_rnd_t)
+    int  mpc_set_q_q(mpc_ptr, mpq_srcptr, mpq_srcptr, mpc_rnd_t)
+    int  mpc_set_si(mpc_ptr, long int, mpc_rnd_t)
+    int  mpc_set_si_si(mpc_ptr, long int, long int, mpc_rnd_t)
+    int  mpc_set_ui(mpc_ptr, unsigned long int, mpc_rnd_t)
+    int  mpc_set_ui_ui(mpc_ptr, unsigned long int, unsigned long int, mpc_rnd_t)
+    int  mpc_set_z(mpc_ptr, mpz_srcptr, mpc_rnd_t)
+    int  mpc_set_z_z(mpc_ptr, mpz_srcptr, mpz_srcptr, mpc_rnd_t)
+    void mpc_swap(mpc_ptr, mpc_ptr)
+    int  mpc_fma(mpc_ptr, mpc_srcptr, mpc_srcptr, mpc_srcptr, mpc_rnd_t)
+
+    void mpc_set_nan(mpc_ptr)
+
+    int  mpc_real(mpfr_ptr, mpc_srcptr, mpfr_rnd_t)
+    int  mpc_imag(mpfr_ptr, mpc_srcptr, mpfr_rnd_t)
+    int  mpc_arg(mpfr_ptr, mpc_srcptr, mpfr_rnd_t)
+    int  mpc_proj(mpc_ptr, mpc_srcptr, mpc_rnd_t)
+    int  mpc_cmp(mpc_srcptr, mpc_srcptr)
+    int  mpc_cmp_si(mpc_srcptr, long int)
+    int  mpc_cmp_si_si(mpc_srcptr, long int, long int)
+    int  mpc_cmp_abs(mpc_srcptr, mpc_srcptr)
+    int  mpc_exp(mpc_ptr, mpc_srcptr, mpc_rnd_t)
+    int  mpc_log(mpc_ptr, mpc_srcptr, mpc_rnd_t)
+    int  mpc_log10(mpc_ptr, mpc_srcptr, mpc_rnd_t)
+    int  mpc_sin(mpc_ptr, mpc_srcptr, mpc_rnd_t)
+    int  mpc_cos(mpc_ptr, mpc_srcptr, mpc_rnd_t)
+    int  mpc_sin_cos(mpc_ptr, mpc_ptr, mpc_srcptr, mpc_rnd_t, mpc_rnd_t)
+    int  mpc_tan(mpc_ptr, mpc_srcptr, mpc_rnd_t)
+    int  mpc_sinh(mpc_ptr, mpc_srcptr, mpc_rnd_t)
+    int  mpc_cosh(mpc_ptr, mpc_srcptr, mpc_rnd_t)
+    int  mpc_tanh(mpc_ptr, mpc_srcptr, mpc_rnd_t)
+    int  mpc_asin(mpc_ptr, mpc_srcptr, mpc_rnd_t)
+    int  mpc_acos(mpc_ptr, mpc_srcptr, mpc_rnd_t)
+    int  mpc_atan(mpc_ptr, mpc_srcptr, mpc_rnd_t)
+    int  mpc_asinh(mpc_ptr, mpc_srcptr, mpc_rnd_t)
+    int  mpc_acosh(mpc_ptr, mpc_srcptr, mpc_rnd_t)
+    int  mpc_atanh(mpc_ptr, mpc_srcptr, mpc_rnd_t)
+    int  mpc_rootofunity(mpc_ptr, unsigned long int, unsigned long int, mpc_rnd_t)
+    void mpc_clear(mpc_ptr)
+    int  mpc_urandom(mpc_ptr, gmp_randstate_t)
+    void mpc_init2(mpc_ptr, mpfr_prec_t)
+    void mpc_init3(mpc_ptr, mpfr_prec_t, mpfr_prec_t)
+    mpfr_prec_t mpc_get_prec(mpc_srcptr x)
+    void mpc_get_prec2(mpfr_prec_t *pr, mpfr_prec_t *pi, mpc_srcptr x)
+    void mpc_set_prec(mpc_ptr, mpfr_prec_t)
+    const char * mpc_get_version()
+
+    int  mpc_strtoc(mpc_ptr, const char *, char **, int, mpc_rnd_t)
+    int  mpc_set_str(mpc_ptr, const char *, int, mpc_rnd_t)
+    char * mpc_get_str(int, size_t, mpc_srcptr, mpc_rnd_t)
+    void mpc_free_str(char *)
+
+    int mpc_inp_str(mpc_ptr, FILE *, size_t *, int, mpc_rnd_t)
+    size_t mpc_out_str(FILE *, int, size_t, mpc_srcptr, mpc_rnd_t)
+
+    mpfr_t mpc_realref(mpc_t op)
+    mpfr_t mpc_imagref(mpc_t op)
+
+    int MPC_INEX_RE(int)
+    int MPC_INEX_IM(int)
diff --git a/src/sage/libs/mpc/types.pxd b/src/sage/libs/mpc/types.pxd
new file mode 100644
index 00000000000..72565c08630
--- /dev/null
+++ b/src/sage/libs/mpc/types.pxd
@@ -0,0 +1,27 @@
+from sage.libs.mpfr.types cimport mpfr_t
+
+cdef extern from "mpc.h":
+    ctypedef struct __mpc_struct:
+        mpfr_t re
+        mpfr_t im
+    ctypedef __mpc_struct mpc_t[1]
+    ctypedef __mpc_struct* mpc_ptr
+    ctypedef __mpc_struct* mpc_srcptr
+
+    ctypedef enum mpc_rnd_t:
+        MPC_RNDNN
+        MPC_RNDZN
+        MPC_RNDUN
+        MPC_RNDDN
+        MPC_RNDNZ
+        MPC_RNDZZ
+        MPC_RNDUZ
+        MPC_RNDDZ
+        MPC_RNDNU
+        MPC_RNDZU
+        MPC_RNDUU
+        MPC_RNDDU
+        MPC_RNDND
+        MPC_RNDZD
+        MPC_RNDUD
+        MPC_RNDDD
diff --git a/src/sage/rings/complex_mpc.pxd b/src/sage/rings/complex_mpc.pxd
index 11e1c162b59..762c38afbdc 100644
--- a/src/sage/rings/complex_mpc.pxd
+++ b/src/sage/rings/complex_mpc.pxd
@@ -1,4 +1,4 @@
-from sage.libs.mpc cimport mpc_t, mpc_rnd_t
+from sage.libs.mpc.types cimport mpc_t, mpc_rnd_t
 
 cimport sage.structure.element
 cimport sage.rings.ring

From 999dcfba45b3b896f74aaa63f2300fde6532f7d4 Mon Sep 17 00:00:00 2001
From: Travis Scrimshaw <tcscrims at gmail.com>
Date: Tue, 16 Jan 2018 09:29:40 -0600
Subject: [PATCH 089/128] Fixes in virasoro.VermaModule.

---
 src/sage/algebras/lie_algebras/virasoro.py | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/src/sage/algebras/lie_algebras/virasoro.py b/src/sage/algebras/lie_algebras/virasoro.py
index 21b74defae9..6a2b0814150 100644
--- a/src/sage/algebras/lie_algebras/virasoro.py
+++ b/src/sage/algebras/lie_algebras/virasoro.py
@@ -690,7 +690,7 @@ class VermaModule(CombinatorialFreeModule):
     """
     A Verma module of the Virasoro algebra.
 
-    The Virasoro algebra admits a trianglar decomposition of
+    The Virasoro algebra admits a triangular decomposition
 
     .. MATH::
 

From 3fa75f5d2dde0f3c7e7e984000e1d2c242ce2991 Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?Fr=C3=A9d=C3=A9ric=20Chapoton?=
 <chapoton@math.univ-lyon1.fr>
Date: Tue, 16 Jan 2018 16:55:50 +0100
Subject: [PATCH 090/128] py3: adding a few __hash_ functions

---
 src/sage/finance/markov_multifractal.py | 12 ++++++++++++
 src/sage/finance/stock.py               | 16 ++++++++++++++++
 src/sage/games/sudoku.py                | 12 ++++++++++++
 src/sage/knots/link.py                  | 12 ++++++++++++
 src/sage/quivers/morphism.py            | 19 +++++++++++++++++++
 5 files changed, 71 insertions(+)

diff --git a/src/sage/finance/markov_multifractal.py b/src/sage/finance/markov_multifractal.py
index a664674c52d..1e271c92d36 100644
--- a/src/sage/finance/markov_multifractal.py
+++ b/src/sage/finance/markov_multifractal.py
@@ -79,6 +79,18 @@ def __eq__(self, other):
                 self.__gamma_kbar == other.__gamma_kbar and
                 self.__kbar == other.__kbar)
 
+    def __hash__(self):
+        """
+        Return the hash of ``self``.
+
+        EXAMPLES::
+
+            sage: msm = finance.MarkovSwitchingMultifractal(8,1.4,1.0,0.95,3)
+            sage: H = hash(msm)
+        """
+        return hash((self.__m0, self.__sigma, self.__b, self.__gamma_kbar,
+                     self.__kbar))
+
     def __ne__(self, other):
         """
         Test inequality of ``self`` and ``other``.
diff --git a/src/sage/finance/stock.py b/src/sage/finance/stock.py
index 0997142a5ce..3f7d810be8e 100644
--- a/src/sage/finance/stock.py
+++ b/src/sage/finance/stock.py
@@ -96,6 +96,22 @@ def __eq__(self, other):
                 self.close == other.close and
                 self.volume == other.volume)
 
+    def __hash__(self):
+        """
+        Return the hash of ``self``.
+
+        EXAMPLES::
+
+            sage: ohlc = sage.finance.stock.OHLC('18-Aug-04', 100.01, 104.06, 95.96, 100.34, 22353092)
+            sage: H = hash(ohlc)
+        """
+        return hash((self.timestamp,
+                     self.open,
+                     self.high,
+                     self.low,
+                     self.close ,
+                     self.volume))
+
     def __ne__(self, other):
         """
         Compare ``self`` and ``other``.
diff --git a/src/sage/games/sudoku.py b/src/sage/games/sudoku.py
index 94ba6eb61c0..33cee27951b 100644
--- a/src/sage/games/sudoku.py
+++ b/src/sage/games/sudoku.py
@@ -227,6 +227,18 @@ def __eq__(self, other):
         """
         return self.puzzle == tuple(other.to_list())
 
+    def __hash__(self):
+        """
+        Return the hash of ``self``.
+
+        EXAMPLES::
+
+            sage: a = Sudoku('.4..32....14..3.')
+            sage: hash(a) == hash(a.puzzle)
+            True
+        """
+        return hash(self.puzzle)
+
     def __ne__(self, other):
         """
         Check that ``self`` is not equal to ``other``.
diff --git a/src/sage/knots/link.py b/src/sage/knots/link.py
index c22c477d1cc..6c3f4094ad5 100644
--- a/src/sage/knots/link.py
+++ b/src/sage/knots/link.py
@@ -559,6 +559,18 @@ def __eq__(self, other):
                 return True
         return self.braid() == other.braid()
 
+    def __hash__(self):
+        """
+        Return the hash of ``self``.
+
+        EXAMPLES::
+
+            sage: B = BraidGroup(8)
+            sage: L1 = Link(B([-1, -1, -1, -2, 1, -2, 3, -2, 5, 4]))
+            sage: H = hash(L1)
+        """
+        return hash(self.braid())
+
     def __ne__(self, other):
         """
         Check inequality.
diff --git a/src/sage/quivers/morphism.py b/src/sage/quivers/morphism.py
index b6cd04e27bd..18232b2413f 100644
--- a/src/sage/quivers/morphism.py
+++ b/src/sage/quivers/morphism.py
@@ -515,6 +515,25 @@ def __eq__(self, other):
         # If all that holds just check the vectors
         return self._vector == other._vector
 
+    def __hash__(self):
+        """
+        Return the hash of ``self``.
+
+        EXAMPLES::
+
+            sage: Q = DiGraph({1:{2:['a', 'b']}, 2:{3:['c']}}).path_semigroup()
+            sage: spaces = {1: QQ^2, 2: QQ^2, 3:QQ^1}
+            sage: maps = {(1, 2, 'a'): [[1, 0], [0, 0]], (1, 2, 'b'): [[0, 0], [0, 1]], (2, 3, 'c'): [[1], [1]]}
+            sage: M = Q.representation(QQ, spaces, maps)
+            sage: spaces2 = {2: QQ^1, 3: QQ^1}
+            sage: S = Q.representation(QQ, spaces2)
+            sage: x = M({2: (1, -1)})
+            sage: y = M({3: (1,)})
+            sage: g = S.hom([x, y], M)
+            sage: H = hash(g)
+        """
+        return hash(tuple(self._vector))
+
     def __ne__(self, other):
         """
         This function overrides the ``!=`` operator

From 53386ed9aa2f86cb1d957a46a41ee6ac6eda614f Mon Sep 17 00:00:00 2001
From: "Erik M. Bray" <erik.bray@lri.fr>
Date: Wed, 3 Jan 2018 10:44:19 +0000
Subject: [PATCH 091/128] Fix several 'raise StopIteration' statements in
 generator functions.

Explicitly raising StopIteration from a generator is deprecated due to PEP-479.  Instead, it's just as easily to simply return from the generator.
---
 src/sage/combinat/integer_matrices.py                  |  2 +-
 src/sage/combinat/species/series.py                    |  5 ++---
 src/sage/combinat/species/stream.py                    |  1 -
 src/sage/combinat/tiling.py                            |  5 +++--
 src/sage/combinat/words/abstract_word.py               | 10 ++++------
 src/sage/databases/stein_watkins.py                    |  2 +-
 .../geometry/hyperplane_arrangement/arrangement.py     |  2 +-
 src/sage/geometry/triangulation/point_configuration.py |  2 +-
 src/sage/graphs/digraph_generators.py                  |  3 ++-
 src/sage/graphs/graph_generators.py                    |  3 ++-
 src/sage/graphs/hypergraph_generators.py               |  3 ++-
 src/sage/matrix/matrix_space.py                        |  2 +-
 src/sage/monoids/automatic_semigroup.py                |  7 ++++++-
 src/sage/monoids/string_monoid_element.py              |  5 ++---
 src/sage/numerical/linear_functions.pyx                |  4 ++--
 src/sage/rings/number_field/number_field.py            |  4 ++--
 src/sage/rings/rational_field.py                       |  4 ++--
 src/sage/schemes/toric/points.py                       |  2 +-
 18 files changed, 35 insertions(+), 31 deletions(-)

diff --git a/src/sage/combinat/integer_matrices.py b/src/sage/combinat/integer_matrices.py
index cd8b2236c2b..ec35259808a 100644
--- a/src/sage/combinat/integer_matrices.py
+++ b/src/sage/combinat/integer_matrices.py
@@ -323,7 +323,7 @@ def integer_matrices_generator(row_sums, column_sums):
     """
     column_sums = list(column_sums)
     if sum(row_sums) != sum(column_sums):
-        raise StopIteration
+        return
     if not row_sums:
         yield []
     elif len(row_sums) == 1:
diff --git a/src/sage/combinat/species/series.py b/src/sage/combinat/species/series.py
index bdad43ef40f..aee88a4ea5e 100644
--- a/src/sage/combinat/species/series.py
+++ b/src/sage/combinat/species/series.py
@@ -1488,7 +1488,7 @@ def _integral_zero_gen(self, ao):
             #Check to see if the stream is finite
             if self.is_finite(n-1):
                 yield self._stream[n-1]
-                raise StopIteration
+                break
             else:
                 yield (Integer(1)/Integer(n))*self._stream[n-1]
                 n += 1
@@ -1511,7 +1511,6 @@ def _integral_nonzero_gen(self, integration_constant):
 
         if ao == inf:
             yield self._zero
-            raise StopIteration
         else:
             for _ in range(ao-1):
                 yield self._zero
@@ -1523,7 +1522,7 @@ def _integral_nonzero_gen(self, integration_constant):
                 #Check to see if the stream is finite
                 if self.is_finite(n-1):
                     yield self.coefficient(n-1)
-                    raise StopIteration
+                    break
                 else:
                     yield (Integer(1)/Integer(n))*self.coefficient(n-1)
                     n += 1
diff --git a/src/sage/combinat/species/stream.py b/src/sage/combinat/species/stream.py
index 4b1335975e8..1040411f1b2 100644
--- a/src/sage/combinat/species/stream.py
+++ b/src/sage/combinat/species/stream.py
@@ -358,7 +358,6 @@ def __iter__(self):
             except IndexError:
                 break
             i += 1
-        raise StopIteration
 
     def __len__(self):
         """
diff --git a/src/sage/combinat/tiling.py b/src/sage/combinat/tiling.py
index 206d7f6b639..f761f8f2c97 100644
--- a/src/sage/combinat/tiling.py
+++ b/src/sage/combinat/tiling.py
@@ -1834,7 +1834,8 @@ def _dlx_solutions_iterator(self):
             [[0, 7, 14], [0, 12, 10], [6, 13, 5], [6, 14, 2], [11, 9, 5], [11, 10, 3]]
         """
         if len(self.rows()) == 0:
-            raise StopIteration
+            return
+
         x = self.dlx_solver()
         while x.search() == 1:
             yield x.get_solution()
@@ -2047,7 +2048,7 @@ def solve(self, partial=None):
 
         """
         if not self.is_suitable():
-            raise StopIteration
+            return
         if partial is None:
             it = self._dlx_solutions_iterator()
         elif partial == 'common_prefix':
diff --git a/src/sage/combinat/words/abstract_word.py b/src/sage/combinat/words/abstract_word.py
index 4dd0b0f092e..9b859ae16ea 100644
--- a/src/sage/combinat/words/abstract_word.py
+++ b/src/sage/combinat/words/abstract_word.py
@@ -470,9 +470,7 @@ def _longest_common_prefix_iterator(self, other):
             if b == c:
                 yield b
             else:
-                raise StopIteration
-        else:
-            raise StopIteration
+                break
 
     def longest_common_prefix(self, other, length='unknown'):
         r"""
@@ -600,11 +598,11 @@ def _longest_periodic_prefix_iterator(self, period=1):
             sage: list(Word([1,2,1,2,1,3])._longest_periodic_prefix_iterator(2))
             [1, 2, 1, 2, 1]
         """
-        for i,l in enumerate(self):
-            if self[i%period] == l:
+        for i, l in enumerate(self):
+            if self[i % period] == l:
                 yield l
             else:
-                raise StopIteration
+                break
 
     def longest_periodic_prefix(self, period=1):
         r"""
diff --git a/src/sage/databases/stein_watkins.py b/src/sage/databases/stein_watkins.py
index 3bf373a1d14..eeb2bcb5981 100644
--- a/src/sage/databases/stein_watkins.py
+++ b/src/sage/databases/stein_watkins.py
@@ -300,7 +300,7 @@ def iter_levels(self):
             except StopIteration:
                 if C != []:
                     yield C
-                raise StopIteration
+                return
             if E.conductor != N:
                 if C != []:
                     yield C
diff --git a/src/sage/geometry/hyperplane_arrangement/arrangement.py b/src/sage/geometry/hyperplane_arrangement/arrangement.py
index 31a37e0723d..a27a4515b5f 100644
--- a/src/sage/geometry/hyperplane_arrangement/arrangement.py
+++ b/src/sage/geometry/hyperplane_arrangement/arrangement.py
@@ -1182,7 +1182,7 @@ def echelon_col_iter(row_iter):
             """helper to iterat over the echelon pivot column indices"""
             for row in row_iter:
                 if row == 0:
-                    raise StopIteration
+                    return
                 for pivot in range(self.dimension()):
                     if row[pivot] != 0:
                         break
diff --git a/src/sage/geometry/triangulation/point_configuration.py b/src/sage/geometry/triangulation/point_configuration.py
index 74c4518d079..f84d2d42d93 100644
--- a/src/sage/geometry/triangulation/point_configuration.py
+++ b/src/sage/geometry/triangulation/point_configuration.py
@@ -661,7 +661,7 @@ def _TOPCOM_exec(cls, executable, input_string, verbose=True):
                 yield line.strip()
             except GeneratorExit:
                 proc.close(force=True)
-                raise StopIteration
+                return
 
         if verbose:
             print("#######################")
diff --git a/src/sage/graphs/digraph_generators.py b/src/sage/graphs/digraph_generators.py
index 8689b1b9600..b42e6749f9a 100644
--- a/src/sage/graphs/digraph_generators.py
+++ b/src/sage/graphs/digraph_generators.py
@@ -560,7 +560,8 @@ def tournaments_nauty(self, n,
             try:
                 s = next(gen)
             except StopIteration:
-                raise StopIteration("Exhausted list of graphs from nauty geng")
+                # Exhausted list of graphs from nauty geng
+                return
 
             G = DiGraph(n)
             i = 0
diff --git a/src/sage/graphs/graph_generators.py b/src/sage/graphs/graph_generators.py
index da142cc7fd2..dfe823ee99a 100644
--- a/src/sage/graphs/graph_generators.py
+++ b/src/sage/graphs/graph_generators.py
@@ -894,7 +894,8 @@ def nauty_geng(self, options="", debug=False):
             try:
                 s = next(gen)
             except StopIteration:
-                raise StopIteration("Exhausted list of graphs from nauty geng")
+                # Exhausted list of graphs from nauty geng
+                return
             G = graph.Graph(s[:-1], format='graph6')
             yield G
 
diff --git a/src/sage/graphs/hypergraph_generators.py b/src/sage/graphs/hypergraph_generators.py
index d131b56a1c8..658c5c0bb90 100644
--- a/src/sage/graphs/hypergraph_generators.py
+++ b/src/sage/graphs/hypergraph_generators.py
@@ -150,7 +150,8 @@ def nauty(self, number_of_sets, number_of_vertices,
             try:
                 s = next(gen)
             except StopIteration:
-                raise StopIteration("Exhausted list of graphs from nauty geng")
+                # Exhausted list of graphs from nauty geng
+                return
 
             from sage.graphs.graph import Graph
             G = Graph(s[:-1], format='graph6')
diff --git a/src/sage/matrix/matrix_space.py b/src/sage/matrix/matrix_space.py
index 4f5bc14b05b..0854fb3c1a8 100644
--- a/src/sage/matrix/matrix_space.py
+++ b/src/sage/matrix/matrix_space.py
@@ -1322,7 +1322,7 @@ def __iter__(self):
         #yield the empty matrix in that case and return
         if number_of_entries == 0:
             yield self(0)
-            raise StopIteration
+            return
 
         import sage.combinat.integer_vector
 
diff --git a/src/sage/monoids/automatic_semigroup.py b/src/sage/monoids/automatic_semigroup.py
index 2de54a47b73..3f7e745b776 100644
--- a/src/sage/monoids/automatic_semigroup.py
+++ b/src/sage/monoids/automatic_semigroup.py
@@ -680,7 +680,12 @@ def _iter_concurrent(self):
             # been called before we move on to the next line
             i += 1
             if i == len(self._elements) and not self._constructed:
-                next(self._iter)
+                try:
+                    next(self._iter)
+                except StopIteration:
+                    # Don't allow StopIteration to bubble up from generator
+                    # see PEP-479
+                    break
 
     def cardinality(self):
         """
diff --git a/src/sage/monoids/string_monoid_element.py b/src/sage/monoids/string_monoid_element.py
index e4bf95f1314..f1ac8335740 100644
--- a/src/sage/monoids/string_monoid_element.py
+++ b/src/sage/monoids/string_monoid_element.py
@@ -231,11 +231,10 @@ def __iter__(self):
             [S, H, R, U, B, B, E, R, Y]
         """
         l = len(self._element_list)
-        i=0
+        i = 0
         while i < l:
             yield self[i]
-            i+=1
-        raise StopIteration
+            i += 1
 
     def __getitem__(self, n):
         """
diff --git a/src/sage/numerical/linear_functions.pyx b/src/sage/numerical/linear_functions.pyx
index de1bf534ff9..4120cf67fdf 100644
--- a/src/sage/numerical/linear_functions.pyx
+++ b/src/sage/numerical/linear_functions.pyx
@@ -1570,7 +1570,7 @@ cdef class LinearConstraint(LinearFunctionOrConstraint):
             3 == x_2
         """
         if not self.is_equation() or self.is_trivial():
-            raise StopIteration
+            return
         term_iter = iter(self)
         lhs = next(term_iter)
         rhs = next(term_iter)
@@ -1603,7 +1603,7 @@ cdef class LinearConstraint(LinearFunctionOrConstraint):
             3 <= x_2
         """
         if not self.is_less_or_equal() or self.is_trivial():
-            raise StopIteration
+            return
         term_iter = iter(self)
         lhs = next(term_iter)
         rhs = next(term_iter)
diff --git a/src/sage/rings/number_field/number_field.py b/src/sage/rings/number_field/number_field.py
index 9dbf23b8cf2..4f36f4e0f6a 100644
--- a/src/sage/rings/number_field/number_field.py
+++ b/src/sage/rings/number_field/number_field.py
@@ -3469,8 +3469,8 @@ def primes_of_bounded_norm_iter(self, B):
             except (TypeError, AttributeError):
                 raise TypeError("%s is not valid bound on prime ideals" % B)
 
-        if B<2:
-            raise StopIteration
+        if B < 2:
+            return
 
         if self is QQ:
             for p in arith.primes(B+1):
diff --git a/src/sage/rings/rational_field.py b/src/sage/rings/rational_field.py
index 64be36a52bc..d217584dc4c 100644
--- a/src/sage/rings/rational_field.py
+++ b/src/sage/rings/rational_field.py
@@ -531,8 +531,8 @@ def primes_of_bounded_norm_iter(self, B):
         except (TypeError, AttributeError):
             raise TypeError("%s is not valid bound on prime ideals" % B)
 
-        if B<2:
-            raise StopIteration
+        if B < 2:
+            return
 
         from sage.arith.all import primes
         for p in primes(B+1):
diff --git a/src/sage/schemes/toric/points.py b/src/sage/schemes/toric/points.py
index 6d83d0af779..8ba5a8d876e 100644
--- a/src/sage/schemes/toric/points.py
+++ b/src/sage/schemes/toric/points.py
@@ -915,7 +915,7 @@ def solutions(self, inhomogeneous_equations, log_range):
         if len(log_range) <= 2:
             for log_t in self.solutions_serial(inhomogeneous_equations, log_range):
                 yield log_t
-            raise StopIteration
+            return
         # Parallelize the outermost loop of the Cartesian product
         work = [([[r]] + log_range[1:],) for r in log_range[0]]
         from sage.parallel.decorate import Parallel

From f6ce9a341fff0acb52ae10f068b21b08d728b403 Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?Fr=C3=A9d=C3=A9ric=20Chapoton?=
 <chapoton@math.univ-lyon1.fr>
Date: Wed, 17 Jan 2018 14:33:39 +0100
Subject: [PATCH 092/128] small cleanup of AbelianGroupMorphism

---
 .../abelian_gps/abelian_group_morphism.py     | 94 +++++++++++--------
 1 file changed, 55 insertions(+), 39 deletions(-)

diff --git a/src/sage/groups/abelian_gps/abelian_group_morphism.py b/src/sage/groups/abelian_gps/abelian_group_morphism.py
index c7d4688bc05..725adaf9c75 100644
--- a/src/sage/groups/abelian_gps/abelian_group_morphism.py
+++ b/src/sage/groups/abelian_gps/abelian_group_morphism.py
@@ -1,11 +1,11 @@
 """
 Homomorphisms of abelian groups
 
-TODO:
+.. TODO::
 
-- there must be a homspace first
+    - there must be a homspace first
 
-- there should be hom and Hom methods in abelian group
+    - there should be hom and Hom methods in abelian group
 
 AUTHORS:
 
@@ -28,8 +28,10 @@
 
 from sage.misc.all import prod
 
+
 def is_AbelianGroupMorphism(f):
-    return isinstance(f, AbelianGroupMorphism);
+    return isinstance(f, AbelianGroupMorphism)
+
 
 class AbelianGroupMap(Morphism):
     """
@@ -44,6 +46,7 @@ def __init__(self, parent):
     def _repr_type(self):
         return "AbelianGroup"
 
+
 class AbelianGroupMorphism_id(AbelianGroupMap):
     """
     Return the identity homomorphism from X to itself.
@@ -54,7 +57,8 @@ def __init__(self, X):
         AbelianGroupMorphism.__init__(self, X.Hom(X))
 
     def _repr_defn(self):
-        return "Identity map of "+str(X)
+        return "Identity map of " + str(X)
+
 
 class AbelianGroupMorphism(Morphism):
     """
@@ -72,11 +76,17 @@ class AbelianGroupMorphism(Morphism):
         Multiplicative Abelian group isomorphic to C2 x C3
         sage: x,y = H.gens()
 
-    ::
-
         sage: from sage.groups.abelian_gps.abelian_group_morphism import AbelianGroupMorphism
         sage: phi = AbelianGroupMorphism(H,G,[x,y],[a,b])
 
+    TESTS::
+
+        sage: G.<x,y> = AbelianGroup(2,[2,3])
+        sage: H.<a,b,c> = AbelianGroup(3,[2,3,4])
+        sage: phi = AbelianGroupMorphism(G,H,[x,y],[a,b])
+        sage: Hom(G,H) == phi.parent()
+        True
+
     AUTHORS:
 
     - David Joyner (2006-02)
@@ -100,11 +110,11 @@ class AbelianGroupMorphism(Morphism):
 #    raise TypeError, "Sorry, the list %s must generate G."%genss
 #TypeError: Sorry, the list [a*b, c^2] must generate G.
 
-    def __init__(self, G, H, genss, imgss ):
+    def __init__(self, G, H, genss, imgss):
         from sage.categories.homset import Hom
         Morphism.__init__(self, Hom(G, H))
         if len(genss) != len(imgss):
-            raise TypeError("Sorry, the lengths of %s, %s must be equal."%(genss,imgss))
+            raise TypeError("Sorry, the lengths of %s, %s must be equal." % (genss, imgss))
         self._domain = G
         self._codomain = H
         if not(G.is_abelian()):
@@ -113,14 +123,14 @@ def __init__(self, G, H, genss, imgss ):
             raise TypeError("Sorry, the groups must be abelian groups.")
         G_domain = G.subgroup(genss)
         if G_domain.order() != G.order():
-            raise TypeError("Sorry, the list %s must generate G."%genss)
+            raise TypeError("Sorry, the list %s must generate G." % genss)
         # self.domain_invs = G.gens_orders()
         # self.codomaininvs = H.gens_orders()
         self.domaingens = genss
         self.codomaingens = imgss
         for i in range(len(self.domaingens)):
             if (self.domaingens[i]).order() != (self.codomaingens[i]).order():
-                raise TypeError("Sorry, the orders of the corresponding elements in %s, %s must be equal."%(genss,imgss))
+                raise TypeError("Sorry, the orders of the corresponding elements in %s, %s must be equal." % (genss, imgss))
 
     def _gap_init_(self):
         """
@@ -140,22 +150,22 @@ def _gap_init_(self):
         """
         G  = (self.domain())._gap_init_()
         H  = (self.codomain())._gap_init_()
-        s3 = 'G:=%s; H:=%s'%(G,H)
+        s3 = 'G:=%s; H:=%s' % (G, H)
         gap.eval(s3)
-        gensG = self.domain().variable_names()                    ## the Sage group generators
+        gensG = self.domain().variable_names()  # the Sage group generators
         gensH = self.codomain().variable_names()
-        s1 = "gensG := GeneratorsOfGroup(G)"          ## the GAP group generators
+        s1 = "gensG := GeneratorsOfGroup(G)"    # the GAP group generators
         gap.eval(s1)
         s2 = "gensH := GeneratorsOfGroup(H)"
         gap.eval(s2)
-        for i in range(len(gensG)):                      ## making the Sage group gens
-           cmd = ("%s := gensG["+str(i+1)+"]")%gensG[i]  ## correspond to the Sage group gens
+        for i in range(len(gensG)):             # making the Sage group gens
+           cmd = ("%s := gensG["+str(i+1)+"]") % gensG[i]  # correspond to the Sage group gens
            gap.eval(cmd)
         for i in range(len(gensH)):
-           cmd = ("%s := gensH["+str(i+1)+"]")%gensH[i]
+           cmd = ("%s := gensH[" + str(i + 1) + "]") % gensH[i]
            gap.eval(cmd)
-        args = str(self.domaingens)+","+ str(self.codomaingens)
-        gap.eval("phi := GroupHomomorphismByImages(G,H,"+args+")")
+        args = str(self.domaingens) + "," + str(self.codomaingens)
+        gap.eval("phi := GroupHomomorphismByImages(G,H," + args + ")")
         self.gap_hom_string = "phi := GroupHomomorphismByImages(G,H,"+args+")"
         return self.gap_hom_string
 
@@ -166,8 +176,9 @@ def kernel(self):
         """
         Only works for finite groups.
 
-        TODO: not done yet; returns a gap object but should return a Sage
-        group.
+        .. TODO::
+
+            not done yet; returns a gap object but should return a Sage group.
 
         EXAMPLES::
 
@@ -180,35 +191,43 @@ def kernel(self):
             sage: phi = AbelianGroupMorphism(G,H,[x,y],[a,b])
             sage: phi.kernel()
             'Group([  ])'
+
+            sage: H = AbelianGroup(3,[2,2,2],names="abc")
+            sage: a,b,c = H.gens()
+            sage: G = AbelianGroup(2,[2,2],names="x")
+            sage: x,y = G.gens()
+            sage: phi = AbelianGroupMorphism(G,H,[x,y],[a,a])
+            sage: phi.kernel()
+            'Group([ f1*f2 ])'
         """
         cmd = self._gap_init_()
         gap.eval(cmd)
         return gap.eval("Kernel(phi)")
 
-    def image(self, J):
+    def image(self, S):
         """
-        Only works for finite groups.
+        Return the image of the subgroup ``S`` by the morphism.
+
+        This only works for finite groups.
 
-        J must be a subgroup of G. Computes the subgroup of H which is the
-        image of J.
+        INPUT:
+
+        - ``S`` -- a subgroup of the domain group ``G``
 
         EXAMPLES::
 
             sage: G = AbelianGroup(2,[2,3],names="xy")
             sage: x,y = G.gens()
+            sage: subG = G.subgroup([x])
             sage: H = AbelianGroup(3,[2,3,4],names="abc")
             sage: a,b,c = H.gens()
             sage: phi = AbelianGroupMorphism(G,H,[x,y],[a,b])
+            sage: phi.image(subG)
+            Multiplicative Abelian subgroup isomorphic to C2 generated by {a}
         """
-        G = self.domain()
-        gensJ = J.gens()
-        for g in gensJ:
-            print(g)
-            print(self(g), "\n")
-        L = [self(g) for g in gensJ]
-        return G.subgroup(L)
-
-    def _call_( self, g ):
+        return self.codomain().subgroup([self(g) for g in S.gens()])
+
+    def _call_(self, g):
         """
         Some python code for wrapping GAP's Images function but only for
         permutation groups. Returns an error if g is not in G.
@@ -225,10 +244,7 @@ def _call_( self, g ):
             sage: phi(y^2)
             b^2
         """
-        G = g.parent()
-        w = g.word_problem(self.domaingens)
-        n = len(w)
         # g.word_problem is faster in general than word_problem(g)
         gens = self.codomaingens
-        h = prod([gens[(self.domaingens).index(w[i][0])]**(w[i][1]) for i in range(n)])
-        return h
+        return prod(gens[(self.domaingens).index(wi[0])]**wi[1]
+                    for wi in g.word_problem(self.domaingens))

From 2ea979393a461ea05d7729e7df206c538f189c46 Mon Sep 17 00:00:00 2001
From: "Erik M. Bray" <erik.bray@lri.fr>
Date: Tue, 16 Jan 2018 14:58:59 +0000
Subject: [PATCH 093/128] Minor Python 3 fixes to this test:

* Explicitly close the file object at the end of the test to avoid a
  ResourceWarning
* The test involving piping to ipython exits with error code 120 on
  Python 3 due to this change to how the interpreter handles exiting
  upon a broken stdout: https://bugs.python.org/issue5319
---
 src/sage/interfaces/tests.py | 3 ++-
 1 file changed, 2 insertions(+), 1 deletion(-)

diff --git a/src/sage/interfaces/tests.py b/src/sage/interfaces/tests.py
index af9797abcdf..6bcbfef37b2 100644
--- a/src/sage/interfaces/tests.py
+++ b/src/sage/interfaces/tests.py
@@ -37,10 +37,11 @@
     0
     sage: subprocess.call("echo syntax error | gp", **kwds)
     0
-    sage: subprocess.call("echo syntax error | ipython", **kwds) in (0,1)
+    sage: subprocess.call("echo syntax error | ipython", **kwds) in (0, 1, 120)
     True
     sage: subprocess.call("echo syntax error | Singular", **kwds)
     0
+    sage: f.close()
 """
 from __future__ import print_function
 from __future__ import absolute_import

From 57e6c27771ad3885d5243f57aef11f8c0f3d8735 Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?Fr=C3=A9d=C3=A9ric=20Chapoton?=
 <chapoton@math.univ-lyon1.fr>
Date: Wed, 17 Jan 2018 20:54:13 +0100
Subject: [PATCH 094/128] trac 24539 using a polynomial tau and a variable z

---
 src/sage/rings/fraction_field.py | 7 +++----
 1 file changed, 3 insertions(+), 4 deletions(-)

diff --git a/src/sage/rings/fraction_field.py b/src/sage/rings/fraction_field.py
index ffb782a10c3..67e72a18e73 100644
--- a/src/sage/rings/fraction_field.py
+++ b/src/sage/rings/fraction_field.py
@@ -577,14 +577,13 @@ def _element_constructor_(self, x, y=None, coerce=True):
 
         Check that :trac:`24539` is fixed::
 
-            sage: var('tau')
-            tau
-            sage: R = PolynomialRing(CyclotomicField(2), 'tau').fraction_field()(
+            sage: tau = polygen(QQ, 'tau')
+            sage: R = PolynomialRing(CyclotomicField(2), 'z').fraction_field()(
             ....:     tau/(1+tau))
             Traceback (most recent call last):
             ...
             TypeError: cannot convert tau/(tau + 1)/1 to an element of Fraction
-            Field of Univariate Polynomial Ring in tau over Cyclotomic Field of
+            Field of Univariate Polynomial Ring in z over Cyclotomic Field of
             order 2 and degree 1
         """
         if y is None:

From d97ef5ab590ffcc2b566e710d6bb5dba1fdec8bd Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?Jori=20M=C3=A4ntysalo?= <jori.mantysalo@uta.fi>
Date: Thu, 18 Jan 2018 07:27:19 +0200
Subject: [PATCH 095/128] Add the map of Africa.

---
 src/sage/graphs/generators/world_map.py | 77 +++++++++++++++++++++++++
 src/sage/graphs/generic_graph.py        | 14 ++++-
 2 files changed, 90 insertions(+), 1 deletion(-)

diff --git a/src/sage/graphs/generators/world_map.py b/src/sage/graphs/generators/world_map.py
index 39e48d50d16..3dc1b6977f5 100644
--- a/src/sage/graphs/generators/world_map.py
+++ b/src/sage/graphs/generators/world_map.py
@@ -18,6 +18,83 @@
 # import from Sage library
 from sage.graphs.graph import Graph
 
+def AfricaMap(continental=False, year=2018):
+    """
+    Return African states as a graph of common border.
+
+    "African state" here is defined as an independent
+    state having the capital city in Africa. The graph
+    has an edge between those countries that have common
+    *land* border.
+
+    INPUT:
+
+    - ``continental``, a Boolean -- if set, only return states in
+      the continental Africa
+    - ``year`` -- reserved for future use
+
+    EXAMPLES::
+
+        sage: Africa = graphs.AfricaMap(); Africa
+        Africa Map: Graph on 54 vertices
+        sage: sorted(Africa.neighbors('Libya'))
+        ['Algeria', 'Chad', 'Egypt', 'Niger', 'Sudan', 'Tunisia']
+
+        sage: cont_Africa = graphs.AfricaMap(continental=True)
+        sage: cont_Africa.order()
+        48
+        sage: 'Madagaskar' in cont_Africa
+        False
+    """
+    if year != 2018:
+        raise ValueError("currently only year 2018 is implemented")
+
+    common_border = {
+     'Algeria': ['Libya', 'Mali', 'Mauritania', 'Morocco', 'Niger', 'Tunisia'],
+     'Angola': ['Namibia', 'Zambia'],
+     'Benin': ['Burkina Faso', 'Niger', 'Nigeria', 'Togo'],
+     'Botswana': ['Namibia', 'South Africa', 'Zimbabwe'],
+     'Burkina Faso': ['Ghana', 'Ivory Coast', 'Mali', 'Niger', 'Togo'],
+     'Cameroon': ['Central Africa', 'Chad', 'Equatorial Guinea', 'Gabon', 'Nigeria'],
+     'Central Africa': ['Chad', 'South Sudan', 'Sudan'],
+     'Chad': ['Libya', 'Niger', 'Nigeria', 'Sudan'],
+     'Republic of the Congo': ['Gabon', 'Cameroon', 'Central Africa', 'Angola',
+                               'Democratic Republic of the Congo'],
+     'Democratic Republic of the Congo': ['Zambia', 'South Sudan', 'Tanzania', 'Burundi',
+                                          'Rwanda', 'Uganda', 'Central Africa', 'Angola'],
+     'Djibouti': ['Eritrea', 'Ethiopia', 'Somalia'],
+     'Ethiopia': ['Eritrea', 'Kenya', 'Somalia', 'South Sudan', 'Sudan'],
+     'Gabon': ['Equatorial Guinea'],
+     'Ghana': ['Ivory Coast', 'Togo'],
+     'Guinea': ['Guinea-Bissau', 'Ivory Coast', 'Liberia', 'Sierra Leone'],
+     'Kenya': ['Somalia', 'South Sudan', 'Tanzania', 'Uganda'],
+     'Liberia': ['Ivory Coast', 'Sierra Leone'],
+     'Libya': ['Egypt', 'Niger', 'Sudan', 'Tunisia'],
+     'Mali': ['Guinea', 'Ivory Coast', 'Mauritania', 'Niger', 'Senegal'],
+     'Mozambique': ['Malawi', 'South Africa', 'Swaziland', 'Zimbabwe'],
+     'Niger': ['Nigeria'],
+     'Rwanda': ['Burundi', 'Tanzania', 'Uganda'],
+     'Senegal': ['Guinea', 'Guinea-Bissau', 'Mauritania', 'Gambia'],
+     'South Africa': ['Lesotho', 'Namibia', 'Swaziland', 'Zimbabwe'],
+     'South Sudan': ['Uganda', 'Sudan', 'Democratic Republic of the Congo'],
+     'Sudan': ['Egypt', 'Eritrea'],
+     'Tanzania': ['Burundi', 'Malawi', 'Mozambique', 'Uganda', 'Zambia'],
+     'Zambia': ['Malawi', 'Mozambique', 'Namibia', 'Zimbabwe']
+     }
+
+    no_land_border = ['Cape Verde', 'Seychelles', 'Mauritius', 'S\xc3\xa3o Tom\xc3\xa9 and Pr\xc3\xadncipe', 'Madagascar', 'Comoros']
+
+    G = Graph(common_border, format='dict_of_lists')
+
+    if continental:
+        G = G.subgraph(G.connected_component_containing_vertex('Central Africa'))
+        G.name(new="Continental Africa Map")
+    else:
+        G.add_vertices(no_land_border)
+        G.name(new="Africa Map")
+
+    return G
+
 def EuropeMap(continental=False, year=2018):
     """
     Return European states as a graph of common border.
diff --git a/src/sage/graphs/generic_graph.py b/src/sage/graphs/generic_graph.py
index 6cfe42a0952..9f71bbe0f66 100644
--- a/src/sage/graphs/generic_graph.py
+++ b/src/sage/graphs/generic_graph.py
@@ -14743,7 +14743,16 @@ def center(self, by_weight=False, algorithm=None, weight_function=None,
         - ``check_weight`` (boolean) - if ``True``, we check that the
           weight_function outputs a number for each edge.
 
-        EXAMPLES::
+        EXAMPLES:
+
+        Is Central African Republic in the center of Africa in graph theoretic
+        sense? Yes::
+
+            sage: A = graphs.AfricaMap(continental=True)
+            sage: sorted(A.center())
+            ['Cameroon', 'Central Africa']
+
+        Some other graphs. Center can be the whole graph::
 
             sage: G = graphs.DiamondGraph()
             sage: G.center()
@@ -14754,6 +14763,9 @@ def center(self, by_weight=False, algorithm=None, weight_function=None,
             sage: S = graphs.StarGraph(19)
             sage: S.center()
             [0]
+
+        TESTS::
+
             sage: G = Graph()
             sage: G.center()
             []

From 53e2802b03ab7d4de768d237b4d78db148423fe6 Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?Jori=20M=C3=A4ntysalo?= <jori.mantysalo@uta.fi>
Date: Thu, 18 Jan 2018 10:24:43 +0200
Subject: [PATCH 096/128] Link function to right place.

---
 src/sage/graphs/graph_generators.py | 4 +++-
 1 file changed, 3 insertions(+), 1 deletion(-)

diff --git a/src/sage/graphs/graph_generators.py b/src/sage/graphs/graph_generators.py
index 751d19d1833..31ebbceef25 100644
--- a/src/sage/graphs/graph_generators.py
+++ b/src/sage/graphs/graph_generators.py
@@ -336,7 +336,8 @@ def __append_to_doc(methods):
 
 __append_to_doc(
     ["WorldMap",
-     "EuropeMap"]
+     "EuropeMap",
+     "AfricaMap"]
     )
 
 __doc__ += """
@@ -2106,6 +2107,7 @@ def quadrangulations(self, order, minimum_degree=None, minimum_connectivity=None
     import sage.graphs.generators.world_map
     WorldMap = staticmethod(sage.graphs.generators.world_map.WorldMap)
     EuropeMap = staticmethod(sage.graphs.generators.world_map.EuropeMap)
+    AfricaMap = staticmethod(sage.graphs.generators.world_map.AfricaMap)
 
 ###########################################################################
 # Degree Sequence

From 7406b309e697faf79583345463cec6ebe75ad4e4 Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?Fr=C3=A9d=C3=A9ric=20Chapoton?=
 <chapoton@math.univ-lyon1.fr>
Date: Thu, 18 Jan 2018 11:37:03 +0100
Subject: [PATCH 097/128] allow easy access to m-Tamari lattices

---
 src/sage/combinat/tamari_lattices.py | 26 +++++++++++++++++++-------
 1 file changed, 19 insertions(+), 7 deletions(-)

diff --git a/src/sage/combinat/tamari_lattices.py b/src/sage/combinat/tamari_lattices.py
index 2dfba4b6b6b..5c5f2f7aaea 100644
--- a/src/sage/combinat/tamari_lattices.py
+++ b/src/sage/combinat/tamari_lattices.py
@@ -222,21 +222,26 @@ def covers(p):
                               for p in paths_in_triangle(a, b, a, b)]))
 
 
-def TamariLattice(n):
+def TamariLattice(n, m=1):
     r"""
     Return the `n`-th Tamari lattice.
 
+    Using the slope parameter `m`, one can also get the `m`-Tamari lattices.
+
     INPUT:
 
-    - `n` a nonnegative integer
+    - `n` -- a nonnegative integer (the index)
+
+    - `m` -- an optional nonnegative integer (the slope, default to 1)
 
     OUTPUT:
 
-    - a finite lattice
+    a finite lattice
 
-    The elements of the lattice are
-    :func:`Dyck paths<sage.combinat.dyck_word.DyckWord>`
-    in the `(n+1 \times n)`-rectangle.
+    In the usual case, the elements of the lattice are :func:`Dyck
+    paths<sage.combinat.dyck_word.DyckWord>` in the `(n+1 \times
+    n)`-rectangle. For a general slope `m`, the elements are Dyck
+    paths in the `(m n+1 \times n)`-rectangle.
 
     See :wikipedia:`Tamari lattice<Tamari_lattice>` for mathematical
     background.
@@ -245,5 +250,12 @@ def TamariLattice(n):
 
         sage: posets.TamariLattice(3)
         Finite lattice containing 5 elements
+
+        sage: posets.TamariLattice(3, 2)
+        Finite lattice containing 12 elements
+
+    REFERENCES:
+
+    - [BMFPR]_
     """
-    return GeneralizedTamariLattice(n + 1, n, 1)
+    return GeneralizedTamariLattice(m * n + 1, n, m)

From 2b614588ac014d88bf4592a5a2411a500df54c04 Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?Fr=C3=A9d=C3=A9ric=20Chapoton?=
 <chapoton@math.univ-lyon1.fr>
Date: Thu, 18 Jan 2018 15:49:39 +0100
Subject: [PATCH 098/128] one detail about times

---
 src/sage/combinat/tamari_lattices.py | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/src/sage/combinat/tamari_lattices.py b/src/sage/combinat/tamari_lattices.py
index 5c5f2f7aaea..39aabcee00b 100644
--- a/src/sage/combinat/tamari_lattices.py
+++ b/src/sage/combinat/tamari_lattices.py
@@ -163,7 +163,7 @@ def GeneralizedTamariLattice(a, b, m=1):
 
     - `a` and `b` coprime integers with `a \geq b`
 
-    - `m` a nonnegative integer such that `a \geq b \times m`
+    - `m` a nonnegative integer such that `a \geq b m`
 
     OUTPUT:
 

From 8f1f51d83fc198a31683740001bcffe9a3d30bbc Mon Sep 17 00:00:00 2001
From: John Cremona <john.cremona@gmail.com>
Date: Thu, 18 Jan 2018 16:10:47 +0000
Subject: [PATCH 099/128] #10017: fix deprecation warning for
 Minkowski_embedding

---
 src/sage/rings/number_field/number_field.py | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/src/sage/rings/number_field/number_field.py b/src/sage/rings/number_field/number_field.py
index 2dc757dc414..3c91e823722 100644
--- a/src/sage/rings/number_field/number_field.py
+++ b/src/sage/rings/number_field/number_field.py
@@ -5619,7 +5619,7 @@ def reduced_basis(self, prec=None):
             from sage.matrix.constructor import matrix
             T = pari(matrix(ZZ, d, d, [[(x*y).trace() for x in ZK]  for y in ZK])).qflllgram()
         else:
-            M = self.Minkowski_embedding(ZK, prec=prec)
+            M = self.minkowski_embedding(ZK, prec=prec)
             T = pari(M).qflll()
 
         return [ sum([ ZZ(T[i][j]) * ZK[j] for j in range(d)])  for i in range(d)]

From 06155e22e66116bba13c398c1f816b9669cdcb97 Mon Sep 17 00:00:00 2001
From: "Erik M. Bray" <erik.bray@lri.fr>
Date: Fri, 19 Jan 2018 08:56:20 +0000
Subject: [PATCH 100/128] Update this test, since a value is no longer returned
 in the StopIteration exception

---
 src/sage/graphs/graph_generators.py | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/src/sage/graphs/graph_generators.py b/src/sage/graphs/graph_generators.py
index dfe823ee99a..4aeaf50cf9b 100644
--- a/src/sage/graphs/graph_generators.py
+++ b/src/sage/graphs/graph_generators.py
@@ -857,7 +857,7 @@ def nauty_geng(self, options="", debug=False):
             sage: next(gen)
             Traceback (most recent call last):
             ...
-            StopIteration: Exhausted list of graphs from nauty geng
+            StopIteration
 
         A list of all graphs on 7 vertices.  This agrees with
         :oeis:`A000088`.  ::

From 607d9f8dc60a9ba3dcc666253e26e21e1b0cff19 Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?Fr=C3=A9d=C3=A9ric=20Chapoton?=
 <chapoton@math.univ-lyon1.fr>
Date: Fri, 19 Jan 2018 11:23:34 +0100
Subject: [PATCH 101/128] little cleanup of abstract trees

---
 src/sage/combinat/abstract_tree.py | 55 +++++++++++++++++-------------
 1 file changed, 31 insertions(+), 24 deletions(-)

diff --git a/src/sage/combinat/abstract_tree.py b/src/sage/combinat/abstract_tree.py
index 1bdede02f5c..4ced7fca867 100644
--- a/src/sage/combinat/abstract_tree.py
+++ b/src/sage/combinat/abstract_tree.py
@@ -72,6 +72,8 @@
 # Unfortunately Cython forbids multiple inheritance. Therefore, we do not
 # inherit from SageObject to be able to inherit from Element or a subclass
 # of it later.
+
+
 class AbstractTree(object):
     """
     Abstract Tree.
@@ -1049,7 +1051,7 @@ def node_number(self):
             5
         """
         if self.is_empty():
-            return 0
+            return Integer(0)
         else:
             return sum((i.node_number() for i in self), Integer(1))
 
@@ -1151,7 +1153,8 @@ def _ascii_art_(self):
                        /  /
                       14 15
         """
-        node_to_str = lambda t: str(t.label()) if hasattr(t, "label") else "o"
+        def node_to_str(t):
+            return str(t.label()) if hasattr(t, "label") else "o"
 
         if self.is_empty():
             from sage.typeset.ascii_art import empty_ascii_art
@@ -1159,15 +1162,15 @@ def _ascii_art_(self):
 
         from sage.typeset.ascii_art import AsciiArt
         if len(self) == 0:
-            t_repr = AsciiArt( [node_to_str(self)] )
+            t_repr = AsciiArt([node_to_str(self)])
             t_repr._root = 1
             return t_repr
         if len(self) == 1:
             repr_child = self[0]._ascii_art_()
-            sep = AsciiArt( [" "*(repr_child._root-1)] )
-            t_repr = AsciiArt( [node_to_str(self)] )
+            sep = AsciiArt([" "*(repr_child._root-1)])
+            t_repr = AsciiArt([node_to_str(self)])
             t_repr._root = 1
-            repr_root = (sep + t_repr)*(sep + AsciiArt( ["|"] ))
+            repr_root = (sep + t_repr)*(sep + AsciiArt(["|"]))
             t_repr = repr_root * repr_child
             t_repr._root = repr_child._root
             t_repr._baseline = t_repr._h - 1
@@ -1182,12 +1185,12 @@ def _ascii_art_(self):
             t_repr = l_repr.pop(0)
             acc += AsciiArt([" "]) + t_repr
             if len(l_repr) == 0:
-                lf_sep += "_"*(t_repr._root+1)
+                lf_sep += "_" * (t_repr._root + 1)
             else:
-                lf_sep += "_"*(t_repr._l+1)
+                lf_sep += "_" * (t_repr._l + 1)
             ls_sep += " "*(t_repr._root) + "/" + " "*(t_repr._l-t_repr._root)
         mid = whitesep + (len(lf_sep) - whitesep) // 2
-        node = node_to_str( self )
+        node = node_to_str(self)
         t_repr = AsciiArt([lf_sep[:mid-1] + node + lf_sep[mid+len(node)-1:], ls_sep]) * acc
         t_repr._root = mid
         t_repr._baseline = t_repr._h - 1
@@ -1302,8 +1305,8 @@ def node_to_str(t):
             tr = l_repr.pop(0)
             acc += UnicodeArt([u" "]) + tr
             if not len(l_repr):
-                lf_sep += u"─" * (tr._root) + u"╮" # + u" " * (tr._l - tr._root)
-                ls_sep += u" " * (tr._root) + u"│" # + u" " * (tr._l - tr._root)
+                lf_sep += u"─" * (tr._root) + u"╮"
+                ls_sep += u" " * (tr._root) + u"│"
             else:
                 lf_sep += u"─" * (tr._root) + u"┬" + u"─" * (tr._l - tr._root)
                 ls_sep += u" " * (tr._root) + u"│" + u" " * (tr._l - tr._root)
@@ -1316,7 +1319,7 @@ def node_to_str(t):
         t_repr._baseline = t_repr._h - 1
         return t_repr
 
-    def canonical_labelling(self,shift=1):
+    def canonical_labelling(self, shift=1):
         """
         Returns a labelled version of ``self``.
 
@@ -1345,9 +1348,9 @@ def canonical_labelling(self,shift=1):
         liste = []
         deca = 1
         for subtree in self:
-            liste += [subtree.canonical_labelling(shift+deca)]
+            liste += [subtree.canonical_labelling(shift + deca)]
             deca += subtree.node_number()
-        return LTR._element_constructor_(liste,label=shift)
+        return LTR._element_constructor_(liste, label=shift)
 
     def to_hexacode(self):
         r"""
@@ -1419,7 +1422,7 @@ def tree_factorial(self):
         """
         nb = self.node_number()
         if nb <= 1:
-            return 1
+            return Integer(1)
         return nb * prod(s.tree_factorial() for s in self)
 
     def _latex_(self):
@@ -1474,12 +1477,16 @@ def _latex_(self):
         space = " "*9
         sepspace = sep + space
         spacesep = space + sep
-        node_to_str = lambda node: " " + node + " " * (len(space) - 1 - len(node))
+
+        def node_to_str(node):
+            return " " + node + " " * (len(space) - 1 - len(node))
         # # TODO:: modify how to create nodes --> new_cmd : \\node[...] in create_node
         num = [0]
 
         def resolve(self):
-            nodes = []; matrix = []; edges = []
+            nodes = []
+            matrix = []
+            edges = []
 
             def create_node(self):
                 r"""
@@ -2034,7 +2041,7 @@ class AbstractLabelledTree(AbstractTree):
 
     .. SEEALSO:: :class:`AbstractTree`
     """
-    def __init__(self, parent, children, label = None, check = True):
+    def __init__(self, parent, children, label=None, check=True):
         """
         TESTS::
 
@@ -2100,7 +2107,7 @@ def _repr_(self):
             sage: LabelledOrderedTree([[],LabelledOrderedTree([[]], label=2)], label=3)
             3[None[], 2[None[]]]
         """
-        return "%s%s"%(self._label, self[:])
+        return "%s%s" % (self._label, self[:])
 
     def label(self, path=None):
         """
@@ -2177,7 +2184,7 @@ def leaf_labels(self):
             sage: LBT(None).leaf_labels()
             []
         """
-        return [t.label() for t in self.subtrees() if t.node_number()==1]
+        return [t.label() for t in self.subtrees() if t.node_number() == 1]
 
     def __eq__(self, other):
         """
@@ -2201,8 +2208,8 @@ def __eq__(self, other):
             sage: t1 == t2
             False
         """
-        return ( super(AbstractLabelledTree, self).__eq__(other) and
-                 self._label == other._label )
+        return (super(AbstractLabelledTree, self).__eq__(other) and
+                self._label == other._label)
 
     def _hash_(self):
         """
@@ -2292,8 +2299,8 @@ def as_digraph(self):
            Digraph on 4 vertices
         """
         from sage.graphs.digraph import DiGraph
-        resu = dict([[self.label(),
-                    [t.label() for t in self if not t.is_empty()]]])
+        resu = {self.label():
+                [t.label() for t in self if not t.is_empty()]}
         resu = DiGraph(resu, format="dict_of_lists")
         for t in self:
             if not t.is_empty():

From 188a3ab5e10c8148e3400e093193f1d673cc5632 Mon Sep 17 00:00:00 2001
From: "Erik M. Bray" <erik.bray@lri.fr>
Date: Wed, 10 Jan 2018 14:15:48 +0000
Subject: [PATCH 102/128] Minor Python 3 fix for sage.libs.flint.fmpz_poly

---
 src/sage/libs/flint/fmpz_poly.pyx | 5 +++--
 1 file changed, 3 insertions(+), 2 deletions(-)

diff --git a/src/sage/libs/flint/fmpz_poly.pyx b/src/sage/libs/flint/fmpz_poly.pyx
index fee3b2cf5b7..3d83acd4505 100644
--- a/src/sage/libs/flint/fmpz_poly.pyx
+++ b/src/sage/libs/flint/fmpz_poly.pyx
@@ -23,6 +23,7 @@ from cpython.sequence cimport *
 from cysignals.memory cimport sig_free
 
 from sage.arith.long cimport pyobject_to_long
+from sage.cpython.string cimport char_to_str, str_to_bytes
 from sage.structure.sage_object cimport SageObject
 from sage.rings.integer cimport Integer
 from sage.libs.flint.fmpz_poly cimport *
@@ -51,7 +52,7 @@ cdef class Fmpz_poly(SageObject):
         cdef long c
         cdef Integer w
         if isinstance(v, str):
-            if not fmpz_poly_set_str(self.poly, v):
+            if not fmpz_poly_set_str(self.poly, str_to_bytes(v)):
                 return
             else:
                 raise ValueError("Unable to create Fmpz_poly from that string.")
@@ -117,7 +118,7 @@ cdef class Fmpz_poly(SageObject):
             8  0 0 0 0 0 0 0 1
         """
         cdef char* ss = fmpz_poly_get_str(self.poly)
-        cdef object s = ss
+        cdef object s = char_to_str(ss)
         sig_free(ss)
         return s
 

From 40ff125111d176c05e8e13d79fb00401d93045a7 Mon Sep 17 00:00:00 2001
From: "Erik M. Bray" <erik.bray@lri.fr>
Date: Fri, 19 Jan 2018 14:12:54 +0000
Subject: [PATCH 103/128] py3: minor str/bytes fix for
 sage.graphs.generic_graph_pyx

---
 src/sage/graphs/generic_graph_pyx.pyx | 8 +++++---
 1 file changed, 5 insertions(+), 3 deletions(-)

diff --git a/src/sage/graphs/generic_graph_pyx.pyx b/src/sage/graphs/generic_graph_pyx.pyx
index cce996ed280..f31e6e2b743 100644
--- a/src/sage/graphs/generic_graph_pyx.pyx
+++ b/src/sage/graphs/generic_graph_pyx.pyx
@@ -31,6 +31,7 @@ include "sage/data_structures/binary_matrix.pxi"
 from libc.math cimport sqrt, fabs
 from libc.string cimport memset
 
+from sage.cpython.string cimport char_to_str
 from sage.libs.gmp.mpz cimport *
 from sage.misc.prandom import random
 from sage.ext.memory_allocator cimport MemoryAllocator
@@ -398,10 +399,11 @@ def int_to_binary_string(n):
         '11111010111'
     """
     cdef mpz_t i
+    cdef char* s
     mpz_init(i)
-    mpz_set_ui(i,n)
-    cdef char* s=mpz_get_str(NULL, 2, i)
-    t=str(s)
+    mpz_set_ui(i, n)
+    s = mpz_get_str(NULL, 2, i)
+    t = char_to_str(s)
     sig_free(s)
     mpz_clear(i)
     return t

From 36e36c21cab721e0d45237629a1fa3637f1aa20c Mon Sep 17 00:00:00 2001
From: "Erik M. Bray" <erik.bray@lri.fr>
Date: Fri, 19 Jan 2018 14:13:18 +0000
Subject: [PATCH 104/128] py3: minor str/bytes fix for sage.libs.homfly

---
 src/sage/libs/homfly.pyx | 16 +++++++++-------
 1 file changed, 9 insertions(+), 7 deletions(-)

diff --git a/src/sage/libs/homfly.pyx b/src/sage/libs/homfly.pyx
index a10e2c59760..172783f60c4 100644
--- a/src/sage/libs/homfly.pyx
+++ b/src/sage/libs/homfly.pyx
@@ -32,8 +32,10 @@ AUTHORS:
 
 from cysignals.signals cimport sig_on, sig_off
 
+from sage.cpython.string cimport str_to_bytes, char_to_str
+
 cdef extern from "homfly.h":
-    ctypedef int  word; 
+    ctypedef int  word;
     ctypedef signed long int sb4;
     ctypedef unsigned short int ub2;
     ctypedef signed short int sb2;
@@ -67,12 +69,12 @@ def homfly_polynomial_string(link):
         sage: homfly_polynomial_string(trefoil) # optional - libhomfly
         ' - L^-4 - 2L^-2 + M^2L^-2'
     """
-    cdef char* c_string = link
+    link = str_to_bytes(link)
     sig_on()
-    cdef char* c_output = homfly_str(c_string)
+    cdef char* c_output = homfly_str(link)
     sig_off()
-    output = <bytes> c_output
-    return output
+    return char_to_str(c_output)
+
 
 def homfly_polynomial_dict(link):
     """
@@ -93,10 +95,10 @@ def homfly_polynomial_dict(link):
         sage: homfly_polynomial_dict(trefoil) # optional - libhomfly
         {(-4, 0): -1, (-2, 0): -2, (-2, 2): 1}
     """
-    cdef char* c_string = link
+    link = str_to_bytes(link)
     cdef Term ter
     sig_on()
-    cdef Poly* c_output = homfly(c_string)
+    cdef Poly* c_output = homfly(link)
     sig_off()
     cdef int l = c_output.len
     d = dict()

From 5e094522ac87f0567921fcf67baf1aae670ca7a4 Mon Sep 17 00:00:00 2001
From: Friedrich Wiemer <friedrich.wiemer@rub.de>
Date: Fri, 19 Jan 2018 15:45:24 +0100
Subject: [PATCH 105/128] fix off by one in truth_table size check

---
 src/sage/crypto/boolean_function.pyx | 4 ++--
 1 file changed, 2 insertions(+), 2 deletions(-)

diff --git a/src/sage/crypto/boolean_function.pyx b/src/sage/crypto/boolean_function.pyx
index f3ab09ffd5e..35a1fcc1790 100644
--- a/src/sage/crypto/boolean_function.pyx
+++ b/src/sage/crypto/boolean_function.pyx
@@ -636,14 +636,14 @@ cdef class BooleanFunction(SageObject):
             1
             sage: B([1,0])
             1
-            sage: B(7)
+            sage: B(4)
             Traceback (most recent call last):
             ...
             IndexError: index out of bound
 
         """
         if isinstance(x, (int,long,Integer)):
-            if x > self._truth_table.size:
+            if x >= self._truth_table.size:
                 raise IndexError("index out of bound")
             return bitset_in(self._truth_table,x)
         elif isinstance(x, list):

From c5b0e9dba123ad0e02ffccfd902611e7f24f6877 Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?Fr=C3=A9d=C3=A9ric=20Chapoton?=
 <chapoton@math.univ-lyon1.fr>
Date: Fri, 19 Jan 2018 15:57:39 +0100
Subject: [PATCH 106/128] py3 : more care for range

---
 src/sage/geometry/pseudolines.py              |  2 +-
 .../perm_gps/partn_ref/data_structures.pyx    |  6 ++---
 src/sage/matrix/matrix_integer_dense.pyx      |  3 +--
 src/sage/matrix/special.py                    | 25 +++++++++++--------
 src/sage/plot/plot.py                         |  3 +--
 5 files changed, 21 insertions(+), 18 deletions(-)

diff --git a/src/sage/geometry/pseudolines.py b/src/sage/geometry/pseudolines.py
index 27a6dcb2f74..9e69bdba70c 100644
--- a/src/sage/geometry/pseudolines.py
+++ b/src/sage/geometry/pseudolines.py
@@ -265,7 +265,7 @@ def __init__(self, seq, encoding = "auto"):
 
             seq = deepcopy(seq)
             self._n = len(seq)
-            ordering = range(self._n)
+            ordering = list(range(self._n))
 
             self._permutations = [[] for i in range(self._n)]
 
diff --git a/src/sage/groups/perm_gps/partn_ref/data_structures.pyx b/src/sage/groups/perm_gps/partn_ref/data_structures.pyx
index 0db8f9efe4f..9a1c29923c7 100644
--- a/src/sage/groups/perm_gps/partn_ref/data_structures.pyx
+++ b/src/sage/groups/perm_gps/partn_ref/data_structures.pyx
@@ -1287,10 +1287,10 @@ def SC_test_list_perms(list L, int n, int limit, bint gap, bint limit_complain,
         ....:     m = n//3
         ....:     perm1 = list(range(2*m))
         ....:     shuffle(perm1)
-        ....:     perm1 += range(2*m,n)
-        ....:     perm2 = range(m,n)
+        ....:     perm1 += list(range(2*m,n))
+        ....:     perm2 = list(range(m,n))
         ....:     shuffle(perm2)
-        ....:     perm2 = range(m) + perm2
+        ....:     perm2 = list(range(m)) + perm2
         ....:     SC_test_list_perms([perm1, perm2], n, limit, gap, 0, contains)
         sage: for n in [4..9]:                     # long time
         ....:     for _ in range(2):                 # long time
diff --git a/src/sage/matrix/matrix_integer_dense.pyx b/src/sage/matrix/matrix_integer_dense.pyx
index 125c82a392e..36b1e180342 100644
--- a/src/sage/matrix/matrix_integer_dense.pyx
+++ b/src/sage/matrix/matrix_integer_dense.pyx
@@ -305,8 +305,7 @@ cdef class Matrix_integer_dense(Matrix_dense):
         Actually it is only necessary that the input can be coerced to a
         list, so the following also works::
 
-            sage: v = reversed(range(4)); type(v)
-            <... 'listreverseiterator'>
+            sage: v = reversed(range(4))
             sage: A(v)
             [3 2]
             [1 0]
diff --git a/src/sage/matrix/special.py b/src/sage/matrix/special.py
index ad7309185e8..c698ba5e97e 100644
--- a/src/sage/matrix/special.py
+++ b/src/sage/matrix/special.py
@@ -750,12 +750,12 @@ def diagonal_matrix(arg0=None, arg1=None, arg2=None, sparse=True):
         sage: A.parent()
         Full MatrixSpace of 0 by 0 sparse matrices over Integer Ring
 
-    Giving the entries improperly may first complain about not having a length.  ::
+    Giving the entries improperly may first complain about not being iterable::
 
         sage: diagonal_matrix(QQ, 5, 10)
         Traceback (most recent call last):
         ...
-        TypeError: unable to determine number of entries for diagonal matrix construction
+        TypeError: 'sage.rings.integer.Integer' object is not iterable
 
     Giving too many entries will raise an error. ::
 
@@ -771,16 +771,21 @@ def diagonal_matrix(arg0=None, arg1=None, arg2=None, sparse=True):
         ...
         ValueError: number of diagonal matrix entries (1) exceeds the requested matrix size (-2)
 
-    Types for the entries are limited, even though they may have a length.  ::
+    Types for the entries need to be iterable (tuple, list, vector, NumPy array,
+    etc)::
 
         sage: diagonal_matrix(x^2)
         Traceback (most recent call last):
         ...
-        TypeError: diagonal matrix entries are not a supported type (list, tuple, vector, or NumPy array)
+        TypeError: 'sage.symbolic.expression.Expression' object is not iterable
+
+    TESTS::
+
+        sage: A = diagonal_matrix(reversed(range(4)))
 
     AUTHOR:
 
-        - Rob Beezer (2011-01-11): total rewrite
+    - Rob Beezer (2011-01-11): total rewrite
     """
     # Roll arguments leftward
     #
@@ -801,6 +806,11 @@ def diagonal_matrix(arg0=None, arg1=None, arg2=None, sparse=True):
     # Formats 1, 2, 3, 4
     entries = arg0
 
+    # sanity check for entries
+    from numpy import ndarray
+    if not isinstance(entries, (list, tuple, ndarray)):
+        entries = list(entries)
+
     # Reconcile matrix size and number of entries
     try:
         nentries = len(entries)
@@ -816,11 +826,6 @@ def diagonal_matrix(arg0=None, arg1=None, arg2=None, sparse=True):
     if len(entries) == 0 and ring is None:
       ring = rings.ZZ
 
-    # Sanity check on entries (partially, e.g. a list of lists will survive this check)
-    from numpy import ndarray
-    if not any([isinstance(entries, (list, tuple)), isinstance(entries, ndarray), is_Vector(entries)]):
-        raise TypeError('diagonal matrix entries are not a supported type (list, tuple, vector, or NumPy array)')
-
     # Convert entries to a list v over a common ring
     from sage.modules.free_module_element import prepare
     v, ring = prepare(entries, ring)
diff --git a/src/sage/plot/plot.py b/src/sage/plot/plot.py
index 43229875ace..2928e093ec3 100644
--- a/src/sage/plot/plot.py
+++ b/src/sage/plot/plot.py
@@ -3292,7 +3292,7 @@ def list_plot_semilogy(data, plotjoined=False, **kwds):
 
         ::
 
-            sage: xl = [2**k for k in range(12)]; yl = range(len(xl))
+            sage: xl = [2**k for k in range(12)]; yl = list(range(len(xl)))
             sage: list_plot_semilogy(list(zip(xl,yl))) # plot empty due to (1,0)
             Graphics object consisting of 1 graphics primitive
 
@@ -3301,7 +3301,6 @@ def list_plot_semilogy(data, plotjoined=False, **kwds):
             sage: list_plot_semilogy(list(zip(xl[1:],yl[1:])))
             Graphics object consisting of 1 graphics primitive
 
-
     ::
 
         sage: list_plot_semilogy([2, 4, 6, 8, 16, 31], base=2) # with base 2

From 1aa054511b865a961036251b5cc76870d3f41ee8 Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?Fr=C3=A9d=C3=A9ric=20Chapoton?=
 <chapoton@math.univ-lyon1.fr>
Date: Fri, 19 Jan 2018 16:14:25 +0100
Subject: [PATCH 107/128] py3: using the new tags py2 and py3 in the rst files

---
 src/doc/de/tutorial/afterword.rst   | 2 +-
 src/doc/de/tutorial/tour_help.rst   | 4 ++--
 src/doc/en/tutorial/programming.rst | 2 +-
 src/doc/en/tutorial/tour_help.rst   | 4 ++--
 src/doc/es/tutorial/tour_help.rst   | 4 ++--
 src/doc/fr/tutorial/afterword.rst   | 2 +-
 src/doc/fr/tutorial/tour_help.rst   | 4 ++--
 src/doc/ja/tutorial/afterword.rst   | 2 +-
 src/doc/ja/tutorial/programming.rst | 2 +-
 src/doc/ja/tutorial/tour_help.rst   | 4 ++--
 src/doc/pt/tutorial/afterword.rst   | 2 +-
 src/doc/pt/tutorial/programming.rst | 2 +-
 src/doc/pt/tutorial/tour_help.rst   | 4 ++--
 src/doc/ru/tutorial/afterword.rst   | 2 +-
 src/doc/ru/tutorial/tour_help.rst   | 4 ++--
 src/sage/misc/sageinspect.py        | 2 +-
 src/sage/repl/load.py               | 4 ++--
 17 files changed, 25 insertions(+), 25 deletions(-)

diff --git a/src/doc/de/tutorial/afterword.rst b/src/doc/de/tutorial/afterword.rst
index 271ac92d543..cc38bcdef05 100644
--- a/src/doc/de/tutorial/afterword.rst
+++ b/src/doc/de/tutorial/afterword.rst
@@ -121,7 +121,7 @@ sein, also verhält sich Sage an manchen Stellen anders als Python.
        Rational Field
        sage: 2//3
        0
-       sage: int(2)/int(3)    # optional - python2
+       sage: int(2)/int(3)    # py2
        0
 
 -  **Große ganze Zahlen:** Python besitzt von Hause aus Unterstützung
diff --git a/src/doc/de/tutorial/tour_help.rst b/src/doc/de/tutorial/tour_help.rst
index 5e0884ad5e5..f15eb9e8ee3 100644
--- a/src/doc/de/tutorial/tour_help.rst
+++ b/src/doc/de/tutorial/tour_help.rst
@@ -262,9 +262,9 @@ verwendet haben, eine Liste (python 2):
 
 ::
 
-    sage: range(2,10)   # optional - python2
+    sage: range(2,10)   # py2
     [2, 3, 4, 5, 6, 7, 8, 9]
-    sage: list(range(2,10))   # optional - python3
+    sage: list(range(2,10))   # py3
     [2, 3, 4, 5, 6, 7, 8, 9]
 
 Hier ist eine etwas kompliziertere Liste:
diff --git a/src/doc/en/tutorial/programming.rst b/src/doc/en/tutorial/programming.rst
index a2e8147f695..febe20200f1 100644
--- a/src/doc/en/tutorial/programming.rst
+++ b/src/doc/en/tutorial/programming.rst
@@ -672,7 +672,7 @@ the Python int ``1`` is unique, but the Sage Integer ``1`` is not:
 
     sage: 1 is 2/2
     False
-    sage: int(1) is int(2)/int(2)   # optional - python2
+    sage: int(1) is int(2)/int(2)   # py2
     True
     sage: 1 is 1
     False
diff --git a/src/doc/en/tutorial/tour_help.rst b/src/doc/en/tutorial/tour_help.rst
index b290d3e949d..800777882dc 100644
--- a/src/doc/en/tutorial/tour_help.rst
+++ b/src/doc/en/tutorial/tour_help.rst
@@ -259,9 +259,9 @@ the ``range`` command that we used creates a list (in python 2):
 
 ::
 
-    sage: range(2,10)   # optional - python2
+    sage: range(2,10)   # py2
     [2, 3, 4, 5, 6, 7, 8, 9]
-    sage: list(range(2,10))   # optional - python3
+    sage: list(range(2,10))   # py3
     [2, 3, 4, 5, 6, 7, 8, 9]
 
 Here is a more complicated list:
diff --git a/src/doc/es/tutorial/tour_help.rst b/src/doc/es/tutorial/tour_help.rst
index c759d1b0fb6..efbb2880940 100644
--- a/src/doc/es/tutorial/tour_help.rst
+++ b/src/doc/es/tutorial/tour_help.rst
@@ -258,9 +258,9 @@ Por ejemplo, el comando ``range`` que hemos usado crea una lista (python 2):
 
 ::
 
-    sage: range(2,10)   # optional - python2
+    sage: range(2,10)   # py2
     [2, 3, 4, 5, 6, 7, 8, 9]
-    sage: list(range(2,10))   # optional - python3
+    sage: list(range(2,10))   # py3
     [2, 3, 4, 5, 6, 7, 8, 9]
 
 He aquí una lista más complicada:
diff --git a/src/doc/fr/tutorial/afterword.rst b/src/doc/fr/tutorial/afterword.rst
index 4355559abf2..1a470f08cfe 100644
--- a/src/doc/fr/tutorial/afterword.rst
+++ b/src/doc/fr/tutorial/afterword.rst
@@ -132,7 +132,7 @@ Aussi, Sage se comporte différemment de Python à plusieurs égards.
        Rational Field
        sage: 2//3
        0
-       sage: int(2)/int(3)   # optional - python2
+       sage: int(2)/int(3)   # py2
        0
 
 -  **Entiers longs :** Python possède nativement un support pour les entiers de
diff --git a/src/doc/fr/tutorial/tour_help.rst b/src/doc/fr/tutorial/tour_help.rst
index 9e853c11659..3ad0435ec8c 100644
--- a/src/doc/fr/tutorial/tour_help.rst
+++ b/src/doc/fr/tutorial/tour_help.rst
@@ -264,9 +264,9 @@ liste (en python 2):
 
 ::
 
-    sage: range(2,10)   # optional - python2
+    sage: range(2,10)   # py2
     [2, 3, 4, 5, 6, 7, 8, 9]
-    sage: list(range(2,10))   # optional - python3
+    sage: list(range(2,10))   # py3
     [2, 3, 4, 5, 6, 7, 8, 9]
 
 Voici un exemple plus compliqué de liste :
diff --git a/src/doc/ja/tutorial/afterword.rst b/src/doc/ja/tutorial/afterword.rst
index 47371fecdda..68403ea6216 100644
--- a/src/doc/ja/tutorial/afterword.rst
+++ b/src/doc/ja/tutorial/afterword.rst
@@ -96,7 +96,7 @@ Pythonの数学機能には混乱を招きがちな面があり，SageにはPyth
        Rational Field
        sage: 2//3
        0
-       sage: int(2)/int(3)   # optional - python2
+       sage: int(2)/int(3)   # py2
        0
 
 -  **長整数:** Python本体は，C言語由来のint型だけではなく任意精度整数をサポートしている．
diff --git a/src/doc/ja/tutorial/programming.rst b/src/doc/ja/tutorial/programming.rst
index 082853703c3..f390e5744d9 100644
--- a/src/doc/ja/tutorial/programming.rst
+++ b/src/doc/ja/tutorial/programming.rst
@@ -647,7 +647,7 @@ Sageにおける異種オブジェクト間の比較演算では，まず対象
 
     sage: 1 is 2/2
     False
-    sage: int(1) is int(2)/int(2)  # optional - python2
+    sage: int(1) is int(2)/int(2)  # py2
     True
     sage: 1 is 1
     False
diff --git a/src/doc/ja/tutorial/tour_help.rst b/src/doc/ja/tutorial/tour_help.rst
index a319a189e06..7c3994930e5 100644
--- a/src/doc/ja/tutorial/tour_help.rst
+++ b/src/doc/ja/tutorial/tour_help.rst
@@ -254,9 +254,9 @@ Sageにおける最も基本的なデータ構造はリストで，名前の示
 
 ::
 
-    sage: range(2,10)   # optional - python2
+    sage: range(2,10)   # py2
     [2, 3, 4, 5, 6, 7, 8, 9]
-    sage: list(range(2,10))   # optional - python3
+    sage: list(range(2,10))   # py3
     [2, 3, 4, 5, 6, 7, 8, 9]
 
 もう少し複雑なリストの例として:
diff --git a/src/doc/pt/tutorial/afterword.rst b/src/doc/pt/tutorial/afterword.rst
index a218562c045..5318a424766 100644
--- a/src/doc/pt/tutorial/afterword.rst
+++ b/src/doc/pt/tutorial/afterword.rst
@@ -113,7 +113,7 @@ se comporta diferentemente do Python em diversas situações.
        Rational Field
        sage: 2//3
        0
-       sage: int(2)/int(3)   # optional - python2
+       sage: int(2)/int(3)   # py2
        0
 
 -  **Inteiros longos:** O Python possui suporte nativo para inteiros
diff --git a/src/doc/pt/tutorial/programming.rst b/src/doc/pt/tutorial/programming.rst
index 71ef68e996b..82ba2c538f8 100644
--- a/src/doc/pt/tutorial/programming.rst
+++ b/src/doc/pt/tutorial/programming.rst
@@ -693,7 +693,7 @@ o int ``1`` do Python é único, mas o Inteiro ``1`` do Sage não é.
 
     sage: 1 is 2/2
     False
-    sage: int(1) is int(2)/int(2)  # optional - python2
+    sage: int(1) is int(2)/int(2)  # py2
     True
     sage: 1 is 1
     False
diff --git a/src/doc/pt/tutorial/tour_help.rst b/src/doc/pt/tutorial/tour_help.rst
index e31190a4e8c..7b4f5243ddb 100644
--- a/src/doc/pt/tutorial/tour_help.rst
+++ b/src/doc/pt/tutorial/tour_help.rst
@@ -260,9 +260,9 @@ exemplo, o comando ``range`` que usamos acima cria uma lista:
 
 ::
 
-    sage: range(2,10)   # optional - python2
+    sage: range(2,10)   # py2
     [2, 3, 4, 5, 6, 7, 8, 9]
-    sage: list(range(2,10))   # optional - python3
+    sage: list(range(2,10))   # py3
     [2, 3, 4, 5, 6, 7, 8, 9]
 
 Abaixo segue uma lista mais complicada:
diff --git a/src/doc/ru/tutorial/afterword.rst b/src/doc/ru/tutorial/afterword.rst
index 6b59856ea52..6465ec04a8f 100644
--- a/src/doc/ru/tutorial/afterword.rst
+++ b/src/doc/ru/tutorial/afterword.rst
@@ -106,7 +106,7 @@ Sage ведет себя немного другим образом.
        Rational Field
        sage: 2//3
        0
-       sage: int(2)/int(3)   # optional - python2
+       sage: int(2)/int(3)   # py2
        0
 
 -  **Большие целые числа:** Python имеет встроенную поддержку целых чисел
diff --git a/src/doc/ru/tutorial/tour_help.rst b/src/doc/ru/tutorial/tour_help.rst
index 5650c9d70f9..57d4da60df4 100644
--- a/src/doc/ru/tutorial/tour_help.rst
+++ b/src/doc/ru/tutorial/tour_help.rst
@@ -246,9 +246,9 @@ tanh, taylor``. Данная функция является хорошим сп
 
 ::
 
-    sage: range(2,10)   # optional - python2
+    sage: range(2,10)   # py2
     [2, 3, 4, 5, 6, 7, 8, 9]
-    sage: list(range(2,10))   # optional - python3
+    sage: list(range(2,10))   # py3
     [2, 3, 4, 5, 6, 7, 8, 9]
 
 Далее показан пример более сложного списка:
diff --git a/src/sage/misc/sageinspect.py b/src/sage/misc/sageinspect.py
index 9bde19dc187..61791093840 100644
--- a/src/sage/misc/sageinspect.py
+++ b/src/sage/misc/sageinspect.py
@@ -680,7 +680,7 @@ def visit_BinOp(self, node):
             sage: import ast, sage.misc.sageinspect as sms
             sage: visitor = sms.SageArgSpecVisitor()
             sage: vis = lambda x: visitor.visit(ast.parse(x).body[0].value)
-            sage: [vis(d) for d in ['(3+(2*4))', '7|8', '5^3', '7/3', '7//3', '3<<4']] #indirect doctest # optional - python2
+            sage: [vis(d) for d in ['(3+(2*4))', '7|8', '5^3', '7/3', '7//3', '3<<4']] #indirect doctest # py2
             [11, 15, 6, 2, 2, 48]
         """
         op = node.op.__class__.__name__
diff --git a/src/sage/repl/load.py b/src/sage/repl/load.py
index e54e14cf005..e6028426aef 100644
--- a/src/sage/repl/load.py
+++ b/src/sage/repl/load.py
@@ -98,9 +98,9 @@ def load(filename, globals, attach=False):
         sage: t = tmp_filename(ext='.py')
         sage: _ = open(t,'w').write("print 'hi', 2/3; z = -2/7")
         sage: z = 1
-        sage: sage.repl.load.load(t, globals())  # optional - python2
+        sage: sage.repl.load.load(t, globals())  # py2
         hi 0
-        sage: z  # optional - python2
+        sage: z  # py2
         -1
 
     A ``.sage`` file *is* preparsed::

From 8a14ff243559425fb729d12cdb25b01d2c5dac75 Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?Fr=C3=A9d=C3=A9ric=20Chapoton?=
 <chapoton@math.univ-lyon1.fr>
Date: Fri, 19 Jan 2018 17:22:41 +0100
Subject: [PATCH 108/128] py3: some care for map

---
 src/sage/graphs/generators/smallgraphs.py        | 2 +-
 src/sage/numerical/interactive_simplex_method.py | 2 +-
 src/sage/rings/polynomial/polydict.pyx           | 2 +-
 3 files changed, 3 insertions(+), 3 deletions(-)

diff --git a/src/sage/graphs/generators/smallgraphs.py b/src/sage/graphs/generators/smallgraphs.py
index 0428f69ee5b..bf86674d765 100644
--- a/src/sage/graphs/generators/smallgraphs.py
+++ b/src/sage/graphs/generators/smallgraphs.py
@@ -4902,7 +4902,7 @@ def JankoKharaghaniGraph(v):
     q = m*t+1
     K = GF(q,'alpha')
     a = K.primitive_element()
-    Ci= [[K(0)]] + map(set,[[a**(k*j+i) for j in range(t)] for i in range(m)])
+    Ci= [[K(0)]] + [set(a**(k*j+i) for j in range(t)) for i in range(m)]
     Kelem_to_Ci = {v:i for i,s in enumerate(Ci) for v in s} # maps v to [0,...,12]
 
     W = ([[0]+ [1]*(len(K))] +
diff --git a/src/sage/numerical/interactive_simplex_method.py b/src/sage/numerical/interactive_simplex_method.py
index 9ead04316ed..852ff329193 100644
--- a/src/sage/numerical/interactive_simplex_method.py
+++ b/src/sage/numerical/interactive_simplex_method.py
@@ -1631,7 +1631,7 @@ def plot_feasible_set(self, xmin=None, xmax=None, ymin=None, ymax=None,
             b = b.n().change_ring(QQ)
         F = self.feasible_set()
         if ymax is None:
-            ymax = max(map(abs, b) + [v[1] for v in F.vertices()])
+            ymax = max([abs(bb) for bb in b] + [v[1] for v in F.vertices()])
         if ymin is None:
             ymin = min([-ymax/4.0] + [v[1] for v in F.vertices()])
         if xmax is None:
diff --git a/src/sage/rings/polynomial/polydict.pyx b/src/sage/rings/polynomial/polydict.pyx
index 3ce87c8862b..b045e6bc5e5 100644
--- a/src/sage/rings/polynomial/polydict.pyx
+++ b/src/sage/rings/polynomial/polydict.pyx
@@ -303,7 +303,7 @@ cdef class PolyDict:
         return min(_min)
 
     def total_degree(PolyDict self):
-        return max([-1] + map(sum, self.__repn.keys()))
+        return max([-1] + [sum(k) for k in self.__repn.keys()])
 
     def monomial_coefficient(PolyDict self, mon):
         """

From 2008ba1318c182056afdf860f2064f66d603d738 Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?Fr=C3=A9d=C3=A9ric=20Chapoton?=
 <chapoton@math.univ-lyon1.fr>
Date: Fri, 19 Jan 2018 20:20:48 +0100
Subject: [PATCH 109/128] fix doctest

---
 src/sage/structure/parent.pyx | 3 +--
 1 file changed, 1 insertion(+), 2 deletions(-)

diff --git a/src/sage/structure/parent.pyx b/src/sage/structure/parent.pyx
index 41f7421a12e..19229698f89 100644
--- a/src/sage/structure/parent.pyx
+++ b/src/sage/structure/parent.pyx
@@ -1853,10 +1853,9 @@ cdef class Parent(sage.structure.category_object.CategoryObject):
         We check that :trac:`23184` has been resolved::
 
             sage: QQ['x', 'y']._generic_coerce_map(QQ).category_for()
-            Category of unique factorization domains
+            Category of infinite unique factorization domains
             sage: QQ[['x']].coerce_map_from(QQ).category_for()
             Category of euclidean domains
-
         """
         if isinstance(S, type):
             category = None

From e54bc124fb6007ce259bb99172657ec2dadb56fb Mon Sep 17 00:00:00 2001
From: Travis Scrimshaw <tcscrims at gmail.com>
Date: Sat, 20 Jan 2018 00:42:07 -0600
Subject: [PATCH 110/128] Catch NotImplementedError in mrange._is_finite and
 ValueError in CartesianProduct_iters.

---
 src/sage/combinat/cartesian_product.py | 22 ++++++++++++++++------
 src/sage/misc/mrange.py                |  2 +-
 2 files changed, 17 insertions(+), 7 deletions(-)

diff --git a/src/sage/combinat/cartesian_product.py b/src/sage/combinat/cartesian_product.py
index 0082a28710d..1dfb80c4473 100644
--- a/src/sage/combinat/cartesian_product.py
+++ b/src/sage/combinat/cartesian_product.py
@@ -19,8 +19,7 @@
 
 from six.moves import range
 
-from sage.categories.infinite_enumerated_sets import InfiniteEnumeratedSets
-from sage.categories.finite_enumerated_sets import FiniteEnumeratedSets
+from sage.categories.enumerated_sets import EnumeratedSets
 from sage.sets.set_from_iterator import EnumeratedSetFromIterator
 
 from inspect import isgenerator
@@ -92,7 +91,6 @@ def CartesianProduct(*iters):
     deprecation(18411, "CartesianProduct is deprecated. Use cartesian_product instead")
 
     from sage.combinat.misc import IterableFunctionCall
-    from sage.sets.set_from_iterator import EnumeratedSetFromIterator
     deprecate_ifc = False
     iiters = []
     for a in iters:
@@ -163,16 +161,28 @@ def __init__(self, *iters):
         """
         TESTS::
 
-            sage: import sage.combinat.cartesian_product as cartesian_product
-            sage: cp = cartesian_product.CartesianProduct_iters([1,2],[3,4]); cp
+            sage: from sage.combinat.cartesian_product import CartesianProduct_iters
+            sage: cp = CartesianProduct_iters([1,2],[3,4]); cp
             Cartesian product of [1, 2], [3, 4]
             sage: loads(dumps(cp)) == cp
             True
             sage: TestSuite(cp).run(skip='_test_an_element')
+
+        Check that :trac:`24558` is fixed::
+
+            sage: from sage.combinat.cartesian_product import CartesianProduct_iters
+            sage: from sage.sets.set_from_iterator import EnumeratedSetFromIterator
+            sage: I = EnumeratedSetFromIterator(Integers)
+            sage: CartesianProduct_iters(I, I)
+            Cartesian product of {0, 1, -1, 2, -2, ...}, {0, 1, -1, 2, -2, ...}
         """
         self.iters = iters
         self._mrange = xmrange_iter(iters)
-        category = FiniteEnumeratedSets() if self.is_finite() else InfiniteEnumeratedSets()
+        category = EnumeratedSets()
+        try:
+            category = category.Finite() if self.is_finite() else category.Infinite()
+        except ValueError: # Unable to determine if it is finite or not
+            pass
         def iterfunc():
             # we can not use self.__iterate__ directly because
             # that leads to an infinite recursion in __eq__
diff --git a/src/sage/misc/mrange.py b/src/sage/misc/mrange.py
index 08567bf5fd8..36cbf6c2232 100644
--- a/src/sage/misc/mrange.py
+++ b/src/sage/misc/mrange.py
@@ -82,7 +82,7 @@ def _is_finite(L, fallback=True):
 
     try:
         n = _len(L)
-    except (TypeError, AttributeError):
+    except (TypeError, AttributeError, NotImplementedError):
         # We usually assume L is finite for speed reasons
         return fallback
 

From 9a71f1c203ff4e2e075dc3b0460cdce66fdd90c0 Mon Sep 17 00:00:00 2001
From: David Coudert <david.coudert@inria.fr>
Date: Sat, 20 Jan 2018 11:22:03 +0100
Subject: [PATCH 111/128] trac #24512: restore use of networkx for the creation
 of the graph

---
 src/sage/graphs/generators/families.py | 18 ++++++++++--------
 1 file changed, 10 insertions(+), 8 deletions(-)

diff --git a/src/sage/graphs/generators/families.py b/src/sage/graphs/generators/families.py
index 131ef8f5028..de20a8469a5 100644
--- a/src/sage/graphs/generators/families.py
+++ b/src/sage/graphs/generators/families.py
@@ -2537,16 +2537,18 @@ def WheelGraph(n):
         sage: spring23.show() # long time
         sage: posdict23.show() # long time
     """
-    from sage.graphs.generators.basic import CycleGraph
     if n < 4:
-        G = CycleGraph(n)
+        from sage.graphs.generators.basic import CycleGraph
+        pos_dict = CycleGraph(n).get_pos()
     else:
-        G = CycleGraph(n-1)
-        G.relabel(perm=list(range(1, n)), inplace=True)
-        G.add_edges([(0, i) for i in range(1, n)])
-        G._pos[0] = (0, 0)
-    G.name("Wheel graph")
-    return G
+        pos_dict = {0: (0, 0)}
+        for i in range(1,n):
+            x = float(cos((pi/2) + ((2*pi)/(n-1))*(i-1)))
+            y = float(sin((pi/2) + ((2*pi)/(n-1))*(i-1)))
+            pos_dict[i] = (x,y)
+    import networkx
+    G = networkx.wheel_graph(n)
+    return Graph(G, pos=pos_dict, name="Wheel graph")
 
 def WindmillGraph(k, n):
     r"""

From 7e3c6f7072a30a372e11b29e78690a6809b49571 Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?Fr=C3=A9d=C3=A9ric=20Chapoton?=
 <chapoton@math.univ-lyon1.fr>
Date: Sat, 20 Jan 2018 11:47:01 +0100
Subject: [PATCH 112/128] py3: get rid of __cmp__ for words (last one in
 combinat folder)

---
 src/sage/combinat/words/abstract_word.py   | 159 +++++++--------------
 src/sage/combinat/words/word_datatypes.pyx |  69 +++------
 2 files changed, 71 insertions(+), 157 deletions(-)

diff --git a/src/sage/combinat/words/abstract_word.py b/src/sage/combinat/words/abstract_word.py
index 4dd0b0f092e..48cd1d10524 100644
--- a/src/sage/combinat/words/abstract_word.py
+++ b/src/sage/combinat/words/abstract_word.py
@@ -39,8 +39,11 @@
 from sage.combinat.words.word_options import word_options
 from itertools import islice, groupby
 from sage.rings.all import Integers, ZZ, Infinity
+from sage.structure.richcmp import (richcmp_method, rich_to_bool,
+                                    richcmp, op_LT, op_GT)
 
 
+@richcmp_method
 class Word_class(SageObject):
     def parent(self):
         r"""
@@ -258,93 +261,43 @@ def __len__(self):
             raise TypeError(msg)
         return int(L)
 
-    def __cmp__(self, other):
+    def __richcmp__(self, other, op):
         r"""
-        Compares two words lexicographically according to the ordering
-        defined by the parent of self. This corresponds to Python's built-in
+        Compare two words lexicographically according to the ordering
+        defined by the parent of ``self``.
+
+        This corresponds to Python's built-in
         ordering when no parent nor alphabet was used to defined the word.
 
         Provides for all normal comparison operators.
 
         .. NOTE::
 
-            This function will not terminate if self and other are equal
-            infinite words!
+            This function will not terminate if ``self`` and ``other``
+            are equal infinite words!
 
         EXAMPLES::
 
             sage: W = Word
             sage: from itertools import count
-            sage: W(range(1,10)).__cmp__(W(range(10))) > 0
+            sage: W(range(1,10)) > W(range(10))
             True
-            sage: W(range(10)).__cmp__(W(range(1,10))) < 0
+            sage: W(range(10)) < W(range(1,10))
             True
-            sage: W(range(10)).__cmp__(W(range(10))) == 0
+            sage: W(range(10)) == W(range(10))
             True
-            sage: W(range(10)).__cmp__(W(count())) < 0
+            sage: W(range(10)) < W(count())
             True
-            sage: W(count()).__cmp__(W(range(10))) > 0
+            sage: W(count()) > W(range(10))
             True
 
         ::
 
             sage: W = Words(['a', 'b', 'c'])
-            sage: W('a').__cmp__(W([]))
-            1
-            sage: W([]).__cmp__(W('a'))
-            -1
-        """
-        if not isinstance(other, Word_class):
-            return NotImplemented
-        self_it, other_it = iter(self), iter(other)
-        cmp_key = self._parent.sortkey_letters
-        while True:
-            try:
-                cs = next(self_it)
-            except StopIteration:
-                try:
-                    co = next(other_it)
-                except StopIteration:
-                    # If both self_it and other_it are exhausted then
-                    # self == other. Return 0.
-                    return 0
-                else:
-                    # If self_it is exhausted, but not other_it, then
-                    # self is a proper prefix of other: return -1
-                    return -1
-            else:
-                try:
-                    co = next(other_it)
-                except StopIteration:
-                    # If self_it is not exhausted but other_it is, then
-                    # other is a proper prefix of self: return 1.
-                    return 1
-                else:
-                    key_cs = cmp_key(cs)
-                    key_co = cmp_key(co)
-                    if key_cs < key_co:
-                        return -1
-                    elif key_cs > key_co:
-                        return 1
-
-    def __eq__(self, other):
-        r"""
-        Returns True if self is equal to other and False otherwise.
-
-        INPUT:
-
-        - ``other`` - a word
-
-        OUTPUT:
-
-            boolean
-
-        .. NOTE::
-
-            This function will not terminate if self and other are equal
-            infinite words!
-
-        EXAMPLES::
+            sage: W('a') > W([])
+            True
+            sage: W([]) < W('a')
+            True
 
             sage: Word('abc') == Word(['a','b','c'])
             True
@@ -369,11 +322,21 @@ def __eq__(self, other):
             sage: Word(lambda n:n) == Word(range(20))
             False
 
-        Beware the following does not halt!::
+        Beware the following does not halt! ::
 
             sage: from itertools import count
             sage: Word(lambda n:n) == Word(count()) #not tested
 
+        Examples for unequality::
+
+            sage: w = Word(range(10))
+            sage: z = Word(range(10))
+            sage: w != z
+            False
+            sage: u = Word(range(12))
+            sage: u != w
+            True
+
         TESTS::
 
             sage: Word(count())[:20] == Word(range(20))
@@ -388,6 +351,7 @@ def __eq__(self, other):
         if not isinstance(other, Word_class):
             return NotImplemented
         self_it, other_it = iter(self), iter(other)
+        cmp_key = self._parent.sortkey_letters
         while True:
             try:
                 cs = next(self_it)
@@ -397,50 +361,25 @@ def __eq__(self, other):
                 except StopIteration:
                     # If both self_it and other_it are exhausted then
                     # self == other. Return 0.
-                    return True
+                    return rich_to_bool(op, 0)
                 else:
                     # If self_it is exhausted, but not other_it, then
                     # self is a proper prefix of other: return -1
-                    return False
+                    return rich_to_bool(op, -1)
             else:
                 try:
                     co = next(other_it)
                 except StopIteration:
                     # If self_it is not exhausted but other_it is, then
                     # other is a proper prefix of self: return 1.
-                    return False
+                    return rich_to_bool(op, 1)
                 else:
-                    if cs != co:
-                        return False
-
-    def __ne__(self, other):
-        r"""
-        Returns True if self is not equal to other and False otherwise.
-
-        INPUT:
-
-        - ``other`` - a word
-
-        OUTPUT:
-
-            boolean
-
-        .. NOTE::
-
-            This function will not terminate if self and other are equal
-            infinite words!
-
-        EXAMPLES::
-
-            sage: w = Word(range(10))
-            sage: z = Word(range(10))
-            sage: w != z
-            False
-            sage: u = Word(range(12))
-            sage: u != w
-            True
-        """
-        return not self == other
+                    key_cs = cmp_key(cs)
+                    key_co = cmp_key(co)
+                    if key_cs < key_co:
+                        return rich_to_bool(op, -1)
+                    elif key_cs > key_co:
+                        return rich_to_bool(op, 1)
 
     def _longest_common_prefix_iterator(self, other):
         r"""
@@ -770,7 +709,7 @@ def lex_less(self, other):
             sage: t[:10].lex_less(t)
             True
         """
-        return self < other
+        return richcmp(self, other, op_LT)
 
     def lex_greater(self, other):
         r"""
@@ -800,9 +739,9 @@ def lex_greater(self, other):
             sage: t.lex_greater(t[:10])
             True
         """
-        return self > other
+        return richcmp(self, other, op_GT)
 
-    def apply_morphism(self,morphism):
+    def apply_morphism(self, morphism):
         r"""
         Returns the word obtained by applying the morphism to self.
 
@@ -874,13 +813,14 @@ def _delta_iterator(self):
 
     def delta(self):
         r"""
-        Returns the image of self under the delta morphism. This is the
-        word composed of the length of consecutive runs of the same letter
-        in a given word.
+        Returns the image of self under the delta morphism.
+
+        This is the word composed of the length of consecutive runs of
+        the same letter in a given word.
 
         OUTPUT:
 
-            Word over integers
+        Word over integers
 
         EXAMPLES:
 
@@ -903,7 +843,8 @@ def delta(self):
             word: 1211222112112112221122211222112112112221...
         """
         from sage.combinat.words.word import Word
-        return Word(self._delta_iterator())
+        from sage.rings.semirings.non_negative_integer_semiring import NN
+        return Word(self._delta_iterator(), alphabet=NN)
 
     def _iterated_right_palindromic_closure_iterator(self, f=None):
         r"""
diff --git a/src/sage/combinat/words/word_datatypes.pyx b/src/sage/combinat/words/word_datatypes.pyx
index 9d9654f7270..5ba87408f43 100644
--- a/src/sage/combinat/words/word_datatypes.pyx
+++ b/src/sage/combinat/words/word_datatypes.pyx
@@ -174,24 +174,15 @@ cdef class WordDatatype_list(WordDatatype):
 
         http://docs.cython.org/docs/special_methods.html
         """
-        if op == Py_EQ:
-            if isinstance(other, WordDatatype_list):
+        if isinstance(other, WordDatatype_list):
+            if op == Py_EQ:
                 return self._data == other._data
-            else:
-                # Otherwise, force FiniteWord_class.__eq__ to do it
-                # (if we don't force it, then __cmp__ is called before)
-                from sage.combinat.words.word import FiniteWord_class
-                return FiniteWord_class.__eq__(self, other)
-        elif op == Py_NE:
-            if isinstance(other, WordDatatype_list):
+            elif op == Py_NE:
                 return self._data != other._data
-            else:
-                # Otherwise, force FiniteWord_class.__eq__ to do it
-                # (if we don't force it, then __cmp__ is called before)
-                from sage.combinat.words.word import FiniteWord_class
-                return not FiniteWord_class.__eq__(self,other)
-        else:
-            return NotImplemented
+
+        # Otherwise, force FiniteWord_class.__richcmp__ to do it
+        from sage.combinat.words.word import FiniteWord_class
+        return FiniteWord_class.__richcmp__(self, other, op)
 
     def __len__(self):
         r"""
@@ -385,24 +376,15 @@ cdef class WordDatatype_str(WordDatatype):
 
         http://docs.cython.org/docs/special_methods.html
         """
-        if op == Py_EQ:
-            if isinstance(other, WordDatatype_str):
+        if isinstance(other, WordDatatype_str):
+            if op == Py_EQ:
                 return self._data == other._data
-            else:
-                # Otherwise, force FiniteWord_class.__eq__ to do it
-                # (if we don't force it, then __cmp__ is called before)
-                from sage.combinat.words.word import FiniteWord_class
-                return FiniteWord_class.__eq__(self,other)
-        elif op == Py_NE:
-            if isinstance(other, WordDatatype_str):
+            elif op == Py_NE:
                 return self._data != other._data
-            else:
-                # Otherwise, force FiniteWord_class.__eq__ to do it
-                # (if we don't force it, then __cmp__ is called before)
-                from sage.combinat.words.word import FiniteWord_class
-                return not FiniteWord_class.__eq__(self,other)
-        else:
-            return NotImplemented
+
+        # Otherwise, force FiniteWord_class.__richcmp__ to do it
+        from sage.combinat.words.word import FiniteWord_class
+        return FiniteWord_class.__richcmp__(self, other, op)
 
     def __contains__(self, a):
         r"""
@@ -998,24 +980,15 @@ cdef class WordDatatype_tuple(WordDatatype):
 
         http://docs.cython.org/docs/special_methods.html
         """
-        if op == Py_EQ:
-            if isinstance(other, WordDatatype_tuple):
+        if isinstance(other, WordDatatype_tuple):
+            if op == Py_EQ:
                 return self._data == other._data
-            else:
-                # Otherwise, force FiniteWord_class.__eq__ to do it
-                # (if we don't force it, then __cmp__ is called before)
-                from sage.combinat.words.word import FiniteWord_class
-                return FiniteWord_class.__eq__(self,other)
-        elif op == Py_NE:
-            if isinstance(other, WordDatatype_tuple):
+            elif op == Py_NE:
                 return self._data != other._data
-            else:
-                # Otherwise, force FiniteWord_class.__eq__ to do it
-                # (if we don't force it, then __cmp__ is called before)
-                from sage.combinat.words.word import FiniteWord_class
-                return not FiniteWord_class.__eq__(self,other)
-        else:
-            return NotImplemented
+
+        # Otherwise, force FiniteWord_class.__richcmp__ to do it
+        from sage.combinat.words.word import FiniteWord_class
+        return FiniteWord_class.__richcmp__(self, other, op)
 
     def __len__(self):
         r"""

From 06bd4a39cc55b52a110b4680c652fe76caeb58fb Mon Sep 17 00:00:00 2001
From: David Coudert <david.coudert@inria.fr>
Date: Sat, 20 Jan 2018 15:19:35 +0100
Subject: [PATCH 113/128] trac #24512: stop using networkx in wheelgraph

---
 src/sage/graphs/generators/families.py | 18 ++++++++----------
 1 file changed, 8 insertions(+), 10 deletions(-)

diff --git a/src/sage/graphs/generators/families.py b/src/sage/graphs/generators/families.py
index de20a8469a5..131ef8f5028 100644
--- a/src/sage/graphs/generators/families.py
+++ b/src/sage/graphs/generators/families.py
@@ -2537,18 +2537,16 @@ def WheelGraph(n):
         sage: spring23.show() # long time
         sage: posdict23.show() # long time
     """
+    from sage.graphs.generators.basic import CycleGraph
     if n < 4:
-        from sage.graphs.generators.basic import CycleGraph
-        pos_dict = CycleGraph(n).get_pos()
+        G = CycleGraph(n)
     else:
-        pos_dict = {0: (0, 0)}
-        for i in range(1,n):
-            x = float(cos((pi/2) + ((2*pi)/(n-1))*(i-1)))
-            y = float(sin((pi/2) + ((2*pi)/(n-1))*(i-1)))
-            pos_dict[i] = (x,y)
-    import networkx
-    G = networkx.wheel_graph(n)
-    return Graph(G, pos=pos_dict, name="Wheel graph")
+        G = CycleGraph(n-1)
+        G.relabel(perm=list(range(1, n)), inplace=True)
+        G.add_edges([(0, i) for i in range(1, n)])
+        G._pos[0] = (0, 0)
+    G.name("Wheel graph")
+    return G
 
 def WindmillGraph(k, n):
     r"""

From 01f35a35647930d9d8e2f3a044551e4b7ac6f7f6 Mon Sep 17 00:00:00 2001
From: David Coudert <david.coudert@inria.fr>
Date: Sat, 20 Jan 2018 15:40:20 +0100
Subject: [PATCH 114/128] trac #24512: fix doctests in graphic_matroid

---
 src/sage/matroids/graphic_matroid.py | 12 +++++++-----
 1 file changed, 7 insertions(+), 5 deletions(-)

diff --git a/src/sage/matroids/graphic_matroid.py b/src/sage/matroids/graphic_matroid.py
index e4667b27ecc..8586af297ad 100644
--- a/src/sage/matroids/graphic_matroid.py
+++ b/src/sage/matroids/graphic_matroid.py
@@ -1079,9 +1079,9 @@ def _is_isomorphic(self, other, certificate=False):
             sage: M = Matroid(Graph(edgelist))
             sage: N = Matroid(range(6), graphs.WheelGraph(4))
             sage: M._is_isomorphic(N, certificate=True)
-            (True, {'a': 0, 'b': 1, 'c': 2, 'd': 3, 'e': 4, 'f': 5})
+            (True, {'a': 2, 'b': 4, 'c': 5, 'd': 0, 'e': 1, 'f': 3})
             sage: N._is_isomorphic(M, certificate=True)
-            (True, {0: 'a', 1: 'b', 2: 'c', 3: 'd', 4: 'e', 5: 'f'})
+            (True, {0: 'd', 1: 'e', 2: 'a', 3: 'f', 4: 'b', 5: 'c'})
             sage: O = Matroid(range(6), graphs.CycleGraph(6))
             sage: M._is_isomorphic(O)
             False
@@ -1145,7 +1145,7 @@ def _isomorphism(self, other):
             sage: M = Matroid(Graph(edgelist))
             sage: N = Matroid(range(6), graphs.WheelGraph(4))
             sage: M._isomorphism(N)
-            {'a': 0, 'b': 1, 'c': 2, 'd': 3, 'e': 4, 'f': 5}
+            {'a': 2, 'b': 4, 'c': 5, 'd': 0, 'e': 1, 'f': 3}
             sage: O = Matroid(Graph(edgelist), regular=True)
             sage: M._isomorphism(O)
             {'a': 'a', 'b': 'c', 'c': 'b', 'd': 'e', 'e': 'd', 'f': 'f'}
@@ -1497,7 +1497,8 @@ def graphic_coextension(self, u, v=None, X=None, element=None):
 
         EXAMPLES::
 
-            sage: M = Matroid(range(8), graphs.WheelGraph(5))
+            sage: G = Graph([(0, 1, 0), (0, 2, 1), (0, 3, 2), (0, 4, 3), (1, 2, 4), (1, 4, 5), (2, 3, 6), (3, 4, 7)])
+            sage: M = Matroid(G)
             sage: M1 = M.graphic_coextension(0, X=[1,2], element='a')
             sage: M1.graph().edges()
             [(0, 1, 0),
@@ -1625,7 +1626,8 @@ def graphic_coextensions(self, vertices=None, v=None, element=None, cosimple=Fal
 
         EXAMPLES::
 
-            sage: M = Matroid(range(8), graphs.WheelGraph(5))
+            sage: G = Graph([(0, 1), (0, 2), (0, 3), (0, 4), (1, 2), (1, 4), (2, 3), (3, 4)])
+            sage: M = Matroid(range(8), G)
             sage: I = M.graphic_coextensions(vertices=[0], element='a')
             sage: for N in I:
             ....:     N.graph().edges_incident(0)

From 31eb6c72f542ababb2c42c074bd379ad3ebfaf51 Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?Fr=C3=A9d=C3=A9ric=20Chapoton?=
 <chapoton@math.univ-lyon1.fr>
Date: Sat, 20 Jan 2018 18:09:12 +0100
Subject: [PATCH 115/128] trac 24569 undo change in plot

---
 src/sage/plot/plot.py | 3 ++-
 1 file changed, 2 insertions(+), 1 deletion(-)

diff --git a/src/sage/plot/plot.py b/src/sage/plot/plot.py
index 2928e093ec3..33d22191655 100644
--- a/src/sage/plot/plot.py
+++ b/src/sage/plot/plot.py
@@ -3292,7 +3292,7 @@ def list_plot_semilogy(data, plotjoined=False, **kwds):
 
         ::
 
-            sage: xl = [2**k for k in range(12)]; yl = list(range(len(xl)))
+            sage: xl = [2**k for k in range(12)]; yl = range(len(xl))
             sage: list_plot_semilogy(list(zip(xl,yl))) # plot empty due to (1,0)
             Graphics object consisting of 1 graphics primitive
 
@@ -3314,6 +3314,7 @@ def list_plot_semilogy(data, plotjoined=False, **kwds):
     """
     return list_plot(data, plotjoined=plotjoined, scale='semilogy', **kwds)
 
+
 def to_float_list(v):
     """
     Given a list or tuple or iterable v, coerce each element of v to a

From 79c3b7a524455c3f2e58a6a13d4853abc5d41d80 Mon Sep 17 00:00:00 2001
From: Jeroen Demeyer <jdemeyer@cage.ugent.be>
Date: Sun, 21 Jan 2018 17:06:31 +0100
Subject: [PATCH 116/128] Preparations for adding a gfortran package

---
 build/pkgs/gcc/spkg-install |  3 +-
 configure.ac                | 13 +++++-
 m4/ax_compiler_vendor.m4    | 88 +++++++++++++++++++++++++++++++++++++
 3 files changed, 101 insertions(+), 3 deletions(-)
 create mode 100644 m4/ax_compiler_vendor.m4

diff --git a/build/pkgs/gcc/spkg-install b/build/pkgs/gcc/spkg-install
index e9a068f8675..a346ae73af0 100644
--- a/build/pkgs/gcc/spkg-install
+++ b/build/pkgs/gcc/spkg-install
@@ -123,8 +123,9 @@ $MAKE install
 
 
 # Force re-installation of gmp, mpir, mpfr and mpc with the GCC we just built.
+# Also mark gfortran as not installed.
 cd "$SAGE_SPKG_INST"
-rm -f gmp-* mpir-* mpfr-* mpc-*
+rm -f gmp-* mpir-* mpfr-* mpc-* gfortran-*
 
 # Force re-configuration: the next time that "make" is run, we don't
 # want GCC to be built again, see Trac #19324
diff --git a/configure.ac b/configure.ac
index a6900c297ad..fbe94eb4ff7 100644
--- a/configure.ac
+++ b/configure.ac
@@ -70,7 +70,7 @@ AM_INIT_AUTOMAKE([1.9.6 foreign])
 # Allow "configure --disable-maintainer-mode" to disable timestamp checking
 AM_MAINTAINER_MODE([enable])
 
-dnl Make sure the path to our own m4 macros is always properly set 
+dnl Make sure the path to our own m4 macros is always properly set
 dnl and doesn't depend on how autoconf is called.
 AC_CONFIG_MACRO_DIR([m4])
 
@@ -212,7 +212,7 @@ then
     AC_MSG_NOTICE([On some systems it can be found in /usr/ccs/bin])
     AC_MSG_NOTICE([See also http://www.gnu.org/software/m4/])
     AC_MSG_ERROR([Exiting, as the macro processor 'm4' can not be found.])
-fi 
+fi
 
 AC_CHECK_PROG(found_ranlib, ranlib, yes, no)
 if test x$found_ranlib != xyes
@@ -355,6 +355,8 @@ AC_DEFUN([SAGE_MUST_INSTALL_GCC], [
 
 # By default, do not install GCC
 need_to_install_gcc=no
+# or GFORTRAN
+need_to_install_gfortran=no
 
 if test -f "$SAGE_LOCAL/bin/gcc"; then
     # Special value for SAGE_INSTALL_GCC if GCC is already installed
@@ -381,6 +383,13 @@ AC_SUBST(CC)
 AC_SUBST(CXX)
 AC_SUBST(FC)
 
+# Figuring out if we are using clang instead of gcc.
+AX_COMPILER_VENDOR()
+IS_REALLY_GCC=no
+if test "x$ax_cv_c_compiler_vendor" = xgnu ; then
+    IS_REALLY_GCC=yes
+fi
+
 # On darwin, also set the objective C/C++ compilers
 # Checking on all platforms doesn't hurt and stops
 # configure from sending an error when run on non-darwin.
diff --git a/m4/ax_compiler_vendor.m4 b/m4/ax_compiler_vendor.m4
new file mode 100644
index 00000000000..0256bbaf82c
--- /dev/null
+++ b/m4/ax_compiler_vendor.m4
@@ -0,0 +1,88 @@
+# ===========================================================================
+#    https://www.gnu.org/software/autoconf-archive/ax_compiler_vendor.html
+# ===========================================================================
+#
+# SYNOPSIS
+#
+#   AX_COMPILER_VENDOR
+#
+# DESCRIPTION
+#
+#   Determine the vendor of the C/C++ compiler, e.g., gnu, intel, ibm, sun,
+#   hp, borland, comeau, dec, cray, kai, lcc, metrowerks, sgi, microsoft,
+#   watcom, etc. The vendor is returned in the cache variable
+#   $ax_cv_c_compiler_vendor for C and $ax_cv_cxx_compiler_vendor for C++.
+#
+# LICENSE
+#
+#   Copyright (c) 2008 Steven G. Johnson <stevenj@alum.mit.edu>
+#   Copyright (c) 2008 Matteo Frigo
+#
+#   This program is free software: you can redistribute it and/or modify it
+#   under the terms of the GNU General Public License as published by the
+#   Free Software Foundation, either version 3 of the License, or (at your
+#   option) any later version.
+#
+#   This program is distributed in the hope that it will be useful, but
+#   WITHOUT ANY WARRANTY; without even the implied warranty of
+#   MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General
+#   Public License for more details.
+#
+#   You should have received a copy of the GNU General Public License along
+#   with this program. If not, see <https://www.gnu.org/licenses/>.
+#
+#   As a special exception, the respective Autoconf Macro's copyright owner
+#   gives unlimited permission to copy, distribute and modify the configure
+#   scripts that are the output of Autoconf when processing the Macro. You
+#   need not follow the terms of the GNU General Public License when using
+#   or distributing such scripts, even though portions of the text of the
+#   Macro appear in them. The GNU General Public License (GPL) does govern
+#   all other use of the material that constitutes the Autoconf Macro.
+#
+#   This special exception to the GPL applies to versions of the Autoconf
+#   Macro released by the Autoconf Archive. When you make and distribute a
+#   modified version of the Autoconf Macro, you may extend this special
+#   exception to the GPL to apply to your modified version as well.
+
+#serial 16
+
+AC_DEFUN([AX_COMPILER_VENDOR],
+[AC_CACHE_CHECK([for _AC_LANG compiler vendor], ax_cv_[]_AC_LANG_ABBREV[]_compiler_vendor,
+  dnl Please add if possible support to ax_compiler_version.m4
+  [# note: don't check for gcc first since some other compilers define __GNUC__
+  vendors="intel:     __ICC,__ECC,__INTEL_COMPILER
+           ibm:       __xlc__,__xlC__,__IBMC__,__IBMCPP__
+           pathscale: __PATHCC__,__PATHSCALE__
+           clang:     __clang__
+           cray:      _CRAYC
+           fujitsu:   __FUJITSU
+           gnu:       __GNUC__
+           sun:       __SUNPRO_C,__SUNPRO_CC
+           hp:        __HP_cc,__HP_aCC
+           dec:       __DECC,__DECCXX,__DECC_VER,__DECCXX_VER
+           borland:   __BORLANDC__,__CODEGEARC__,__TURBOC__
+           comeau:    __COMO__
+           kai:       __KCC
+           lcc:       __LCC__
+           sgi:       __sgi,sgi
+           microsoft: _MSC_VER
+           metrowerks: __MWERKS__
+           watcom:    __WATCOMC__
+           portland:  __PGI
+	   tcc:       __TINYC__
+           unknown:   UNKNOWN"
+  for ventest in $vendors; do
+    case $ventest in
+      *:) vendor=$ventest; continue ;;
+      *)  vencpp="defined("`echo $ventest | sed 's/,/) || defined(/g'`")" ;;
+    esac
+    AC_COMPILE_IFELSE([AC_LANG_PROGRAM(,[
+      #if !($vencpp)
+        thisisanerror;
+      #endif
+    ])], [break])
+  done
+  ax_cv_[]_AC_LANG_ABBREV[]_compiler_vendor=`echo $vendor | cut -d: -f1`
+ ])
+])
+

From dfedfbf362f6a8a71f3f17a1bccf691c2254b578 Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?Fr=C3=A9d=C3=A9ric=20Chapoton?=
 <chapoton@math.univ-lyon1.fr>
Date: Sun, 21 Jan 2018 21:13:09 +0100
Subject: [PATCH 117/128] a nice set of typos

---
 src/sage/algebras/orlik_solomon.py                         | 2 +-
 src/sage/calculus/desolvers.py                             | 2 +-
 src/sage/categories/category.py                            | 2 +-
 src/sage/coding/guruswami_sudan/gs_decoder.py              | 2 +-
 src/sage/combinat/binary_recurrence_sequences.py           | 2 +-
 src/sage/combinat/cluster_algebra_quiver/cluster_seed.py   | 3 ++-
 src/sage/combinat/composition.py                           | 2 +-
 src/sage/combinat/root_system/root_lattice_realizations.py | 2 +-
 src/sage/data_structures/blas_dict.pyx                     | 2 +-
 src/sage/databases/sql_db.py                               | 2 +-
 src/sage/dynamics/arithmetic_dynamics/projective_ds.py     | 2 +-
 src/sage/dynamics/interval_exchanges/constructors.py       | 2 +-
 src/sage/game_theory/normal_form_game.py                   | 2 +-
 src/sage/geometry/polyhedron/base.py                       | 2 +-
 src/sage/geometry/polyhedron/ppl_lattice_polygon.py        | 2 +-
 src/sage/graphs/centrality.pyx                             | 6 +++---
 src/sage/graphs/generators/chessboard.py                   | 2 +-
 src/sage/graphs/generic_graph.py                           | 2 +-
 src/sage/graphs/strongly_regular_db.pyx                    | 2 +-
 src/sage/homology/simplicial_complex.py                    | 2 +-
 src/sage/libs/gap/element.pyx                              | 2 +-
 src/sage/libs/gap/util.pyx                                 | 2 +-
 src/sage/libs/pynac/pynac.pyx                              | 2 +-
 src/sage/manifolds/differentiable/automorphismfield.py     | 2 +-
 src/sage/manifolds/differentiable/integrated_curve.py      | 2 +-
 src/sage/matrix/matrix_rational_dense.pyx                  | 2 +-
 src/sage/matroids/graphic_matroid.py                       | 2 +-
 src/sage/matroids/set_system.pyx                           | 2 +-
 src/sage/numerical/backends/cvxopt_backend.pyx             | 2 +-
 src/sage/numerical/backends/glpk_backend.pyx               | 4 ++--
 src/sage/numerical/backends/ppl_backend.pyx                | 2 +-
 src/sage/plot/plot3d/platonic.py                           | 4 ++--
 src/sage/plot/plot3d/shapes2.py                            | 2 +-
 src/sage/plot/plot3d/tachyon.py                            | 2 +-
 src/sage/rings/complex_mpc.pyx                             | 2 +-
 src/sage/rings/invariant_theory.py                         | 3 ++-
 src/sage/rings/padics/padic_generic_element.pyx            | 4 ++--
 src/sage/schemes/elliptic_curves/gal_reps_number_field.py  | 2 +-
 src/sage/schemes/elliptic_curves/height.py                 | 2 +-
 src/sage/schemes/toric/sheaf/klyachko.py                   | 2 +-
 src/sage/sets/recursively_enumerated_set.pyx               | 5 +++--
 src/sage/tensor/modules/free_module_linear_group.py        | 4 ++--
 42 files changed, 52 insertions(+), 49 deletions(-)

diff --git a/src/sage/algebras/orlik_solomon.py b/src/sage/algebras/orlik_solomon.py
index 1a692846c46..5ee9915d980 100644
--- a/src/sage/algebras/orlik_solomon.py
+++ b/src/sage/algebras/orlik_solomon.py
@@ -284,7 +284,7 @@ def product_on_basis(self, a, b):
 
             return R(coeff) * self.subset_image(ns)
 
-        # r is the accumalator
+        # r is the accumulator
         # we reverse a in the product, so add a sign
         # note that l>=2 here
         if len(a) % 4 < 2:
diff --git a/src/sage/calculus/desolvers.py b/src/sage/calculus/desolvers.py
index 192c39a9209..24bc544690b 100644
--- a/src/sage/calculus/desolvers.py
+++ b/src/sage/calculus/desolvers.py
@@ -1178,7 +1178,7 @@ def desolve_rk4(de, dvar, ics=None, ivar=None, end_points=None, step=0.1, output
         [[0, 1], [0.5, 1.12419127424558], [1.0, 1.461590162288825]]
 
     Variant 1 for input - we can pass ODE in the form used by
-    desolve function In this example we integrate bakwards, since
+    desolve function In this example we integrate backwards, since
     ``end_points < ics[0]``::
 
         sage: y = function('y')(x)
diff --git a/src/sage/categories/category.py b/src/sage/categories/category.py
index 78248bb4362..ab7559ea797 100644
--- a/src/sage/categories/category.py
+++ b/src/sage/categories/category.py
@@ -1738,7 +1738,7 @@ def morphism_class(self):
 
         This class contains the methods defined in the nested class
         ``self.MorphismMethods`` (if it exists), and has as bases the
-        morphims classes of the super categories of ``self``.
+        morphism classes of the super categories of ``self``.
 
         .. SEEALSO::
 
diff --git a/src/sage/coding/guruswami_sudan/gs_decoder.py b/src/sage/coding/guruswami_sudan/gs_decoder.py
index ae566604ab4..1630485942c 100644
--- a/src/sage/coding/guruswami_sudan/gs_decoder.py
+++ b/src/sage/coding/guruswami_sudan/gs_decoder.py
@@ -481,7 +481,7 @@ def gs_satisfactory(tau, s, l, C = None, n_k = None):
 
         INPUT:
 
-        - ``tau`` -- an integer, number of errrors one expects Guruswami-Sudan algorithm
+        - ``tau`` -- an integer, number of errors one expects Guruswami-Sudan algorithm
           to correct
         - ``s`` -- an integer, multiplicity parameter of Guruswami-Sudan algorithm
         - ``l`` -- an integer, list size parameter
diff --git a/src/sage/combinat/binary_recurrence_sequences.py b/src/sage/combinat/binary_recurrence_sequences.py
index d8ecf4383c9..6ace53b8e96 100644
--- a/src/sage/combinat/binary_recurrence_sequences.py
+++ b/src/sage/combinat/binary_recurrence_sequences.py
@@ -374,7 +374,7 @@ def period(self, m):
         Return the period of the binary recurrence sequence modulo
         an integer ``m``.
 
-        If `n_1` is congruent to `n_2` modulu ``period(m)``, then `u_{n_1}` is
+        If `n_1` is congruent to `n_2` modulo ``period(m)``, then `u_{n_1}` is
         is congruent to `u_{n_2}` modulo ``m``.
 
         INPUT:
diff --git a/src/sage/combinat/cluster_algebra_quiver/cluster_seed.py b/src/sage/combinat/cluster_algebra_quiver/cluster_seed.py
index 5f96100876b..465e22070ca 100644
--- a/src/sage/combinat/cluster_algebra_quiver/cluster_seed.py
+++ b/src/sage/combinat/cluster_algebra_quiver/cluster_seed.py
@@ -2547,7 +2547,8 @@ def mutate(self, sequence, inplace=True, input_type=None):
         is_vertices = set(seqq).issubset(set(seed._nlist))
         is_indices = set(seqq).issubset(set(range(n)))
 
-        # Note - this does not guarantee that the sequence consists of cluster variables, it only rules out some posibilities.
+        # Note - this does not guarantee that the sequence consists of
+        # cluster variables, it only rules out some possibilities.
         is_cluster_vars = reduce(lambda x, y: isinstance(y, str), seqq, 1) and seed._use_fpolys
 
         # Ensures the sequence has elements of type input_type.
diff --git a/src/sage/combinat/composition.py b/src/sage/combinat/composition.py
index f236b90c536..ab6436b3fa1 100644
--- a/src/sage/combinat/composition.py
+++ b/src/sage/combinat/composition.py
@@ -1226,7 +1226,7 @@ def shuffle_product(self, other, overlap=False):
 
         OUTPUT:
 
-        An enumerated set (allowing for mutliplicities)
+        An enumerated set (allowing for multiplicities)
 
         EXAMPLES:
 
diff --git a/src/sage/combinat/root_system/root_lattice_realizations.py b/src/sage/combinat/root_system/root_lattice_realizations.py
index 6797d671797..6d484917311 100644
--- a/src/sage/combinat/root_system/root_lattice_realizations.py
+++ b/src/sage/combinat/root_system/root_lattice_realizations.py
@@ -2526,7 +2526,7 @@ def plot_hedron(self, **options):
                 sage: RootSystem(["D",3]).ambient_space().plot_hedron()
                 Graphics3d Object
 
-            Surprise: polyhedrons of large dimension know how to
+            Surprise: polyhedra of large dimension know how to
             project themselves nicely::
 
                 sage: RootSystem(["F",4]).ambient_space().plot_hedron() # long time
diff --git a/src/sage/data_structures/blas_dict.pyx b/src/sage/data_structures/blas_dict.pyx
index ca2355731e6..5dfa06dbd86 100644
--- a/src/sage/data_structures/blas_dict.pyx
+++ b/src/sage/data_structures/blas_dict.pyx
@@ -132,7 +132,7 @@ cpdef int iaxpy(a, dict X, dict Y, bint remove_zeros=True, bint factor_on_left=T
                 else:
                     value = value*a
                 if not value:
-                    continue # a is a zero divizor
+                    continue  # a is a zero divisor
             # assert value
             if key in Y:
                 Y[key] += value
diff --git a/src/sage/databases/sql_db.py b/src/sage/databases/sql_db.py
index db2b7317d31..a95b3502b92 100644
--- a/src/sage/databases/sql_db.py
+++ b/src/sage/databases/sql_db.py
@@ -772,7 +772,7 @@ def _merge_queries(self, other, ret, join_table, join_dict, operator):
             if re.search(pattern, self.__query_string__) \
               or re.search(pattern, other.__query_string__):
                 raise TypeError('Input queries have joins but join ' \
-                    + 'paramaters are NoneType')
+                    + 'parameters are NoneType')
             s = ((self.__query_string__).upper()).split('FROM ')
             o = ((other.__query_string__).upper()).split('FROM ')
             s = s[1].split(' WHERE ')
diff --git a/src/sage/dynamics/arithmetic_dynamics/projective_ds.py b/src/sage/dynamics/arithmetic_dynamics/projective_ds.py
index 53dd3ef2c96..d6df92ceeab 100644
--- a/src/sage/dynamics/arithmetic_dynamics/projective_ds.py
+++ b/src/sage/dynamics/arithmetic_dynamics/projective_ds.py
@@ -3530,7 +3530,7 @@ def sigma_invariants(self, n, formal=False, embedding=None, type='point'):
         if type == 'cycle':
             #now we need to deal with having the correct number of factors
             #1 multiplier for each cycle. But we need to be careful about
-            #the length of the cycle and the mutliplicities
+            #the length of the cycle and the multiplicities
             good_res = 1
             if formal:
                 #then we are working with the n-th dynatomic and just need
diff --git a/src/sage/dynamics/interval_exchanges/constructors.py b/src/sage/dynamics/interval_exchanges/constructors.py
index ae2884fdae9..68898ee08ce 100644
--- a/src/sage/dynamics/interval_exchanges/constructors.py
+++ b/src/sage/dynamics/interval_exchanges/constructors.py
@@ -772,7 +772,7 @@ def RauzyDiagram(*args, **kargs):
     interval exchange transformation). The edges correspond to the action of the
     different operations considered.
 
-    It first appeard in the original article of Rauzy [Rau1979]_.
+    It first appeared in the original article of Rauzy [Rau1979]_.
 
     INPUT:
 
diff --git a/src/sage/game_theory/normal_form_game.py b/src/sage/game_theory/normal_form_game.py
index 605496417cc..fa1d5f4c1dd 100644
--- a/src/sage/game_theory/normal_form_game.py
+++ b/src/sage/game_theory/normal_form_game.py
@@ -2107,7 +2107,7 @@ def _solve_indifference(self, support1, support2, M):
                         M[strategy1][support2[strategy_pair2]] -\
                         M[strategy1][support2[strategy_pair2 - 1]]
             # Coefficients of linear system that ensure the vector is
-            # a probability vecotor. ie. sum to 1
+            # a probability vector. ie. sum to 1
             linearsystem[-1, strategy1] = 1
         # Create rhs of linear systems
         linearsystem_rhs = vector([0 for i in range(len(support2))] + [1])
diff --git a/src/sage/geometry/polyhedron/base.py b/src/sage/geometry/polyhedron/base.py
index f94b3ffaf6a..1a8f5b221a4 100644
--- a/src/sage/geometry/polyhedron/base.py
+++ b/src/sage/geometry/polyhedron/base.py
@@ -3085,7 +3085,7 @@ def dilation(self, scalar):
 
         TESTS:
 
-        Dilation of empty polyhedrons works, see :trac:`14987`::
+        Dilation of empty polyhedra works, see :trac:`14987`::
 
             sage: p = Polyhedron(ambient_dim=2); p
             The empty polyhedron in ZZ^2
diff --git a/src/sage/geometry/polyhedron/ppl_lattice_polygon.py b/src/sage/geometry/polyhedron/ppl_lattice_polygon.py
index 019bff803e2..e8084b221b3 100644
--- a/src/sage/geometry/polyhedron/ppl_lattice_polygon.py
+++ b/src/sage/geometry/polyhedron/ppl_lattice_polygon.py
@@ -363,7 +363,7 @@ def is_isomorphic(self, polytope):
 
     def sub_polytopes(self):
         """
-        Returns a list of all lattice sub-polygons up to isomorphsm.
+        Return a list of all lattice sub-polygons up to isomorphism.
 
         OUTPUT:
 
diff --git a/src/sage/graphs/centrality.pyx b/src/sage/graphs/centrality.pyx
index c5c9d355eff..67db9819d8d 100644
--- a/src/sage/graphs/centrality.pyx
+++ b/src/sage/graphs/centrality.pyx
@@ -233,7 +233,7 @@ cdef dict centrality_betweenness_C(G, numerical_type _, normalize=True):
                 for j in range(layer_current_beginning,layer_current_end):
                     u = queue[j]
 
-                    # List the neighors of u
+                    # List the neighbors of u
                     p_tmp = g.neighbors[u]
                     while p_tmp<g.neighbors[u+1]:
                         v = p_tmp[0]
@@ -341,7 +341,7 @@ cdef void _estimate_reachable_vertices_dir(short_digraph g, int* reachL, int* re
         L(C)=|C|+\max_{(C,C') \in \mathcal{E}}L(C') \\
         U(C)=|C|+\max_{(C,C') \in \mathcal{E}}L(C')
 
-    By analyzing strongly connected components in reverse topologial order,
+    By analyzing strongly connected components in reverse topological order,
     we are sure that, as soon as we process component `C`, all components
     `C'` appearing on the right hand side have already been processed.
     A further improvement on these bounds is obtained by exactly computing
@@ -764,7 +764,7 @@ def centrality_closeness_top_k(G, int k=1, int verbose=0):
 
                 u = queue[j]
 
-                # List the neighors of u
+                # List the neighbors of u
                 p_tmp = sd.neighbors[u]
                 while p_tmp<sd.neighbors[u+1] and not stopped:
                     sig_check()
diff --git a/src/sage/graphs/generators/chessboard.py b/src/sage/graphs/generators/chessboard.py
index c902f369e61..4d4b9e3c6be 100644
--- a/src/sage/graphs/generators/chessboard.py
+++ b/src/sage/graphs/generators/chessboard.py
@@ -84,7 +84,7 @@ def ChessboardGraphGenerator(dim_list,
         sage: G.is_isomorphic( graphs.CompleteGraph(4) )
         True
 
-    A Rook's Graph in 2 dimensions is isomporphic to the Cartesian product of 2
+    A Rook's Graph in 2 dimensions is isomorphic to the Cartesian product of 2
     complete graphs::
 
         sage: G, _ = graphs.ChessboardGraphGenerator( [3,4], rook=True, rook_radius=None, bishop=False, knight=False )
diff --git a/src/sage/graphs/generic_graph.py b/src/sage/graphs/generic_graph.py
index 6cfe42a0952..2a66151ff21 100644
--- a/src/sage/graphs/generic_graph.py
+++ b/src/sage/graphs/generic_graph.py
@@ -1532,7 +1532,7 @@ def to_dictionary(self, edge_labels=False, multiple_edges=False):
         .. NOTE::
 
           When used on directed graphs, the explanations above can be understood
-          by replacing the word "neigbours" by "out-neighbors"
+          by replacing the word "neighbors" by "out-neighbors"
 
         EXAMPLES::
 
diff --git a/src/sage/graphs/strongly_regular_db.pyx b/src/sage/graphs/strongly_regular_db.pyx
index 7da68c8977a..e1ba35a0a73 100644
--- a/src/sage/graphs/strongly_regular_db.pyx
+++ b/src/sage/graphs/strongly_regular_db.pyx
@@ -2343,7 +2343,7 @@ def SRG_280_117_44_52():
     """
     from sage.graphs.hypergraph_generators import hypergraphs
 
-    # V is the set of partions {{a,b,c},{d,e,f},{g,h,i}} of {0,...,8}
+    # V is the set of partitions {{a,b,c},{d,e,f},{g,h,i}} of {0,...,8}
     H = hypergraphs.CompleteUniform(9,3)
     g = H.intersection_graph()
     V = g.complement().cliques_maximal()
diff --git a/src/sage/homology/simplicial_complex.py b/src/sage/homology/simplicial_complex.py
index 007402a0d89..6462d2fe9d6 100644
--- a/src/sage/homology/simplicial_complex.py
+++ b/src/sage/homology/simplicial_complex.py
@@ -839,7 +839,7 @@ class SimplicialComplex(Parent, GenericCellComplex):
     (or tuples, etc.) of vertices.  Maximal faces are also known as
     'facets'.
 
-    Alternatively, the maximal faces can be defined from a monotome boolean
+    Alternatively, the maximal faces can be defined from a monotone boolean
     function on the subsets of a set `X`. While defining ``maximal_faces=None``,
     you can thus set ``from_characteristic_function=(f,X)`` where ``X`` is the
     set of points and ``f`` a boolean monotone hereditary function that accepts
diff --git a/src/sage/libs/gap/element.pyx b/src/sage/libs/gap/element.pyx
index c7ca311ad52..e6f1e483925 100644
--- a/src/sage/libs/gap/element.pyx
+++ b/src/sage/libs/gap/element.pyx
@@ -2617,7 +2617,7 @@ cdef class GapElement_List(GapElement):
         """
         Return the list as a vector.
 
-        GAP does not have a special vetor data type, they are just
+        GAP does not have a special vector data type, they are just
         lists. This function converts a GAP list to a Sage vector.
 
         OUTPUT:
diff --git a/src/sage/libs/gap/util.pyx b/src/sage/libs/gap/util.pyx
index abc04d331e4..7bffcfc00d7 100644
--- a/src/sage/libs/gap/util.pyx
+++ b/src/sage/libs/gap/util.pyx
@@ -391,7 +391,7 @@ cdef inline void DEBUG_CHECK(libGAP_Obj obj):
 
 cpdef memory_usage():
     """
-    Return information about the memory useage.
+    Return information about the memory usage.
 
     See :meth:`~sage.libs.gap.libgap.Gap.mem` for details.
     """
diff --git a/src/sage/libs/pynac/pynac.pyx b/src/sage/libs/pynac/pynac.pyx
index 419cc47829c..529386766c7 100644
--- a/src/sage/libs/pynac/pynac.pyx
+++ b/src/sage/libs/pynac/pynac.pyx
@@ -340,7 +340,7 @@ cdef stdstring* py_repr(o, int level):
         else:
             t = s
         # Python complexes are always printed with parentheses
-        # we try to avoid double parantheses
+        # we try to avoid double parentheses
         if type(o) is not complex and \
                 (' ' in t or '/' in t or '+' in t or '-' in t or '*' in t \
                 or '^' in t):
diff --git a/src/sage/manifolds/differentiable/automorphismfield.py b/src/sage/manifolds/differentiable/automorphismfield.py
index 62af1f3b2e3..94956dc89f8 100644
--- a/src/sage/manifolds/differentiable/automorphismfield.py
+++ b/src/sage/manifolds/differentiable/automorphismfield.py
@@ -106,7 +106,7 @@ class AutomorphismField(TensorField):
         sage: W = U.intersection(V)
         sage: a.add_comp_by_continuation(eV, W, c_uv)
 
-    At this stage, the automorphims field `a` is fully defined::
+    At this stage, the automorphism field `a` is fully defined::
 
         sage: a.display(eU)
         a = d/dx*dx + x d/dx*dy + 2 d/dy*dy
diff --git a/src/sage/manifolds/differentiable/integrated_curve.py b/src/sage/manifolds/differentiable/integrated_curve.py
index e8cf9507090..7b5011d702a 100644
--- a/src/sage/manifolds/differentiable/integrated_curve.py
+++ b/src/sage/manifolds/differentiable/integrated_curve.py
@@ -2378,7 +2378,7 @@ class IntegratedAutoparallelCurve(IntegratedCurve):
     the usual embedding of `\mathbb{S}^{2}` in
     `\mathbb{R}^{3}` thanks to using an orthonormal frame,
     since providing the components with respect to the coordinate basis
-    would require mutliplying the second component (i.e. the `\phi`
+    would require multiplying the second component (i.e. the `\phi`
     component) in order to picture the vector in the same way.
     This subtlety will need to be taken into account later when the
     numerical curve will be compared to the analytical solution.
diff --git a/src/sage/matrix/matrix_rational_dense.pyx b/src/sage/matrix/matrix_rational_dense.pyx
index 5c3ad109868..7d79509451a 100644
--- a/src/sage/matrix/matrix_rational_dense.pyx
+++ b/src/sage/matrix/matrix_rational_dense.pyx
@@ -1786,7 +1786,7 @@ cdef class Matrix_rational_dense(Matrix_dense):
 
     def _echelonize_multimodular(self, height_guess=None, proof=None):
         """
-        Echelonize self using mutlimodular recomposition
+        Echelonize ``self`` using multimodular recomposition.
 
         REFERENCE:
 
diff --git a/src/sage/matroids/graphic_matroid.py b/src/sage/matroids/graphic_matroid.py
index e4667b27ecc..0337c4829f9 100644
--- a/src/sage/matroids/graphic_matroid.py
+++ b/src/sage/matroids/graphic_matroid.py
@@ -561,7 +561,7 @@ def _minor(self, contractions=frozenset([]), deletions=frozenset([])):
 
     def _has_minor(self, N, certificate=False):
         """
-        Check if the matroid has a minor isomoprhic to M(H).
+        Check if the matroid has a minor isomorphic to M(H).
 
         INPUT:
 
diff --git a/src/sage/matroids/set_system.pyx b/src/sage/matroids/set_system.pyx
index 0256f042470..62cfc4d359a 100644
--- a/src/sage/matroids/set_system.pyx
+++ b/src/sage/matroids/set_system.pyx
@@ -600,7 +600,7 @@ cdef class SetSystem:
         partition ``P``, and while ``P`` has a partition element ``p`` with
         more than one element, select an arbitrary ``e`` from the first such
         ``p`` and split ``p`` into ``p-e``. Then replace ``P`` with
-        the equitabele refinement of this partition.
+        the equitable refinement of this partition.
 
         INPUT:
 
diff --git a/src/sage/numerical/backends/cvxopt_backend.pyx b/src/sage/numerical/backends/cvxopt_backend.pyx
index 6194549c1a2..cd41098557f 100644
--- a/src/sage/numerical/backends/cvxopt_backend.pyx
+++ b/src/sage/numerical/backends/cvxopt_backend.pyx
@@ -322,7 +322,7 @@ cdef class CVXOPTBackend(GenericBackend):
 
         INPUT:
 
-        - ``indices`` (list of integers) -- this list constains the
+        - ``indices`` (list of integers) -- this list contains the
           indices of the constraints in which the variable's
           coefficient is nonzero
 
diff --git a/src/sage/numerical/backends/glpk_backend.pyx b/src/sage/numerical/backends/glpk_backend.pyx
index 64781bd3a8a..0e81c13dad5 100644
--- a/src/sage/numerical/backends/glpk_backend.pyx
+++ b/src/sage/numerical/backends/glpk_backend.pyx
@@ -154,7 +154,7 @@ cdef class GLPKBackend(GenericBackend):
         Add ``number`` new variables.
 
         This amounts to adding new columns to the matrix. By default,
-        the variables are both positive, real and theor coefficient in
+        the variables are both positive, real and their coefficient in
         the objective function is 0.0.
 
         INPUT:
@@ -786,7 +786,7 @@ cdef class GLPKBackend(GenericBackend):
 
         INPUT:
 
-        - ``indices`` (list of integers) -- this list constains the
+        - ``indices`` (list of integers) -- this list contains the
           indices of the constraints in which the variable's
           coefficient is nonzero
 
diff --git a/src/sage/numerical/backends/ppl_backend.pyx b/src/sage/numerical/backends/ppl_backend.pyx
index 4e4b5707af6..1d089baa2be 100644
--- a/src/sage/numerical/backends/ppl_backend.pyx
+++ b/src/sage/numerical/backends/ppl_backend.pyx
@@ -562,7 +562,7 @@ cdef class PPLBackend(GenericBackend):
 
         INPUT:
 
-        - ``indices`` (list of integers) -- this list constains the
+        - ``indices`` (list of integers) -- this list contains the
           indices of the constraints in which the variable's
           coefficient is nonzero
 
diff --git a/src/sage/plot/plot3d/platonic.py b/src/sage/plot/plot3d/platonic.py
index 4744ee3abe2..c15fdc3af32 100644
--- a/src/sage/plot/plot3d/platonic.py
+++ b/src/sage/plot/plot3d/platonic.py
@@ -222,7 +222,7 @@ def tetrahedron(center=(0, 0, 0), size=1, **kwds):
 
         sphinx_plot(tetrahedron(color='red') + tetrahedron((0,0,-2)).scale([1,1,-1]))
 
-    A Dodecahedral complex of 5 tetrahedrons (a more elaborate example
+    A Dodecahedral complex of 5 tetrahedra (a more elaborate example
     from Peter Jipsen)::
 
         sage: v=(sqrt(5.)/2-5/6, 5/6*sqrt(3.)-sqrt(15.)/2, sqrt(5.)/3)
@@ -579,7 +579,7 @@ def icosahedron(center=(0, 0, 0), size=1, **kwds):
 
         sphinx_plot(icosahedron())
 
-    Two icosahedrons at different positions of different sizes. ::
+    Two icosahedra at different positions of different sizes. ::
 
         sage: p = icosahedron((-1/2,0,1), color='orange')
         sage: p += icosahedron((2,0,1), size=1/2, color='red', aspect_ratio=[1,1,1])
diff --git a/src/sage/plot/plot3d/shapes2.py b/src/sage/plot/plot3d/shapes2.py
index 1dde57433ae..f42658d1dfa 100644
--- a/src/sage/plot/plot3d/shapes2.py
+++ b/src/sage/plot/plot3d/shapes2.py
@@ -93,7 +93,7 @@ def line3d(points, thickness=1, radius=None, arrow_head=False, **kwds):
         ....:        color='green') + line3d([(0,1,0), (1,0,2)])
         Graphics3d Object
 
-    A Dodecahedral complex of 5 tetrahedrons (a more elaborate example
+    A Dodecahedral complex of 5 tetrahedra (a more elaborate example
     from Peter Jipsen)::
 
         sage: def tetra(col):
diff --git a/src/sage/plot/plot3d/tachyon.py b/src/sage/plot/plot3d/tachyon.py
index cdee141efa1..81ef81e7a61 100644
--- a/src/sage/plot/plot3d/tachyon.py
+++ b/src/sage/plot/plot3d/tachyon.py
@@ -698,7 +698,7 @@ def texfunc(self, type=0, center=(0,0,0), rotate=(0,0,0), scale=(1,1,1),
         -  ``scale`` - (default: (1,1,1))
 
 
-        EXAMPLES: We draw an infinite checkboard::
+        EXAMPLES: We draw an infinite checkerboard::
 
             sage: t = Tachyon(camera_center=(2,7,4), look_at=(2,0,0))
             sage: t.texture('black', color=(0,0,0), texfunc=1)
diff --git a/src/sage/rings/complex_mpc.pyx b/src/sage/rings/complex_mpc.pyx
index 824fe55a382..bac78b16bad 100644
--- a/src/sage/rings/complex_mpc.pyx
+++ b/src/sage/rings/complex_mpc.pyx
@@ -2297,7 +2297,7 @@ cdef class MPComplexNumber(sage.structure.element.FieldElement):
 
     def agm(self, right, algorithm="optimal"):
         """
-        Returns the algebraic geometrc mean of ``self`` and ``right``.
+        Return the algebro-geometric mean of ``self`` and ``right``.
 
         EXAMPLES::
 
diff --git a/src/sage/rings/invariant_theory.py b/src/sage/rings/invariant_theory.py
index 63ad78ae3bb..d4d202a4ee8 100644
--- a/src/sage/rings/invariant_theory.py
+++ b/src/sage/rings/invariant_theory.py
@@ -3318,7 +3318,8 @@ def quaternary_biquadratic(self, quadratic1, quadratic2, *args, **kwds):
 
         INPUT:
 
-        - ``quadratic1``, ``quadratic2`` -- two polynomias. Either homogeneous quadratic
+        - ``quadratic1``, ``quadratic2`` -- two polynomials.
+          Either homogeneous quadratic
           in 4 homogeneous variables, or inhomogeneous quadratic
           in 3 variables.
 
diff --git a/src/sage/rings/padics/padic_generic_element.pyx b/src/sage/rings/padics/padic_generic_element.pyx
index 334e544bba2..fa5277899d7 100644
--- a/src/sage/rings/padics/padic_generic_element.pyx
+++ b/src/sage/rings/padics/padic_generic_element.pyx
@@ -852,7 +852,7 @@ cdef class pAdicGenericElement(LocalGenericElement):
             their greatest common divisor is in general not unique (not even up
             to units). For example `O(3)` is a representative for the elements
             0 and 3 in the 3-adic ring `\ZZ_3`. The greatest common
-            divisior of `O(3)` and `O(3)` could be (among others) 3 or 0 which
+            divisor of `O(3)` and `O(3)` could be (among others) 3 or 0 which
             have different valuation. The algorithm implemented here, will
             return an element of minimal valuation among the possible greatest
             common divisors.
@@ -1005,7 +1005,7 @@ cdef class pAdicGenericElement(LocalGenericElement):
             greatest common divisor is in general not unique (not even up to
             units). For example `O(3)` is a representative for the elements 0
             and 3 in the 3-adic ring `\ZZ_3`. The greatest common
-            divisior of `O(3)` and `O(3)` could be (among others) 3 or 0 which
+            divisor of `O(3)` and `O(3)` could be (among others) 3 or 0 which
             have different valuation. The algorithm implemented here, will
             return an element of minimal valuation among the possible greatest
             common divisors.
diff --git a/src/sage/schemes/elliptic_curves/gal_reps_number_field.py b/src/sage/schemes/elliptic_curves/gal_reps_number_field.py
index 9004ce09745..ca268e1dd34 100644
--- a/src/sage/schemes/elliptic_curves/gal_reps_number_field.py
+++ b/src/sage/schemes/elliptic_curves/gal_reps_number_field.py
@@ -532,7 +532,7 @@ def _maybe_borels(E, L, patience=100):
         sage: sage.schemes.elliptic_curves.gal_reps_number_field._maybe_borels(E, primes(20))
         [2, 3]
 
-    Here the curve really does possess isognies of degrees 2 and 3::
+    Here the curve really does possess isogenies of degrees 2 and 3::
 
         sage: [len(E.isogenies_prime_degree(l)) for l in [2,3]]
         [1, 1]
diff --git a/src/sage/schemes/elliptic_curves/height.py b/src/sage/schemes/elliptic_curves/height.py
index 10669a2794f..3d270ebf9d7 100644
--- a/src/sage/schemes/elliptic_curves/height.py
+++ b/src/sage/schemes/elliptic_curves/height.py
@@ -535,7 +535,7 @@ def inf_max_abs(f, g, D):
 
     INPUT:
 
-    - ``f``, ``g`` (polynomials) -- real univariate polynomaials
+    - ``f``, ``g`` (polynomials) -- real univariate polynomials
 
     - ``D`` (UnionOfIntervals) -- a subset of `\RR`
 
diff --git a/src/sage/schemes/toric/sheaf/klyachko.py b/src/sage/schemes/toric/sheaf/klyachko.py
index fcfe90901c9..572cc3cb9d5 100644
--- a/src/sage/schemes/toric/sheaf/klyachko.py
+++ b/src/sage/schemes/toric/sheaf/klyachko.py
@@ -948,7 +948,7 @@ def random_deformation(self, epsilon=None):
 
         OUTPUT:
 
-        A new Klyachko bundle with randomly perturbed moduly. In
+        A new Klyachko bundle with randomly perturbed moduli. In
         particular, the same Chern classes.
 
         EXAMPLES::
diff --git a/src/sage/sets/recursively_enumerated_set.pyx b/src/sage/sets/recursively_enumerated_set.pyx
index d592ec0f7a6..27facd9fc13 100644
--- a/src/sage/sets/recursively_enumerated_set.pyx
+++ b/src/sage/sets/recursively_enumerated_set.pyx
@@ -281,7 +281,7 @@ def RecursivelyEnumeratedSet(seeds, successors, structure=None,
 
     TESTS:
 
-    The succesors method is an attribute::
+    The successors method is an attribute::
 
         sage: R = RecursivelyEnumeratedSet([1], lambda x: [x+1, x-1])
         sage: R.successors(4)
@@ -296,7 +296,8 @@ def RecursivelyEnumeratedSet(seeds, successors, structure=None,
         (1, 2, 3)
     """
     if structure is None:
-        if enumeration is None: enumeration = 'breadth'
+        if enumeration is None:
+            enumeration = 'breadth'
         return RecursivelyEnumeratedSet_generic(seeds, successors,
                 enumeration, max_depth, facade=facade, category=category)
     if structure == 'symmetric':
diff --git a/src/sage/tensor/modules/free_module_linear_group.py b/src/sage/tensor/modules/free_module_linear_group.py
index 156446b0ebb..efdcf021dff 100644
--- a/src/sage/tensor/modules/free_module_linear_group.py
+++ b/src/sage/tensor/modules/free_module_linear_group.py
@@ -1,7 +1,7 @@
 r"""
 General linear group of a free module
 
-The set `\mathrm{GL}(M)` of automorphisms (i.e. invertible endomorphims) of a
+The set `\mathrm{GL}(M)` of automorphisms (i.e. invertible endomorphisms) of a
 free module of finite rank `M` is a group under composition of automorphisms,
 named the *general linear group* of `M`. In other words, `\mathrm{GL}(M)` is
 the group of units (i.e. invertible elements) of `\mathrm{End}(M)`, the
@@ -41,7 +41,7 @@ class FreeModuleLinearGroup(UniqueRepresentation, Parent):
 
     Given a free module of finite rank `M` over a commutative ring `R`, the
     *general linear group* of `M` is the group `\mathrm{GL}(M)` of
-    automorphisms (i.e. invertible endomorphims) of `M`. It is the group of
+    automorphisms (i.e. invertible endomorphisms) of `M`. It is the group of
     units (i.e. invertible elements) of `\mathrm{End}(M)`, the endomorphism
     ring of `M`.
 

From 0a76c59769b415659ce37092a66d2f795ce669f4 Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?Fr=C3=A9d=C3=A9ric=20Chapoton?=
 <chapoton@math.univ-lyon1.fr>
Date: Sun, 21 Jan 2018 21:45:32 +0100
Subject: [PATCH 118/128] a few more

---
 src/sage/coding/guruswami_sudan/gs_decoder.py            | 2 +-
 src/sage/combinat/cluster_algebra_quiver/cluster_seed.py | 2 +-
 src/sage/graphs/generic_graph.py                         | 6 +++---
 3 files changed, 5 insertions(+), 5 deletions(-)

diff --git a/src/sage/coding/guruswami_sudan/gs_decoder.py b/src/sage/coding/guruswami_sudan/gs_decoder.py
index 1630485942c..e731b41c29c 100644
--- a/src/sage/coding/guruswami_sudan/gs_decoder.py
+++ b/src/sage/coding/guruswami_sudan/gs_decoder.py
@@ -390,7 +390,7 @@ def find_integral_max(real_max, f):
             lmax = sqrt(n*s*(s+1.)/(k-1.)) - 1.
             #the best integral value will be
             (l,tau) = find_integral_max(lmax, lambda l: get_tau(s,l))
-            #Note that we have not proven that this ell is minimial in integral
+            #Note that we have not proven that this ell is minimal in integral
             #sense! It just seems that this most often happens
             return (tau,(s,l))
         if l is not None:
diff --git a/src/sage/combinat/cluster_algebra_quiver/cluster_seed.py b/src/sage/combinat/cluster_algebra_quiver/cluster_seed.py
index 465e22070ca..b4fd1b000e7 100644
--- a/src/sage/combinat/cluster_algebra_quiver/cluster_seed.py
+++ b/src/sage/combinat/cluster_algebra_quiver/cluster_seed.py
@@ -4922,7 +4922,7 @@ def is_LeeLiZel_allowable(T,n,m,b,c):
 
 def get_green_vertices(C):
     r"""
-    Get the green vertices from a matrix. Will go through each clumn and return
+    Get the green vertices from a matrix. Will go through each column and return
     the ones where no entry is greater than 0.
 
     INPUT:
diff --git a/src/sage/graphs/generic_graph.py b/src/sage/graphs/generic_graph.py
index 2a66151ff21..3750544377c 100644
--- a/src/sage/graphs/generic_graph.py
+++ b/src/sage/graphs/generic_graph.py
@@ -312,7 +312,7 @@
     :meth:`~GenericGraph.subgraph_search_iterator` | Return an iterator over the labelled copies of ``G`` in ``self``.
     :meth:`~GenericGraph.characteristic_polynomial` | Return the characteristic polynomial of the adjacency matrix of the (di)graph.
     :meth:`~GenericGraph.genus` | Return the minimal genus of the graph.
-    :meth:`~GenericGraph.crossing_number` | Return the minimun number of edge crossings needed to draw the graph.
+    :meth:`~GenericGraph.crossing_number` | Return the minimum number of edge crossings needed to draw the graph.
 
 Methods
 -------
@@ -4892,7 +4892,7 @@ def crossing_number(self):
         """
         Return the crossing number of the graph.
 
-        The crossing number of a graph is the minimun number of
+        The crossing number of a graph is the minimum number of
         edge crossings needed to draw the graph on a plane. It can
         be seen as a measure of non-planarity; a planar graph has
         crossing number zero.
@@ -9125,7 +9125,7 @@ def disjoint_routed_paths(self,pairs, solver=None, verbose=0):
 
         Given a set of pairs `(s_i,t_i)`, a set
         of disjoint routed paths is a set of
-        `s_i-t_i` paths which can interset at their endpoints
+        `s_i-t_i` paths which can intersect at their endpoints
         and are vertex-disjoint otherwise.
 
         INPUT:

From 4eeb90da844846c7fc31bd019df3f4af834e57aa Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?Fr=C3=A9d=C3=A9ric=20Chapoton?=
 <chapoton@math.univ-lyon1.fr>
Date: Sun, 21 Jan 2018 21:46:37 +0100
Subject: [PATCH 119/128] another list of typos

---
 src/sage/combinat/composition_tableau.py       | 18 +++++++++---------
 src/sage/combinat/finite_state_machine.py      |  2 +-
 src/sage/combinat/similarity_class_type.py     |  2 +-
 src/sage/combinat/words/alphabet.py            |  2 +-
 src/sage/cpython/string.pyx                    |  2 +-
 src/sage/geometry/cone.py                      |  2 +-
 src/sage/graphs/graph.py                       |  2 +-
 src/sage/graphs/linearextensions.py            | 14 +++++++-------
 src/sage/groups/finitely_presented.py          |  2 +-
 .../groups/matrix_gps/finitely_generated.py    |  4 ++--
 src/sage/interfaces/gap.py                     |  3 ++-
 src/sage/interfaces/gp.py                      |  3 ++-
 src/sage/interfaces/magma.py                   |  3 ++-
 src/sage/interfaces/r.py                       |  5 +++--
 src/sage/interfaces/scilab.py                  |  3 ++-
 src/sage/interfaces/singular.py                |  3 ++-
 src/sage/matrix/matrix_space.py                |  4 ++--
 src/sage/numerical/backends/coin_backend.pyx   |  2 +-
 .../numerical/backends/glpk_graph_backend.pyx  |  2 +-
 src/sage/rings/finite_rings/element_givaro.pyx |  2 +-
 .../rings/function_field/function_field.py     |  8 +++++---
 src/sage/rings/morphism.pyx                    |  2 +-
 src/sage/rings/polynomial/pbori.pyx            |  2 +-
 .../rings/polynomial/polynomial_element.pyx    |  2 +-
 .../elliptic_curves/ell_number_field.py        |  2 +-
 .../schemes/elliptic_curves/isogeny_class.py   |  2 +-
 .../schemes/hyperelliptic_curves/mestre.py     |  2 +-
 src/sage/schemes/toric/divisor.py              |  2 +-
 src/sage/structure/element.pyx                 |  2 +-
 src/sage/symbolic/expression.pyx               |  2 +-
 .../autogen/interpreters/__init__.py           |  2 +-
 31 files changed, 58 insertions(+), 50 deletions(-)

diff --git a/src/sage/combinat/composition_tableau.py b/src/sage/combinat/composition_tableau.py
index b2f9593a830..1eba224737d 100644
--- a/src/sage/combinat/composition_tableau.py
+++ b/src/sage/combinat/composition_tableau.py
@@ -318,7 +318,7 @@ class CompositionTableaux(UniqueRepresentation, Parent):
          [[3, 3, 3]]]
 
         sage: CT = CompositionTableaux([1,2,1]); CT
-        Composition tableaux of shape [1, 2, 1] and maximun entry 4
+        Composition tableaux of shape [1, 2, 1] and maximum entry 4
         sage: list(CT)
         [[[1], [2, 2], [3]],
          [[1], [2, 2], [4]],
@@ -327,7 +327,7 @@ class CompositionTableaux(UniqueRepresentation, Parent):
          [[2], [3, 3], [4]]]
 
         sage: CT = CompositionTableaux(shape=[1,2,1],max_entry=3); CT
-        Composition tableaux of shape [1, 2, 1] and maximun entry 3
+        Composition tableaux of shape [1, 2, 1] and maximum entry 3
         sage: list(CT)
         [[[1], [2, 2], [3]]]
 
@@ -363,17 +363,17 @@ def __classcall_private__(cls, *args, **kwargs):
             sage: CT = CompositionTableaux(size=3); CT
             Composition Tableaux of size 3 and maximum entry 3
             sage: CT = CompositionTableaux([1,2]); CT
-            Composition tableaux of shape [1, 2] and maximun entry 3
+            Composition tableaux of shape [1, 2] and maximum entry 3
             sage: CT = CompositionTableaux(shape=[1,2]); CT
-            Composition tableaux of shape [1, 2] and maximun entry 3
+            Composition tableaux of shape [1, 2] and maximum entry 3
             sage: CT = CompositionTableaux(shape=[]); CT
-            Composition tableaux of shape [] and maximun entry 0
+            Composition tableaux of shape [] and maximum entry 0
             sage: CT = CompositionTableaux(0); CT
             Composition Tableaux of size 0 and maximum entry 0
             sage: CT = CompositionTableaux(max_entry=3); CT
             Composition tableaux with maximum entry 3
             sage: CT = CompositionTableaux([1,2],max_entry=3); CT
-            Composition tableaux of shape [1, 2] and maximun entry 3
+            Composition tableaux of shape [1, 2] and maximum entry 3
             sage: CT = CompositionTableaux(size=2,shape=[1,2]); CT
             Traceback (most recent call last):
             ...
@@ -737,11 +737,11 @@ def _repr_(self):
         TESTS::
 
             sage: CompositionTableaux([1,2,1])
-            Composition tableaux of shape [1, 2, 1] and maximun entry 4
+            Composition tableaux of shape [1, 2, 1] and maximum entry 4
             sage: CompositionTableaux([1,2,1],max_entry=3)
-            Composition tableaux of shape [1, 2, 1] and maximun entry 3
+            Composition tableaux of shape [1, 2, 1] and maximum entry 3
         """
-        return "Composition tableaux of shape %s and maximun entry %s"%(str(self.shape), str(self.max_entry))
+        return "Composition tableaux of shape %s and maximum entry %s" % (str(self.shape), str(self.max_entry))
 
     def an_element(self):
         r"""
diff --git a/src/sage/combinat/finite_state_machine.py b/src/sage/combinat/finite_state_machine.py
index 68a5ae7da85..9eb981769ca 100644
--- a/src/sage/combinat/finite_state_machine.py
+++ b/src/sage/combinat/finite_state_machine.py
@@ -2706,7 +2706,7 @@ class FiniteStateMachine(sage.structure.sage_object.SageObject):
       process.
 
     - ``store_states_dict`` -- If ``True``, then additionally the states
-      are stored in an interal dictionary for speed up.
+      are stored in an internal dictionary for speed up.
 
     - ``on_duplicate_transition`` -- A function which is called when a
       transition is inserted into ``self`` which already existed (same
diff --git a/src/sage/combinat/similarity_class_type.py b/src/sage/combinat/similarity_class_type.py
index 4e49bbcecd0..2110f05a97f 100644
--- a/src/sage/combinat/similarity_class_type.py
+++ b/src/sage/combinat/similarity_class_type.py
@@ -2,7 +2,7 @@
 Similarity class types of matrices with entries in a finite field
 
 The notion of a matrix conjugacy class type was introduced by J. A. Green in
-[Green55]_, in the context of computing the irreducible charcaters of finite
+[Green55]_, in the context of computing the irreducible characters of finite
 general linear groups. The class types are equivalence classes of similarity
 classes of square matrices with entries in a finite field which, roughly
 speaking, have the same qualitative properties.
diff --git a/src/sage/combinat/words/alphabet.py b/src/sage/combinat/words/alphabet.py
index fd7d97ac78a..9e84451f6af 100644
--- a/src/sage/combinat/words/alphabet.py
+++ b/src/sage/combinat/words/alphabet.py
@@ -142,7 +142,7 @@ def build_alphabet(data=None, names=None, name=None):
     The other families for the option ``name`` are among 'lower', 'upper',
     'space', 'underscore', 'punctuation', 'printable', 'binary', 'octal',
     'decimal', 'hexadecimal', 'radix64' which refer to standard set of
-    charaters. Theses names may be combined by separating them by a space::
+    characters. Theses names may be combined by separating them by a space::
 
         sage: build_alphabet(name="lower")
         {'a', 'b', 'c', 'd', 'e', 'f', 'g', 'h', 'i', 'j', 'k', 'l', 'm', 'n', 'o', 'p', 'q', 'r', 's', 't', 'u', 'v', 'w', 'x', 'y', 'z'}
diff --git a/src/sage/cpython/string.pyx b/src/sage/cpython/string.pyx
index db7164126a7..0cc5e57d68e 100644
--- a/src/sage/cpython/string.pyx
+++ b/src/sage/cpython/string.pyx
@@ -19,7 +19,7 @@ import sys
 
 
 # Provide this as a shortcut to calling sys.getfilesystemencoding(), which
-# after interpeter initialization is constant.
+# after interpreter initialization is constant.
 FS_ENCODING = sys.getfilesystemencoding()
 
 # Functions in this module are implemented in the .pxd file for inlining.
diff --git a/src/sage/geometry/cone.py b/src/sage/geometry/cone.py
index d10fee81dfc..ac2174f73d6 100644
--- a/src/sage/geometry/cone.py
+++ b/src/sage/geometry/cone.py
@@ -4076,7 +4076,7 @@ def Hilbert_basis(self):
         set over `\ZZ` for the integral points `C\cap \ZZ^d`.
 
         If the cone `C` is not strictly convex, this method finds the
-        (unique) minimial set of lattice points that need to be added
+        (unique) minimal set of lattice points that need to be added
         to the defining rays of the cone to generate the whole
         semigroup `C\cap \ZZ^d`. But because the rays of the cone are
         not unique nor necessarily minimal in this case, neither is
diff --git a/src/sage/graphs/graph.py b/src/sage/graphs/graph.py
index ebcfa88dd7d..852e8a06dc9 100644
--- a/src/sage/graphs/graph.py
+++ b/src/sage/graphs/graph.py
@@ -3379,7 +3379,7 @@ def is_semi_symmetric(self):
         """
         Returns true if self is semi-symmetric.
 
-        A graph is semi-symmetric if it is regular, edge-transitve but not
+        A graph is semi-symmetric if it is regular, edge-transitive but not
         vertex-transitive.
 
         See :wikipedia:`the wikipedia article on semi-symmetric graphs
diff --git a/src/sage/graphs/linearextensions.py b/src/sage/graphs/linearextensions.py
index f5368aeb1bb..113a2cd731d 100644
--- a/src/sage/graphs/linearextensions.py
+++ b/src/sage/graphs/linearextensions.py
@@ -93,16 +93,16 @@ def __init__(self, dag):
         #Pruesse and Ruskey
         while dag_copy.num_verts() != 0:
             #Find all the minimal elements of dag_copy
-            minimial_elements = []
+            minimal_elements = []
             for node in dag_copy.vertices():
                 if len(dag_copy.incoming_edges(node)) == 0:
-                    minimial_elements.append(node)
-            if len(minimial_elements) == 1:
-                le.append(minimial_elements[0])
-                dag_copy.delete_vertex(minimial_elements[0])
+                    minimal_elements.append(node)
+            if len(minimal_elements) == 1:
+                le.append(minimal_elements[0])
+                dag_copy.delete_vertex(minimal_elements[0])
             else:
-                ap = minimial_elements[0]
-                bp = minimial_elements[1]
+                ap = minimal_elements[0]
+                bp = minimal_elements[1]
                 a.append(ap)
                 b.append(bp)
                 le.append(ap)
diff --git a/src/sage/groups/finitely_presented.py b/src/sage/groups/finitely_presented.py
index 1c76552994f..59fe82e7523 100644
--- a/src/sage/groups/finitely_presented.py
+++ b/src/sage/groups/finitely_presented.py
@@ -429,7 +429,7 @@ class RewritingSystem(object):
     A rewriting system is a set of rules that allow to transform
     one word in the group to an equivalent one.
 
-    If the rewriting system is confluent, then the transformated
+    If the rewriting system is confluent, then the transformed
     word is a unique reduced form of the element of the group.
 
     .. WARNING::
diff --git a/src/sage/groups/matrix_gps/finitely_generated.py b/src/sage/groups/matrix_gps/finitely_generated.py
index ae24e75385d..4c4837f03f0 100644
--- a/src/sage/groups/matrix_gps/finitely_generated.py
+++ b/src/sage/groups/matrix_gps/finitely_generated.py
@@ -1110,7 +1110,7 @@ def reynolds_operator(self, poly, chi=None):
             sage: G.reynolds_operator(f, chi)
             Traceback (most recent call last):
             ...
-            NotImplementedError: nontrivial characters not implemented for charateristic > 0
+            NotImplementedError: nontrivial characters not implemented for characteristic > 0
             sage: G.reynolds_operator(f)
             x^6
 
@@ -1194,7 +1194,7 @@ def reynolds_operator(self, poly, chi=None):
                     L1 = fields[0].composite_fields(fields[1])[0]
                     L = L1.composite_fields(fields[2])[0]
         else:
-            raise NotImplementedError("nontrivial characters not implemented for charateristic > 0")
+            raise NotImplementedError("nontrivial characters not implemented for characteristic > 0")
         poly = poly.change_ring(L)
         poly_gens = vector(poly.parent().gens())
         F = L.zero()
diff --git a/src/sage/interfaces/gap.py b/src/sage/interfaces/gap.py
index 2202f45964b..434ac77f884 100644
--- a/src/sage/interfaces/gap.py
+++ b/src/sage/interfaces/gap.py
@@ -1129,7 +1129,8 @@ def __init__(self, max_workspace_size=None,
 
     def set_seed(self,seed=None):
         """
-        Sets the seed for gap interpeter.
+        Set the seed for gap interpreter.
+
         The seed should be an integer.
 
         EXAMPLES::
diff --git a/src/sage/interfaces/gp.py b/src/sage/interfaces/gp.py
index ad5bf3d9c73..53381d96308 100644
--- a/src/sage/interfaces/gp.py
+++ b/src/sage/interfaces/gp.py
@@ -221,7 +221,8 @@ def __init__(self, stacksize=10000000,   # 10MB
 
     def set_seed(self, seed=None):
         """
-        Sets the seed for gp interpeter.
+        Set the seed for gp interpreter.
+
         The seed should be an integer.
 
         EXAMPLES::
diff --git a/src/sage/interfaces/magma.py b/src/sage/interfaces/magma.py
index 78f87d27998..7d8f9131e83 100644
--- a/src/sage/interfaces/magma.py
+++ b/src/sage/interfaces/magma.py
@@ -366,7 +366,8 @@ def __init__(self, script_subdirectory=None,
 
     def set_seed(self, seed=None):
         """
-        Sets the seed for the Magma interpeter.
+        Set the seed for the Magma interpreter.
+
         The seed should be an integer.
 
         EXAMPLES::
diff --git a/src/sage/interfaces/r.py b/src/sage/interfaces/r.py
index 8c6d589babc..8b54d985aaa 100644
--- a/src/sage/interfaces/r.py
+++ b/src/sage/interfaces/r.py
@@ -362,7 +362,8 @@ def __init__(self,
 
     def set_seed(self, seed=None):
         """
-        Sets the seed for R interpeter.
+        Set the seed for R interpreter.
+
         The seed should be an integer.
 
         EXAMPLES::
@@ -1889,7 +1890,7 @@ def _sage_(self):
         # c is an ordered list
         # list is a dictionary (where _Names give the entries names.
         #    map entries in names to (value, name) in each entry?
-        # structure is .. see above .. strucuture(DATA,**kw)
+        # structure is .. see above .. structure(DATA,**kw)
         # TODO: thinking of just replacing c( with ( to get a long tuple?
 
 
diff --git a/src/sage/interfaces/scilab.py b/src/sage/interfaces/scilab.py
index 8d9e9605cf4..466347bd9a5 100644
--- a/src/sage/interfaces/scilab.py
+++ b/src/sage/interfaces/scilab.py
@@ -236,7 +236,8 @@ def __init__(self, maxread=None, script_subdirectory=None,
 
     def set_seed(self, seed=None):
         """
-        Sets the seed for gp interpeter.
+        Set the seed for gp interpreter.
+
         The seed should be an integer.
 
         EXAMPLES::
diff --git a/src/sage/interfaces/singular.py b/src/sage/interfaces/singular.py
index 8a02c1b9db0..18f8384c508 100644
--- a/src/sage/interfaces/singular.py
+++ b/src/sage/interfaces/singular.py
@@ -400,7 +400,8 @@ def __init__(self, maxread=None, script_subdirectory=None,
 
     def set_seed(self,seed=None):
         """
-        Sets the seed for singular interpeter.
+        Set the seed for singular interpreter.
+
         The seed should be an integer at least 1
         and not more than 30 bits.
         See
diff --git a/src/sage/matrix/matrix_space.py b/src/sage/matrix/matrix_space.py
index e34a9ba9506..8da53503e80 100644
--- a/src/sage/matrix/matrix_space.py
+++ b/src/sage/matrix/matrix_space.py
@@ -157,7 +157,7 @@ def get_matrix_class(R, nrows, ncols, sparse, implementation):
         sage: get_matrix_class(GF(3), 2, 2, False, 'm4ri')
         Traceback (most recent call last):
         ...
-        ValueError: m4ri matrices are only available in characterstic 2
+        ValueError: m4ri matrices are only available in characteristic 2
         sage: get_matrix_class(Zmod(2**30), 2, 2, False, 'linbox-float')
         Traceback (most recent call last):
         ...
@@ -227,7 +227,7 @@ def get_matrix_class(R, nrows, ncols, sparse, implementation):
 
             if implementation == 'm4ri':
                 if R.order() != 2:
-                    raise ValueError('m4ri matrices are only available in characterstic 2')
+                    raise ValueError('m4ri matrices are only available in characteristic 2')
                 else:
                     return matrix_mod2_dense.Matrix_mod2_dense
             elif implementation == 'linbox-float':
diff --git a/src/sage/numerical/backends/coin_backend.pyx b/src/sage/numerical/backends/coin_backend.pyx
index da527137d21..0e95c7fd02b 100644
--- a/src/sage/numerical/backends/coin_backend.pyx
+++ b/src/sage/numerical/backends/coin_backend.pyx
@@ -445,7 +445,7 @@ cdef class CoinBackend(GenericBackend):
 
         INPUT:
 
-        - ``constraints`` -- an interable containing the indices of the rows to remove
+        - ``constraints`` -- an iterable containing the indices of the rows to remove
 
         EXAMPLES::
 
diff --git a/src/sage/numerical/backends/glpk_graph_backend.pyx b/src/sage/numerical/backends/glpk_graph_backend.pyx
index 52a4b6e8e97..65ca73706f6 100644
--- a/src/sage/numerical/backends/glpk_graph_backend.pyx
+++ b/src/sage/numerical/backends/glpk_graph_backend.pyx
@@ -626,7 +626,7 @@ cdef class GLPKGraphBackend(object):
 
         - ``edges`` -- An iterable container of pairs of the form ``(u, v)``,
           where ``u`` is name (as ``str``) of the tail vertex and ``v`` is the
-          name (as ``str``) of the head vertex or an interable container of
+          name (as ``str``) of the head vertex or an iterable container of
           triples of the form ``(u, v, params)`` where params is a ``dict`` as
           described in ``add_edge``.
 
diff --git a/src/sage/rings/finite_rings/element_givaro.pyx b/src/sage/rings/finite_rings/element_givaro.pyx
index 90e2aabc69a..1c2d5facece 100644
--- a/src/sage/rings/finite_rings/element_givaro.pyx
+++ b/src/sage/rings/finite_rings/element_givaro.pyx
@@ -918,7 +918,7 @@ cdef class FiniteField_givaroElement(FinitePolyExtElement):
 
     def _element(self):
         """
-        Returns the int interally representing this element.
+        Return the int internally representing this element.
 
         EXAMPLES::
 
diff --git a/src/sage/rings/function_field/function_field.py b/src/sage/rings/function_field/function_field.py
index ca90682b5e4..e79308952d0 100644
--- a/src/sage/rings/function_field/function_field.py
+++ b/src/sage/rings/function_field/function_field.py
@@ -1483,9 +1483,11 @@ def genus(self):
             sage: L.genus()
             3
         """
-        # unfortunately singular can not compute the genus with the polynomial_ring()._singular_
-        # object because genus method only accepts a ring of transdental degree 2 over a prime field
-        # not a ring of transdental degree 1 over a rational function field of one variable
+        # unfortunately singular can not compute the genus with the
+        # polynomial_ring()._singular_ object because genus method
+        # only accepts a ring of transcendental degree 2 over a prime
+        # field not a ring of transcendental degree 1 over a rational
+        # function field of one variable
 
         if is_RationalFunctionField(self._base_field) and self._base_field.constant_field().is_prime_field():
 
diff --git a/src/sage/rings/morphism.pyx b/src/sage/rings/morphism.pyx
index bc059af3404..3959e80ba67 100644
--- a/src/sage/rings/morphism.pyx
+++ b/src/sage/rings/morphism.pyx
@@ -1913,7 +1913,7 @@ cdef class FrobeniusEndomorphism_generic(RingHomomorphism):
             raise TypeError("The base ring must be a commutative ring")
         self._p = domain.characteristic()
         if not self._p.is_prime():
-            raise TypeError("The caracteristic of the base ring must be prime")
+            raise TypeError("the characteristic of the base ring must be prime")
         try:
             n = Integer(n)
         except TypeError:
diff --git a/src/sage/rings/polynomial/pbori.pyx b/src/sage/rings/polynomial/pbori.pyx
index 318ff62af75..84eee914412 100644
--- a/src/sage/rings/polynomial/pbori.pyx
+++ b/src/sage/rings/polynomial/pbori.pyx
@@ -6416,7 +6416,7 @@ cdef class ReductionStrategy:
 
         - ``leading_terms`` - all leading terms of generators
 
-        - ``minimial_leading_terms`` - the reduced set of leading terms
+        - ``minimal_leading_terms`` - the reduced set of leading terms
 
         - ``monomials`` -
 
diff --git a/src/sage/rings/polynomial/polynomial_element.pyx b/src/sage/rings/polynomial/polynomial_element.pyx
index afa54f54ac0..56ec619d57f 100644
--- a/src/sage/rings/polynomial/polynomial_element.pyx
+++ b/src/sage/rings/polynomial/polynomial_element.pyx
@@ -9451,7 +9451,7 @@ cdef class Polynomial(CommutativeAlgebraElement):
             sage: f.homogenize('x')
             3*x^2
 
-        In positive characterstic, the degree can drop in this case::
+        In positive characteristic, the degree can drop in this case::
 
             sage: R.<x> = GF(2)[]
             sage: f = x + 1
diff --git a/src/sage/schemes/elliptic_curves/ell_number_field.py b/src/sage/schemes/elliptic_curves/ell_number_field.py
index 022cf77ccae..9764498d6d9 100644
--- a/src/sage/schemes/elliptic_curves/ell_number_field.py
+++ b/src/sage/schemes/elliptic_curves/ell_number_field.py
@@ -2628,7 +2628,7 @@ def isogeny_class(self):
 
         The array of isogenies themselves is not filled out but only
         contains those used to construct the class, the other entries
-        containing the interger 0.  This will be changed when the
+        containing the integer 0.  This will be changed when the
         class :class:`EllipticCurveIsogeny` allowed composition.  In
         this case we used `2`-isogenies to go from 0 to 2 and from 1
         to 3, and `3`-isogenies to go from 0 to 1 and from 2 to 3::
diff --git a/src/sage/schemes/elliptic_curves/isogeny_class.py b/src/sage/schemes/elliptic_curves/isogeny_class.py
index ffe6553fe88..677d5b74ff6 100644
--- a/src/sage/schemes/elliptic_curves/isogeny_class.py
+++ b/src/sage/schemes/elliptic_curves/isogeny_class.py
@@ -619,7 +619,7 @@ def __init__(self, E):
 
         The array of isogenies themselves is not filled out but only
         contains those used to construct the class, the other entries
-        containing the interger 0.  This will be changed when the
+        containing the integer 0.  This will be changed when the
         class :class:`EllipticCurveIsogeny` allowed composition.  In
         this case we used `2`-isogenies to go from 0 to 2 and from 1
         to 3, and `3`-isogenies to go from 0 to 1 and from 2 to 3::
diff --git a/src/sage/schemes/hyperelliptic_curves/mestre.py b/src/sage/schemes/hyperelliptic_curves/mestre.py
index 6107c01c562..e916364e38d 100644
--- a/src/sage/schemes/hyperelliptic_curves/mestre.py
+++ b/src/sage/schemes/hyperelliptic_curves/mestre.py
@@ -108,7 +108,7 @@ def HyperellipticCurve_from_invariants(i, reduced=True, precision=None,
         TypeError: F (=0) must have degree 2
 
 
-    Igusa-Clebsch invariants also only work over fields of charateristic
+    Igusa-Clebsch invariants also only work over fields of characteristic
     different from 2, 3, and 5, so another algorithm will be needed for fields
     of those characteristics. See also :trac:`12200`::
 
diff --git a/src/sage/schemes/toric/divisor.py b/src/sage/schemes/toric/divisor.py
index 6de57b970fc..cb7802a3e57 100644
--- a/src/sage/schemes/toric/divisor.py
+++ b/src/sage/schemes/toric/divisor.py
@@ -742,7 +742,7 @@ def function_value(self, point):
 
         OUTPUT:
 
-        - an interger or a rational number.
+        - an integer or a rational number.
 
         EXAMPLES::
 
diff --git a/src/sage/structure/element.pyx b/src/sage/structure/element.pyx
index af800710aab..405080f1be5 100644
--- a/src/sage/structure/element.pyx
+++ b/src/sage/structure/element.pyx
@@ -3086,7 +3086,7 @@ cdef class CommutativeRingElement(RingElement):
                 if not isinstance(P, IntegralDomain):
                     raise NotImplementedError('sqrt() with all=True is only implemented for integral domains, not for %s' % P)
                 if P.characteristic()==2 or sq_rt==0:
-                    #0 has only one square root, and in charasteristic 2 everything also has only 1 root
+                    #0 has only one square root, and in characteristic 2 everything also has only 1 root
                     return [ sq_rt ]
                 return [ sq_rt, -sq_rt ]
             return sq_rt
diff --git a/src/sage/symbolic/expression.pyx b/src/sage/symbolic/expression.pyx
index dfc65cc5f73..7130898086c 100644
--- a/src/sage/symbolic/expression.pyx
+++ b/src/sage/symbolic/expression.pyx
@@ -2208,7 +2208,7 @@ cdef class Expression(CommutativeRingElement):
 
     def _is_registered_constant_(self):
         """
-        Return True if this symbolic expression is interally represented as
+        Return True if this symbolic expression is internally represented as
         a constant.
 
         This function is intended to provide an interface to query the internal
diff --git a/src/sage_setup/autogen/interpreters/__init__.py b/src/sage_setup/autogen/interpreters/__init__.py
index 8535d0c8095..8dbdae26295 100644
--- a/src/sage_setup/autogen/interpreters/__init__.py
+++ b/src/sage_setup/autogen/interpreters/__init__.py
@@ -139,7 +139,7 @@
                        key=lambda c: c.name)
 
 # Tuple of (filename_root, extension, method) where filename_root is the
-# root of the filename to be joined with "_<interpeter_name>".ext and
+# root of the filename to be joined with "_<interpreter_name>".ext and
 # method is the name of a get_ method on InterpreterGenerator that returns
 # the contents of that file
 _INTERPRETER_SOURCES = [

From 81352f59f223c1dd48e6c85e4b413baaed4a972e Mon Sep 17 00:00:00 2001
From: Thierry Monteil <sage@lma.metelu.net>
Date: Tue, 23 Jan 2018 00:32:11 +0100
Subject: [PATCH 120/128] #24586 : make build/pkgs/texlive/spkg-install
 executable

---
 build/pkgs/texlive/spkg-install | 0
 1 file changed, 0 insertions(+), 0 deletions(-)
 mode change 100644 => 100755 build/pkgs/texlive/spkg-install

diff --git a/build/pkgs/texlive/spkg-install b/build/pkgs/texlive/spkg-install
old mode 100644
new mode 100755

From 7c8d3aaae2fbb05bb251d5fc636815ccafe30213 Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?Fran=C3=A7ois=20Bissey?= <frp.bissey@gmail.com>
Date: Tue, 23 Jan 2018 14:52:31 +1300
Subject: [PATCH 121/128] moving to 1.4.9-45

---
 build/pkgs/giac/checksums.ini       | 6 +++---
 build/pkgs/giac/package-version.txt | 2 +-
 build/pkgs/giac/spkg-src            | 3 +--
 3 files changed, 5 insertions(+), 6 deletions(-)

diff --git a/build/pkgs/giac/checksums.ini b/build/pkgs/giac/checksums.ini
index 1da1baceb03..ae2283791d5 100644
--- a/build/pkgs/giac/checksums.ini
+++ b/build/pkgs/giac/checksums.ini
@@ -1,4 +1,4 @@
 tarball=giac-VERSION.tar.bz2
-sha1=7ba617ef29dde72bb927a0e92541e8a30325a7a4
-md5=45dfd01ee167cc0221d07e54db0c28e2
-cksum=1393477559
+sha1=3b61dd5fe79a76c2e0d4ef60ad1ad90dc3c04bd3
+md5=55308225758c547b061b52d699fa8b13
+cksum=2762392051
diff --git a/build/pkgs/giac/package-version.txt b/build/pkgs/giac/package-version.txt
index 1ccdedf3c0c..f7272f4bb5c 100644
--- a/build/pkgs/giac/package-version.txt
+++ b/build/pkgs/giac/package-version.txt
@@ -1 +1 @@
-1.4.9.39
+1.4.9.45
diff --git a/build/pkgs/giac/spkg-src b/build/pkgs/giac/spkg-src
index 9d52f68ac00..d82372402ef 100755
--- a/build/pkgs/giac/spkg-src
+++ b/build/pkgs/giac/spkg-src
@@ -13,9 +13,8 @@ fi
 # Exit on failure
 set -e
 
-# TODO on the next update: l71 switch from gz to bz2 as wished in #18826
 VERSION="1.4.9"
-VERSIONREV="39"
+VERSIONREV="45"
 
 # The upstream tarball name is: giac"$SOURCEORIG".tar.gz
 SOURCEORIG=_"$VERSION"-"$VERSIONREV"

From 72d9751acefbb271e75ca088e10d8e09a2647110 Mon Sep 17 00:00:00 2001
From: Jeroen Demeyer <jdemeyer@cage.ugent.be>
Date: Fri, 12 Jan 2018 14:19:32 +0100
Subject: [PATCH 122/128] Upgrade some Jupyter packages

---
 build/pkgs/jupyter_client/checksums.ini        |  6 +++---
 build/pkgs/jupyter_client/package-version.txt  |  2 +-
 build/pkgs/notebook/checksums.ini              |  6 +++---
 build/pkgs/notebook/dependencies               |  2 +-
 build/pkgs/notebook/jupyter_notebook_config.py |  5 +++++
 build/pkgs/notebook/package-version.txt        |  2 +-
 build/pkgs/pari_jupyter/SPKG.txt               | 10 +++++-----
 build/pkgs/pari_jupyter/checksums.ini          |  8 ++++----
 build/pkgs/pari_jupyter/dependencies           |  2 +-
 build/pkgs/pari_jupyter/package-version.txt    |  2 +-
 build/pkgs/send2trash/SPKG.txt                 | 17 +++++++++++++++++
 build/pkgs/send2trash/checksums.ini            |  4 ++++
 build/pkgs/send2trash/dependencies             |  5 +++++
 build/pkgs/send2trash/package-version.txt      |  1 +
 build/pkgs/send2trash/spkg-install             |  1 +
 build/pkgs/send2trash/type                     |  1 +
 16 files changed, 54 insertions(+), 20 deletions(-)
 create mode 100644 build/pkgs/send2trash/SPKG.txt
 create mode 100644 build/pkgs/send2trash/checksums.ini
 create mode 100644 build/pkgs/send2trash/dependencies
 create mode 100644 build/pkgs/send2trash/package-version.txt
 create mode 100644 build/pkgs/send2trash/spkg-install
 create mode 100644 build/pkgs/send2trash/type

diff --git a/build/pkgs/jupyter_client/checksums.ini b/build/pkgs/jupyter_client/checksums.ini
index 84292b0761e..d7cb096a9c3 100644
--- a/build/pkgs/jupyter_client/checksums.ini
+++ b/build/pkgs/jupyter_client/checksums.ini
@@ -1,4 +1,4 @@
 tarball=jupyter_client-VERSION.tar.gz
-sha1=1f226cd2d437eed5f9c45d572c0c9efe53437ea9
-md5=990ab28f63861cc29f90585d3f725b10
-cksum=1587833857
+sha1=c45a59eaced3d9641bf96e8dd77b7842aec99fec
+md5=5ff5de46f731c52c91449d88d9b5c54d
+cksum=4141110982
diff --git a/build/pkgs/jupyter_client/package-version.txt b/build/pkgs/jupyter_client/package-version.txt
index 831446cbd27..26d99a283f2 100644
--- a/build/pkgs/jupyter_client/package-version.txt
+++ b/build/pkgs/jupyter_client/package-version.txt
@@ -1 +1 @@
-5.1.0
+5.2.1
diff --git a/build/pkgs/notebook/checksums.ini b/build/pkgs/notebook/checksums.ini
index ce2119db22a..214164b6dd1 100644
--- a/build/pkgs/notebook/checksums.ini
+++ b/build/pkgs/notebook/checksums.ini
@@ -1,4 +1,4 @@
 tarball=notebook-VERSION.tar.gz
-sha1=ebf8ac32b9ca6c981b8936f987d19a5689d0b298
-md5=61a3f3c8d97fe9ce8affd359733717e9
-cksum=2566272680
+sha1=5ef18cf1731383860efd944526454e5e9653b3db
+md5=ea79ad977a3ab25ef5f506065017e1ed
+cksum=2023952192
diff --git a/build/pkgs/notebook/dependencies b/build/pkgs/notebook/dependencies
index 1f206344809..97c7dede39f 100644
--- a/build/pkgs/notebook/dependencies
+++ b/build/pkgs/notebook/dependencies
@@ -1,4 +1,4 @@
-$(PYTHON) | pip ipython jupyter_client ipykernel nbconvert nbformat jinja2 tornado terminado
+$(PYTHON) | pip ipython jupyter_client ipykernel nbconvert nbformat jinja2 tornado terminado send2trash
 
 ----------
 All lines of this file are ignored except the first.
diff --git a/build/pkgs/notebook/jupyter_notebook_config.py b/build/pkgs/notebook/jupyter_notebook_config.py
index 1b0566a32ac..1ea31ce125f 100644
--- a/build/pkgs/notebook/jupyter_notebook_config.py
+++ b/build/pkgs/notebook/jupyter_notebook_config.py
@@ -11,3 +11,8 @@
 # * https://github.com/oreillymedia/thebe/issues/93
 
 c.NotebookApp.disable_check_xsrf = True
+
+# send2trash sometimes doesn't work, so disable that for now
+# See https://github.com/jupyter/notebook/issues/3249
+
+c.FileContentsManager.delete_to_trash = False
diff --git a/build/pkgs/notebook/package-version.txt b/build/pkgs/notebook/package-version.txt
index ce7f2b425b5..c7cb1311a64 100644
--- a/build/pkgs/notebook/package-version.txt
+++ b/build/pkgs/notebook/package-version.txt
@@ -1 +1 @@
-5.2.2
+5.3.1
diff --git a/build/pkgs/pari_jupyter/SPKG.txt b/build/pkgs/pari_jupyter/SPKG.txt
index 681cdc57f23..3a6ad00273c 100644
--- a/build/pkgs/pari_jupyter/SPKG.txt
+++ b/build/pkgs/pari_jupyter/SPKG.txt
@@ -11,12 +11,12 @@ GPL version 3 or later
 == Upstream Contact ==
 
 * https://github.com/jdemeyer/pari_jupyter
-* Jeroen Demeyer <jdemeyer@cage.ugent.be>
+* Jeroen Demeyer <J.Demeyer@UGent.be>
 
 == Dependencies ==
 
+* Python (tested with version 2.7.14 and 3.6.1)
 * Jupyter 4
-* Python (tested with 2.7.9)
-* Cython (git master)
-* PARI (git master)
-* GMP or MPIR (any version which works with PARI)
+* PARI version 2.8.0 or later
+* Readline (any version which works with PARI)
+* Optional: Cython version 0.25 or later
diff --git a/build/pkgs/pari_jupyter/checksums.ini b/build/pkgs/pari_jupyter/checksums.ini
index 8c4503ffb22..0bcc161a9b1 100644
--- a/build/pkgs/pari_jupyter/checksums.ini
+++ b/build/pkgs/pari_jupyter/checksums.ini
@@ -1,4 +1,4 @@
-tarball=pari_jupyter-VERSION.tar.bz2
-sha1=285acc6650ad177b092605938582e16d67e910bb
-md5=ab0dc1d09303d33e861088155b82c965
-cksum=1154883481
+tarball=pari_jupyter-VERSION.tar.gz
+sha1=6eac8e4466e4753fd07a38d16538222bec9b0a53
+md5=4d6e4b12afdb26c53e38b3b7aadfa18f
+cksum=109015385
diff --git a/build/pkgs/pari_jupyter/dependencies b/build/pkgs/pari_jupyter/dependencies
index 516d7089387..9e6b05089de 100644
--- a/build/pkgs/pari_jupyter/dependencies
+++ b/build/pkgs/pari_jupyter/dependencies
@@ -1 +1 @@
-$(PYTHON) pari jupyter_core | pip cython
+$(PYTHON) pari | pip cython notebook jupyter_core
diff --git a/build/pkgs/pari_jupyter/package-version.txt b/build/pkgs/pari_jupyter/package-version.txt
index 23aa8390630..1892b926767 100644
--- a/build/pkgs/pari_jupyter/package-version.txt
+++ b/build/pkgs/pari_jupyter/package-version.txt
@@ -1 +1 @@
-1.2.2
+1.3.2
diff --git a/build/pkgs/send2trash/SPKG.txt b/build/pkgs/send2trash/SPKG.txt
new file mode 100644
index 00000000000..d829cf1573b
--- /dev/null
+++ b/build/pkgs/send2trash/SPKG.txt
@@ -0,0 +1,17 @@
+= Send2Trash =
+
+== Description ==
+
+Send file to trash natively under Mac OS X, Windows and Linux.
+
+Send2Trash is a small package that sends files to the Trash (or Recycle
+Bin) natively and on all platforms. On OS X, it uses native
+FSMoveObjectToTrashSync Cocoa calls, on Windows, it uses native (and
+ugly) SHFileOperation win32 calls. On other platforms, if PyGObject and
+GIO are available, it will use this. Otherwise, it will fallback to its
+own implementation of the trash specifications from freedesktop.org.
+
+ctypes is used to access native libraries, so no compilation is
+necessary.
+
+Send2Trash supports Python 2.7 and up (Python 3 is supported).
diff --git a/build/pkgs/send2trash/checksums.ini b/build/pkgs/send2trash/checksums.ini
new file mode 100644
index 00000000000..f8312979034
--- /dev/null
+++ b/build/pkgs/send2trash/checksums.ini
@@ -0,0 +1,4 @@
+tarball=Send2Trash-VERSION.tar.gz
+sha1=34a01a1b0c25180e8f04c476f2a7cdaaf46e52ae
+md5=3aa42844d608370c9e19d108fdf3782d
+cksum=995505276
diff --git a/build/pkgs/send2trash/dependencies b/build/pkgs/send2trash/dependencies
new file mode 100644
index 00000000000..d5dab729e18
--- /dev/null
+++ b/build/pkgs/send2trash/dependencies
@@ -0,0 +1,5 @@
+$(PYTHON) | pip
+
+----------
+All lines of this file are ignored except the first.
+It is copied by SAGE_ROOT/build/make/install into SAGE_ROOT/build/make/Makefile.
diff --git a/build/pkgs/send2trash/package-version.txt b/build/pkgs/send2trash/package-version.txt
new file mode 100644
index 00000000000..9df886c42a1
--- /dev/null
+++ b/build/pkgs/send2trash/package-version.txt
@@ -0,0 +1 @@
+1.4.2
diff --git a/build/pkgs/send2trash/spkg-install b/build/pkgs/send2trash/spkg-install
new file mode 100644
index 00000000000..deba1bb42bb
--- /dev/null
+++ b/build/pkgs/send2trash/spkg-install
@@ -0,0 +1 @@
+cd src && sdh_pip_install .
diff --git a/build/pkgs/send2trash/type b/build/pkgs/send2trash/type
new file mode 100644
index 00000000000..a6a7b9cd726
--- /dev/null
+++ b/build/pkgs/send2trash/type
@@ -0,0 +1 @@
+standard

From 22c5834e32882ea85b14a8cf13897950f2d75460 Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?Fr=C3=A9d=C3=A9ric=20Chapoton?=
 <chapoton@math.univ-lyon1.fr>
Date: Wed, 24 Jan 2018 10:56:11 +0100
Subject: [PATCH 123/128] trac 19547 Improved documentation of ray_label and
 wall_label

---
 src/sage/geometry/toric_plotter.py | 6 ++++--
 1 file changed, 4 insertions(+), 2 deletions(-)

diff --git a/src/sage/geometry/toric_plotter.py b/src/sage/geometry/toric_plotter.py
index 867b3b0b419..8c9204a2dba 100644
--- a/src/sage/geometry/toric_plotter.py
+++ b/src/sage/geometry/toric_plotter.py
@@ -979,9 +979,11 @@ def options(option=None, **kwds):
 
     - ``font_size`` -- an integer, the size of font used for labels;
 
-    - ``ray_label`` -- a string or a list of strings used for ray labels;
+    - ``ray_label`` -- a string or a list of strings used for ray labels; use
+      ``None`` to hide labels;
 
-    - ``wall_label`` -- a string or a list of strings used for wall labels;
+    - ``wall_label`` -- a string or a list of strings used for wall labels; use
+      ``None`` to hide labels;
 
     - ``radius`` -- a positive number, the radius of the cut-off region for
       "round" mode;

From 37171e816fbebd13b64c4644e15966bb9c13ebef Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?Fr=C3=A9d=C3=A9ric=20Chapoton?=
 <chapoton@math.univ-lyon1.fr>
Date: Wed, 24 Jan 2018 13:33:39 +0100
Subject: [PATCH 124/128] trac 22170 fixing plot3d with mesh in jupyter
 notebook

---
 src/sage/repl/display/jsmol_iframe.py | 17 ++++++++++-------
 1 file changed, 10 insertions(+), 7 deletions(-)

diff --git a/src/sage/repl/display/jsmol_iframe.py b/src/sage/repl/display/jsmol_iframe.py
index 48831ca6611..b664bc6897b 100644
--- a/src/sage/repl/display/jsmol_iframe.py
+++ b/src/sage/repl/display/jsmol_iframe.py
@@ -155,13 +155,16 @@ def script(self):
                 if line.startswith('pmesh'):
                     command, obj, meshfile = line.split(' ', 3)
                     assert command == 'pmesh'
-                    assert meshfile.startswith('"') and meshfile.endswith('"\n')
-                    meshfile = meshfile[1:-2]    # strip quotes
-                    script += [
-                        'pmesh {0} inline "'.format(obj),
-                        self._zip.open(meshfile).read(),
-                        '"\n'
-                    ]
+                    if meshfile not in ['dots\n', 'mesh\n']:
+                        assert meshfile.startswith('"') and meshfile.endswith('"\n')
+                        meshfile = meshfile[1:-2]    # strip quotes
+                        script += [
+                            'pmesh {0} inline "'.format(obj),
+                            self._zip.open(meshfile).read(),
+                            '"\n'
+                        ]
+                    else:
+                        script += [line]
                 else:
                     script += [line]
         return ''.join(script)

From 8a2ffbf875e6aafeeb6ced2a59d618561b6dc728 Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?Fr=C3=A9d=C3=A9ric=20Chapoton?=
 <chapoton@math.univ-lyon1.fr>
Date: Wed, 24 Jan 2018 13:49:51 +0100
Subject: [PATCH 125/128] trac 24487 tentative fix of docbuild

---
 src/sage/plot/plot3d/list_plot3d.py | 7 +++----
 1 file changed, 3 insertions(+), 4 deletions(-)

diff --git a/src/sage/plot/plot3d/list_plot3d.py b/src/sage/plot/plot3d/list_plot3d.py
index 858ff56ed69..193a5d08429 100644
--- a/src/sage/plot/plot3d/list_plot3d.py
+++ b/src/sage/plot/plot3d/list_plot3d.py
@@ -255,8 +255,8 @@ def list_plot3d_matrix(m, texture, **kwds):
     which must take values in (0, 1)::
 
         sage: cm = colormaps.rainbow
-        sage: cf = lambda x, y: ((2*(x-y)/n)**2) % 1
         sage: n = 20
+        sage: cf = lambda x, y: ((2*(x-y)/n)**2) % 1
         sage: list_plot3d(matrix(RDF, n, [cos(pi*(i+j)/n) for i in [1..n]
         ....:   for j in [1..n]]), color=(cf,cm))
         Graphics3d Object
@@ -264,9 +264,8 @@ def list_plot3d_matrix(m, texture, **kwds):
     .. PLOT::
 
         cm = colormaps.rainbow
-        cf = lambda x, y: ((2*(x-y)/n)**2) % 1
-        n = 20
-        expl = list_plot3d(matrix(RDF, n, [cos(pi*(i+j)/n) for i in [1..n] for j in [1..n]]), color=(cf,cm))
+        cf = lambda x, y: ((2*(x-y)/20)**2) % 1
+        expl = list_plot3d(matrix(RDF,20,20,[cos(pi*(i+j)/20) for i in range(1,21) for j in range(1,21)]),color=(cf,cm))
         sphinx_plot(expl)    
     """
     from .parametric_surface import ParametricSurface

From c16e2677f4b3034e12af9efdc15bdfcb0411b030 Mon Sep 17 00:00:00 2001
From: Jeroen Demeyer <jdemeyer@cage.ugent.be>
Date: Thu, 25 Jan 2018 16:19:57 +0100
Subject: [PATCH 126/128] "./sage -f" should clean first before building the
 toolchain

---
 src/bin/sage | 56 ++++++++++++++++++++++++++++------------------------
 1 file changed, 30 insertions(+), 26 deletions(-)

diff --git a/src/bin/sage b/src/bin/sage
index d9fd2897e50..4cfd8c076d6 100755
--- a/src/bin/sage
+++ b/src/bin/sage
@@ -324,40 +324,44 @@ if [ "$1" = '-i' ]; then
     fi
 
     set -e
-
     cd "$SAGE_ROOT"
 
-    # First of all, make sure that the toolchain is up-to-date
-    # (which is a dependency of every package)
-    ./sage --location
-    $MAKE all-toolchain
-    echo
-
+    # Parse options
+    PACKAGES=""         # Packages to install
     INSTALL_OPTIONS=""  # Options to sage-spkg
-    for PKG in "$@"
-    do
-        case "$PKG" in
+    for OPT in "$@"; do
+        case "$OPT" in
             -info|--info)
-                echo >&2 "Error: 'sage -i $PKG <package>' is no longer supported, use 'sage --info <package>' instead."
+                echo >&2 "Error: 'sage -i $OPT <package>' is no longer supported, use 'sage --info <package>' instead."
                 exit 2;;
             -f) FORCE_INSTALL=yes;;
-            -*) INSTALL_OPTIONS="$INSTALL_OPTIONS $PKG";;
-            *)
-                # First check that $PKG is actually a Makefile target
-                if ! grep "^$PKG: " build/make/Makefile >/dev/null; then
-                    echo >&2 "Error: package '$PKG' not found"
-                    echo >&2 "Assuming it is an old-style package... (this is deprecated: use -p instead of -i to install old-style packages)"
-                    echo >&2
-                    sleep 5
-                    ./sage -p $INSTALL_OPTIONS "$PKG"
-                else
-                    if [ x$FORCE_INSTALL = xyes ]; then
-                        $MAKE "$PKG-clean"
-                    fi
-                    $MAKE SAGE_SPKG="sage-spkg $INSTALL_OPTIONS" "$PKG"
-                fi;;
+            -*) INSTALL_OPTIONS="$INSTALL_OPTIONS $OPT";;
+            *) PACKAGES="$PACKAGES $OPT";;
         esac
     done
+
+    # First, uninstall the packages if -f was given
+    if [ "$FORCE_INSTALL" = yes ]; then
+        for PKG in $PACKAGES; do
+            $MAKE "$PKG-clean" || true  # Ignore errors
+        done
+    fi
+
+    # Make sure that the toolchain is up-to-date
+    # (which is a dependency of every package)
+    $MAKE all-toolchain
+
+    # Now install the packages
+    for PKG in $PACKAGES; do
+        echo
+        # First check that $PKG is actually a Makefile target
+        if ! grep "^$PKG: " build/make/Makefile >/dev/null; then
+            echo >&2 "Error: package '$PKG' not found"
+            echo >&2 "Note: if it is an old-style package, use -p instead of -i to install it"
+            exit 1
+        fi
+        $MAKE SAGE_SPKG="sage-spkg $INSTALL_OPTIONS" "$PKG"
+    done
     exit 0
 fi
 

From be91769c7c106956678d33ac6fb2e726a42f5af6 Mon Sep 17 00:00:00 2001
From: Jeroen Demeyer <jdemeyer@cage.ugent.be>
Date: Thu, 25 Jan 2018 17:26:48 +0100
Subject: [PATCH 127/128] Further upgrades of Jupyter packages

---
 build/pkgs/jupyter_client/checksums.ini         | 6 +++---
 build/pkgs/jupyter_client/package-version.txt   | 2 +-
 build/pkgs/singular_jupyter/checksums.ini       | 6 +++---
 build/pkgs/singular_jupyter/package-version.txt | 2 +-
 4 files changed, 8 insertions(+), 8 deletions(-)

diff --git a/build/pkgs/jupyter_client/checksums.ini b/build/pkgs/jupyter_client/checksums.ini
index d7cb096a9c3..ab30f0430b2 100644
--- a/build/pkgs/jupyter_client/checksums.ini
+++ b/build/pkgs/jupyter_client/checksums.ini
@@ -1,4 +1,4 @@
 tarball=jupyter_client-VERSION.tar.gz
-sha1=c45a59eaced3d9641bf96e8dd77b7842aec99fec
-md5=5ff5de46f731c52c91449d88d9b5c54d
-cksum=4141110982
+sha1=2290704671547049ee20b034135a7a191fbc26f1
+md5=03293d63b59a3f71c417ee907852b460
+cksum=3064225526
diff --git a/build/pkgs/jupyter_client/package-version.txt b/build/pkgs/jupyter_client/package-version.txt
index 26d99a283f2..ce7f2b425b5 100644
--- a/build/pkgs/jupyter_client/package-version.txt
+++ b/build/pkgs/jupyter_client/package-version.txt
@@ -1 +1 @@
-5.2.1
+5.2.2
diff --git a/build/pkgs/singular_jupyter/checksums.ini b/build/pkgs/singular_jupyter/checksums.ini
index 9610c182c79..7def85d733f 100644
--- a/build/pkgs/singular_jupyter/checksums.ini
+++ b/build/pkgs/singular_jupyter/checksums.ini
@@ -1,4 +1,4 @@
 tarball=jupyter_kernel_singular-VERSION.tar.gz
-sha1=381319a1a49c4565078392bcd65b306f2dc22707
-md5=915e2e89b759297a8aebcfe8ca400cbb
-cksum=3440281746
+sha1=e10d0894cac9ee111e34c6d6d6e409b26edf108f
+md5=c2acfe07c1094200dac521d2e8dcb2a9
+cksum=970360836
diff --git a/build/pkgs/singular_jupyter/package-version.txt b/build/pkgs/singular_jupyter/package-version.txt
index 2003b639c40..c81aa44afbf 100644
--- a/build/pkgs/singular_jupyter/package-version.txt
+++ b/build/pkgs/singular_jupyter/package-version.txt
@@ -1 +1 @@
-0.9.2
+0.9.7

From 0a674fd488dcd7cb779101d263c10a874a13cf77 Mon Sep 17 00:00:00 2001
From: Volker Braun <vbraun.name@gmail.com>
Date: Sun, 28 Jan 2018 00:22:44 +0100
Subject: [PATCH 128/128] Updated SageMath version to 8.2.beta4

---
 VERSION.txt                              | 2 +-
 build/pkgs/configure/checksums.ini       | 6 +++---
 build/pkgs/configure/package-version.txt | 2 +-
 src/bin/sage-banner                      | 2 +-
 src/bin/sage-version.sh                  | 4 ++--
 src/sage/version.py                      | 4 ++--
 6 files changed, 10 insertions(+), 10 deletions(-)

diff --git a/VERSION.txt b/VERSION.txt
index 20494d07023..b503aeef942 100644
--- a/VERSION.txt
+++ b/VERSION.txt
@@ -1 +1 @@
-SageMath version 8.2.beta3, Release Date: 2018-01-17
+SageMath version 8.2.beta4, Release Date: 2018-01-27
diff --git a/build/pkgs/configure/checksums.ini b/build/pkgs/configure/checksums.ini
index 680bb78988f..41fb4d74819 100644
--- a/build/pkgs/configure/checksums.ini
+++ b/build/pkgs/configure/checksums.ini
@@ -1,4 +1,4 @@
 tarball=configure-VERSION.tar.gz
-sha1=fce3f8df178645228d91b6b65e3a03af0b2b3641
-md5=587c7e18518428f0f30138eeb7743bad
-cksum=144653522
+sha1=499badf9321c53c458652ca71580585463e574a3
+md5=e483eb587a1be5886b718e24f54a84a5
+cksum=3889320352
diff --git a/build/pkgs/configure/package-version.txt b/build/pkgs/configure/package-version.txt
index 1f7e0d6eac6..2197544d04c 100644
--- a/build/pkgs/configure/package-version.txt
+++ b/build/pkgs/configure/package-version.txt
@@ -1 +1 @@
-251
+252
diff --git a/src/bin/sage-banner b/src/bin/sage-banner
index 5116d986fde..d2e95e4428d 100644
--- a/src/bin/sage-banner
+++ b/src/bin/sage-banner
@@ -1,5 +1,5 @@
 ┌────────────────────────────────────────────────────────────────────┐
-│ SageMath version 8.2.beta3, Release Date: 2018-01-17               │
+│ SageMath version 8.2.beta4, Release Date: 2018-01-27               │
 │ Type "notebook()" for the browser-based notebook interface.        │
 │ Type "help()" for help.                                            │
 └────────────────────────────────────────────────────────────────────┘
diff --git a/src/bin/sage-version.sh b/src/bin/sage-version.sh
index b95e9d65275..270e83c3a8a 100644
--- a/src/bin/sage-version.sh
+++ b/src/bin/sage-version.sh
@@ -1,4 +1,4 @@
 # Sage version information for shell scripts
 # This file is auto-generated by the sage-update-version script, do not edit!
-SAGE_VERSION='8.2.beta3'
-SAGE_RELEASE_DATE='2018-01-17'
+SAGE_VERSION='8.2.beta4'
+SAGE_RELEASE_DATE='2018-01-27'
diff --git a/src/sage/version.py b/src/sage/version.py
index 4d100301684..1d98722b54f 100644
--- a/src/sage/version.py
+++ b/src/sage/version.py
@@ -1,4 +1,4 @@
 # Sage version information for Python scripts
 # This file is auto-generated by the sage-update-version script, do not edit!
-version = '8.2.beta3'
-date = '2018-01-17'
+version = '8.2.beta4'
+date = '2018-01-27'