Merge 2c29fc1 into 1de5ffe

bin/coverage_doctest.py

@@ -229,7 +229,7 @@ def _get_arg_list(name, fobj):
         arg_list.append(argspec.keywords)
 
     # Truncate long arguments
-    arg_list = map(lambda x: x[:trunc], arg_list)
+    arg_list = [x[:trunc] for x in arg_list]
 
     # Construct the parameter string (enclosed in brackets)
     str_param = "%s(%s)" % (name, ', '.join(arg_list))
@@ -396,7 +396,7 @@ def coverage(module_path, verbose=False, no_color=False, sphinx=True):
     contained. It then goes through each of the classes/functions to get
     the docstring and doctest coverage of the module. """
 
-    # Import the package and find membmers
+    # Import the package and find members
     m = None
     try:
         __import__(module_path)

examples/advanced/gibbs_phenomenon.py

@@ -26,7 +26,8 @@ def l2_norm(f, lim):
     x ...... the independent variable in f over which to integrate
     a, b ... the limits of the interval
 
-    Example:
+    Examples
+    ========
 
     >>> from sympy import Symbol
     >>> from gibbs_phenomenon import l2_norm
@@ -61,7 +62,8 @@ def l2_gram_schmidt(list, lim):
     """
     Orthonormalizes the "list" of functions using the Gram-Schmidt process.
 
-    Example:
+    Examples
+    ========
 
     >>> from sympy import Symbol
     >>> from gibbs_phenomenon import l2_gram_schmidt

examples/intermediate/vandermonde.py

@@ -40,7 +40,7 @@ def comb_w_rep(n, k):
 
 
 def vandermonde(order, dim=1, syms='a b c d'):
-    """Comptutes a Vandermonde matrix of given order and dimension.
+    """Computes a Vandermonde matrix of given order and dimension.
 
     Define syms to give beginning strings for temporary variables.
 
@@ -118,7 +118,7 @@ def main():
     pprint(V)
 
     print('-'*79)
-    print("Computing the determinate and comparing to \sum_{0<i<j<=3}(a_j - a_i)")
+    print("Computing the determinant and comparing to \sum_{0<i<j<=3}(a_j - a_i)")
 
     det_sum = 1
     for j in range(order + 1):

sympy/assumptions/handlers/calculus.py

@@ -61,7 +61,8 @@ class AskFiniteHandler(CommonHandler):
 
     Test that an expression is finite respect to all its variables.
 
-    Examples of usage:
+    Examples
+    ========
 
     >>> from sympy import Symbol, Q
     >>> from sympy.assumptions.handlers.calculus import AskFiniteHandler
@@ -79,7 +80,8 @@ def Symbol(expr, assumptions):
         """
         Handles Symbol.
 
-        Examples:
+        Examples
+        ========
 
         >>> from sympy import Symbol, Q
         >>> from sympy.assumptions.handlers.calculus import AskFiniteHandler

sympy/assumptions/handlers/order.py

@@ -14,7 +14,8 @@ class AskNegativeHandler(CommonHandler):
 
     Test that an expression is less (strict) than zero.
 
-    Examples:
+    Examples
+    ========
 
     >>> from sympy import ask, Q, pi
     >>> ask(Q.negative(pi+1)) # this calls AskNegativeHandler.Add

sympy/calculus/euler.py

@@ -24,7 +24,7 @@ def euler_equations(L, funcs=(), vars=()):
                       \frac{\partial g(x,y)}{\partial y},x,y\right)
 
         In many cases it is not necessary to provide anything, except the
-        Lagrangian, it will be autodetected (and an error raised if this
+        Lagrangian, it will be auto-detected (and an error raised if this
         couldn't be done).
 
     funcs : Function or an iterable of Functions

sympy/combinatorics/graycode.py

@@ -375,9 +375,9 @@ def get_subset_from_bitstring(super_set, bitstring):
     ========
 
     >>> from sympy.combinatorics.graycode import get_subset_from_bitstring
-    >>> get_subset_from_bitstring(['a','b','c','d'], '0011')
+    >>> get_subset_from_bitstring(['a', 'b', 'c', 'd'], '0011')
     ['c', 'd']
-    >>> get_subset_from_bitstring(['c','a','c','c'], '1100')
+    >>> get_subset_from_bitstring(['c', 'a', 'c', 'c'], '1100')
     ['c', 'a']
 
     See Also
@@ -398,10 +398,10 @@ def graycode_subsets(gray_code_set):
     ========
 
     >>> from sympy.combinatorics.graycode import graycode_subsets
-    >>> list(graycode_subsets(['a','b','c']))
+    >>> list(graycode_subsets(['a', 'b', 'c']))
     [[], ['c'], ['b', 'c'], ['b'], ['a', 'b'], ['a', 'b', 'c'], \
     ['a', 'c'], ['a']]
-    >>> list(graycode_subsets(['a','b','c','c']))
+    >>> list(graycode_subsets(['a', 'b', 'c', 'c']))
     [[], ['c'], ['c', 'c'], ['c'], ['b', 'c'], ['b', 'c', 'c'], \
     ['b', 'c'], ['b'], ['a', 'b'], ['a', 'b', 'c'], ['a', 'b', 'c', 'c'], \
     ['a', 'b', 'c'], ['a', 'c'], ['a', 'c', 'c'], ['a', 'c'], ['a']]

sympy/combinatorics/group_constructs.py

@@ -26,7 +26,7 @@ def DirectProduct(*groups):
     >>> from sympy.combinatorics.group_constructs import DirectProduct
     >>> from sympy.combinatorics.named_groups import CyclicGroup
     >>> C = CyclicGroup(4)
-    >>> G = DirectProduct(C,C,C)
+    >>> G = DirectProduct(C, C, C)
     >>> G.order()
     64
 
@@ -55,7 +55,7 @@ def DirectProduct(*groups):
         for j in range(current_gen, current_gen + gens_count[i]):
             gen = ((groups[i].generators)[j - current_gen]).array_form
             array_gens[j][current_deg:current_deg + degrees[i]] = \
-                [ x + current_deg for x in gen]
+                [x + current_deg for x in gen]
         current_gen += gens_count[i]
         current_deg += degrees[i]
     perm_gens = list(uniq([_af_new(list(a)) for a in array_gens]))

sympy/combinatorics/named_groups.py

@@ -291,7 +291,8 @@ def SymmetricGroup(n):
 
 
 def RubikGroup(n):
-    """Return a group of Rubik's cube generators.
+    """Return a group of Rubik's cube generators
+
     >>> from sympy.combinatorics.named_groups import RubikGroup
     >>> RubikGroup(2).is_group()
     False

sympy/combinatorics/partitions.py

@@ -58,7 +58,7 @@ def __new__(cls, *partition):
         if has_dups(partition):
             raise ValueError("Partition contained duplicated elements.")
 
-        obj = FiniteSet.__new__(cls, *list(map(lambda x: FiniteSet(*x), args)))
+        obj = FiniteSet.__new__(cls, *[FiniteSet(*x) for x in args])
         obj.members = tuple(partition)
         obj.size = len(partition)
         return obj
@@ -323,6 +323,7 @@ def __new__(cls, partition, integer=None):
 
         If the value that the partion should sum to is given first, a check
         will be made to see n error will be raised if there is a discrepancy:
+
         >>> IntegerPartition(10, [5, 4, 3, 1])
         Traceback (most recent call last):
         ...

sympy/combinatorics/perm_groups.py

@@ -2055,11 +2055,11 @@ def orbit(self, alpha, action='tuples'):
 
         >>> from sympy.combinatorics import Permutation
         >>> from sympy.combinatorics.perm_groups import PermutationGroup
-        >>> a = Permutation([1,2,0,4,5,6,3])
+        >>> a = Permutation([1, 2, 0, 4, 5, 6, 3])
         >>> G = PermutationGroup([a])
         >>> G.orbit(0)
         set([0, 1, 2])
-        >>> G.orbit([0,4], 'union')
+        >>> G.orbit([0, 4], 'union')
         set([0, 1, 2, 3, 4, 5, 6])
 
         See Also
@@ -2153,8 +2153,8 @@ def orbits(self, rep=False):
 
         >>> from sympy.combinatorics.permutations import Permutation
         >>> from sympy.combinatorics.perm_groups import PermutationGroup
-        >>> a = Permutation(1,5)(2,3)(4,0,6)
-        >>> b = Permutation(1,5)(3,4)(2,6,0)
+        >>> a = Permutation(1, 5)(2, 3)(4, 0, 6)
+        >>> b = Permutation(1, 5)(3, 4)(2, 6, 0)
         >>> G = PermutationGroup([a, b])
         >>> G.orbits()
         [set([0, 2, 3, 4, 6]), set([1, 5])]
@@ -2725,9 +2725,9 @@ def schreier_vector(self, alpha):
 
         >>> from sympy.combinatorics.perm_groups import PermutationGroup
         >>> from sympy.combinatorics.permutations import Permutation
-        >>> a = Permutation([2,4,6,3,1,5,0])
-        >>> b = Permutation([0,1,3,5,4,6,2])
-        >>> G = PermutationGroup([a,b])
+        >>> a = Permutation([2, 4, 6, 3, 1, 5, 0])
+        >>> b = Permutation([0, 1, 3, 5, 4, 6, 2])
+        >>> G = PermutationGroup([a, b])
         >>> G.schreier_vector(0)
         [-1, None, 0, 1, None, 1, 0]
 
@@ -3085,7 +3085,7 @@ def transitivity_degree(self):
         >>> from sympy.combinatorics.permutations import Permutation
         >>> a = Permutation([1, 2, 0])
         >>> b = Permutation([1, 0, 2])
-        >>> G = PermutationGroup([a,b])
+        >>> G = PermutationGroup([a, b])
         >>> G.transitivity_degree
         3
 
@@ -3223,7 +3223,7 @@ def _orbit(degree, generators, alpha, action='tuples'):
 
     'union' - computes the union of the orbits of the points in the list
     'tuples' - computes the orbit of the list interpreted as an ordered
-    tuple under the group action ( i.e., g((1,2,3)) = (g(1), g(2), g(3)) )
+    tuple under the group action ( i.e., g((1, 2, 3)) = (g(1), g(2), g(3)) )
     'sets' - computes the orbit of the list interpreted as a sets
 
     Examples

sympy/combinatorics/subsets.py

@@ -539,7 +539,8 @@ def subset_indices(self, subset, superset):
         """Return indices of subset in superset in a list; the list is empty
         if all elements of subset are not in superset.
 
-        Examples::
+        Examples
+        ========
 
             >>> from sympy.combinatorics import Subset
             >>> superset = [1, 3, 2, 5, 4]

sympy/combinatorics/tensor_can.py

@@ -1052,11 +1052,13 @@ def tensor_gens(base, gens, list_free_indices, sym=0):
     >>> Permutation.print_cyclic = True
 
     two symmetric tensors with 3 indices without free indices
+
     >>> base, gens = get_symmetric_group_sgs(3)
     >>> tensor_gens(base, gens, [[], []])
     (8, [0, 1, 3, 4], [Permutation(7)(0, 1), Permutation(7)(1, 2), Permutation(7)(3, 4), Permutation(7)(4, 5), Permutation(7)(0, 3)(1, 4)(2, 5)])
 
     two symmetric tensors with 3 indices with free indices in slot 1 and 0
+
     >>> tensor_gens(base, gens, [[1],[0]])
     (8, [0, 4], [Permutation(7)(0, 2), Permutation(7)(4, 5)])
 

sympy/core/basic.py

@@ -1551,14 +1551,17 @@ def rewrite(self, *args, **hints):
         >>> from sympy.abc import x
 
         Unspecified pattern:
+
         >>> sin(x).rewrite(exp)
         -I*(exp(I*x) - exp(-I*x))/2
 
         Pattern as a single function:
+
         >>> sin(x).rewrite(sin, exp)
         -I*(exp(I*x) - exp(-I*x))/2
 
         Pattern as a list of functions:
+
         >>> sin(x).rewrite([sin, ], exp)
         -I*(exp(I*x) - exp(-I*x))/2
 
@@ -1788,7 +1791,8 @@ def skip(self):
         Skip yielding current node's (last yielded node's) subtrees.
 
         Examples
-        --------
+        ========
+
         >>> from sympy.core import symbols
         >>> from sympy.core.basic import preorder_traversal
         >>> x, y, z = symbols('x y z')

sympy/core/compatibility.py

@@ -341,7 +341,7 @@ def default_sort_key(item, order=None):
     Examples
     ========
 
-    >>> from sympy import S, I, default_sort_key
+    >>> from sympy import S, I, default_sort_key, sin, cos, sqrt
     >>> from sympy.core.function import UndefinedFunction
     >>> from sympy.abc import x
 
@@ -419,9 +419,19 @@ def default_sort_key(item, order=None):
     The order of terms obtained when using these keys is the order that would
     be obtained if those terms were *factors* in a product.
 
+    Although it is useful for quickly putting expressions in canonical order,
+    it does not sort expressions based on their complexity defined by the
+    number of operations, power of variables and others:
+
+    >>> sorted([sin(x)*cos(x), sin(x)], key=default_sort_key)
+    [sin(x)*cos(x), sin(x)]
+    >>> sorted([x, x**2, sqrt(x), x**3], key=default_sort_key)
+    [sqrt(x), x, x**2, x**3]
+
     See Also
     ========
 
+    ordered
     sympy.core.expr.Expr.as_ordered_factors
     sympy.core.expr.Expr.as_ordered_terms
     """

sympy/core/expr.py

@@ -2323,6 +2323,9 @@ def is_rational_function(self, *syms):
         See also is_algebraic_expr().
 
         """
+        if self in [S.NaN, S.Infinity, -S.Infinity, S.ComplexInfinity]:
+            return False
+
         if syms:
             syms = set(map(sympify, syms))
         else:

sympy/core/exprtools.py

@@ -1102,7 +1102,9 @@ def factor_nc(expr):
     """Return the factored form of ``expr`` while handling non-commutative
     expressions.
 
-    **examples**
+    Examples
+    ========
+
     >>> from sympy.core.exprtools import factor_nc
     >>> from sympy import Symbol
     >>> from sympy.abc import x

sympy/core/facts.py

@@ -186,7 +186,7 @@ def apply_beta_to_alpha_route(alpha_implications, beta_rules):
                     ximpls.add(bimpl)
 
                     # we introduced new implication - now we have to restore
-                    # completness of the whole set.
+                    # completeness of the whole set.
                     bimpl_impl = x_impl.get(bimpl)
                     if bimpl_impl is not None:
                         ximpls |= bimpl_impl[0]

sympy/core/function.py

@@ -1151,7 +1151,7 @@ def _sort_variables(cls, vars):
         * Derivatives wrt symbols and non-symbols don't commute.
 
         Examples
-        --------
+        ========
 
         >>> from sympy import Derivative, Function, symbols
         >>> vsort = Derivative._sort_variables
@@ -1301,7 +1301,7 @@ def _eval_subs(self, old, new):
                 if match:
                     variables = self_vars_front + self_vars
                     return Derivative(new, *variables)
-        return Derivative(*map(lambda x: x._subs(old, new), self.args))
+        return Derivative(*(x._subs(old, new) for x in self.args))
 
     def _eval_lseries(self, x, logx):
         dx = self.args[1:]
@@ -1937,8 +1937,8 @@ def _eval_expand_hint(self, **hints):
     kind of 'expansion'.  For hints that simply rewrite an expression, use the
     .rewrite() API.
 
-    Example
-    -------
+    Examples
+    ========
 
     >>> from sympy import Expr, sympify
     >>> class MyClass(Expr):

sympy/core/mul.py

@@ -550,7 +550,10 @@ def _handle_for_oo(c_part, coeff_sign):
 
         # 0
         elif coeff is S.Zero:
-            # we know for sure the result will be 0
+            # we know for sure the result will be 0 except the multiplicand
+            # is infinity
+            if any(c.is_finite == False for c in c_part):
+                return [S.NaN], [], order_symbols
             return [coeff], [], order_symbols
 
         # check for straggling Numbers that were produced
@@ -1534,6 +1537,7 @@ def prod(a, start=1):
     True
 
     You can start the product at something other than 1:
+
     >>> prod([1, 2], 3)
     6
 

sympy/core/sympify.py

@@ -28,8 +28,8 @@ class CantSympify(object):
     """
     Mix in this trait to a class to disallow sympification of its instances.
 
-    Example
-    =======
+    Examples
+    ========
 
     >>> from sympy.core.sympify import sympify, CantSympify