Merge #32102

src/sage/manifolds/continuous_map.py

@@ -837,8 +837,7 @@ def image(self, subset=None, inverse=None):
             sage: M = Manifold(2, 'M', structure="topological")
             sage: N = Manifold(1, 'N', ambient=M, structure="topological")
             sage: CM.<x,y> = M.chart()
-            sage: CN.<u> = N.chart()
-            sage: CN.add_restrictions([u > -1, u < 1])
+            sage: CN.<u> = N.chart(coord_restrictions=lambda u: [u > -1, u < 1])
             sage: Phi = N.continuous_map(M, {(CN,CM): [u, u^2]}, name='Phi')
             sage: Phi.image()
             Image of the Continuous map Phi

src/sage/manifolds/continuous_map_image.py

@@ -48,8 +48,7 @@ def __init__(self, map, inverse=None, name=None, latex_name=None, domain_subset=
             sage: M = Manifold(2, 'M', structure="topological")
             sage: N = Manifold(1, 'N', ambient=M, structure="topological")
             sage: CM.<x,y> = M.chart()
-            sage: CN.<u> = N.chart()
-            sage: CN.add_restrictions([u > -1, u < 1])
+            sage: CN.<u> = N.chart(coord_restrictions=lambda u: [u > -1, u < 1])
             sage: Phi = N.continuous_map(M, {(CN,CM): [u, 1 + u^2]}, name='Phi')
             sage: Phi_inv = M.continuous_map(N, {(CM, CN): [x]}, name='Phi_inv')
             sage: Phi_N = Phi.image(inverse=Phi_inv)
@@ -81,8 +80,7 @@ def _repr_(self):
             sage: M = Manifold(2, 'M', structure="topological")
             sage: N = Manifold(1, 'N', ambient=M, structure="topological")
             sage: CM.<x,y> = M.chart()
-            sage: CN.<u> = N.chart()
-            sage: CN.add_restrictions([u > -1, u < 1])
+            sage: CN.<u> = N.chart(coord_restrictions=lambda u: [u > -1, u < 1])
             sage: Phi = N.continuous_map(M, {(CN,CM): [u, 1 + u^2]}, name='Phi')
             sage: Phi.image()                                 # indirect doctest
             Image of the Continuous map Phi
@@ -114,8 +112,7 @@ def _an_element_(self):
             sage: M = Manifold(2, 'M', structure="topological")
             sage: N = Manifold(1, 'N', ambient=M, structure="topological")
             sage: CM.<x,y> = M.chart()
-            sage: CN.<u> = N.chart()
-            sage: CN.add_restrictions([u > -1, u < 1])
+            sage: CN.<u> = N.chart(coord_restrictions=lambda u: [u > -1, u < 1])
             sage: Phi = N.continuous_map(M, {(CN,CM): [u, 1 + u^2]}, name='Phi')
             sage: Phi_N = Phi.image()
             sage: p = Phi_N.an_element(); p   # indirect doctest
@@ -134,8 +131,7 @@ def __contains__(self, point):
             sage: M = Manifold(2, 'M', structure="topological")
             sage: N = Manifold(1, 'N', ambient=M, structure="topological")
             sage: CM.<x,y> = M.chart()
-            sage: CN.<u> = N.chart()
-            sage: CN.add_restrictions([u > -1, u < 1])
+            sage: CN.<u> = N.chart(coord_restrictions=lambda u: [u > -1, u < 1])
             sage: Phi = N.continuous_map(M, {(CN,CM): [u, 1 + u^2]}, name='Phi')
             sage: Phi_inv = M.continuous_map(N, {(CM, CN): [x]}, name='Phi_inv')
             sage: Phi_N = Phi.image(inverse=Phi_inv)

src/sage/manifolds/differentiable/chart.py

@@ -72,10 +72,6 @@ class DiffChart(Chart):
       If no period and no LaTeX spelling are to be set for any coordinate, the
       argument ``coordinates`` can be omitted when the shortcut operator
       ``<,>`` is used to declare the chart (see examples below).
-    - ``names`` -- (default: ``None``) unused argument, except if
-      ``coordinates`` is not provided; it must then be a tuple containing
-      the coordinate symbols (this is guaranteed if the shortcut operator
-      ``<,>`` is used).
     - ``calc_method`` -- (default: ``None``) string defining the calculus
       method for computations involving coordinates of the chart; must be
       one of
@@ -85,6 +81,27 @@ class DiffChart(Chart):
       - ``None``: the default of
         :class:`~sage.manifolds.calculus_method.CalculusMethod` will be
         used
+    - ``names`` -- (default: ``None``) unused argument, except if
+      ``coordinates`` is not provided; it must then be a tuple containing
+      the coordinate symbols (this is guaranteed if the shortcut operator
+      ``<,>`` is used).
+    - ``coord_restrictions``: Additional restrictions on the coordinates.
+      A restriction can be any symbolic equality or inequality involving
+      the coordinates, such as ``x > y`` or ``x^2 + y^2 != 0``. The items
+      of the list (or set or frozenset) ``coord_restrictions`` are combined
+      with the ``and`` operator; if some restrictions are to be combined with
+      the ``or`` operator instead, they have to be passed as a tuple in some
+      single item of the list (or set or frozenset) ``coord_restrictions``.
+      For example::
+
+        coord_restrictions=[x > y, (x != 0, y != 0), z^2 < x]
+
+      means ``(x > y) and ((x != 0) or (y != 0)) and (z^2 < x)``.
+      If the list ``coord_restrictions`` contains only one item, this
+      item can be passed as such, i.e. writing ``x > y`` instead
+      of the single element list ``[x > y]``.  If the chart variables have
+      not been declared as variables yet, ``coord_restrictions`` must
+      be ``lambda``-quoted.
 
     EXAMPLES:
 
@@ -259,7 +276,7 @@ class DiffChart(Chart):
         on differentiable manifolds over `\RR`.
 
     """
-    def __init__(self, domain, coordinates, calc_method=None, periods=None):
+    def __init__(self, domain, coordinates, calc_method=None, periods=None, coord_restrictions=None):
         r"""
         Construct a chart.
 
@@ -276,8 +293,8 @@ def __init__(self, domain, coordinates, calc_method=None, periods=None):
             sage: TestSuite(X).run()
 
         """
-        super().__init__(domain, coordinates,
-                         calc_method=calc_method, periods=periods)
+        super().__init__(domain, coordinates, calc_method=calc_method,
+                         periods=periods, coord_restrictions=coord_restrictions)
         # Construction of the coordinate frame associated to the chart:
         self._frame = CoordFrame(self)
         self._coframe = self._frame._coframe
@@ -709,10 +726,6 @@ class RealDiffChart(DiffChart, RealChart):
       If interval range, no period and no LaTeX spelling are to be set for any
       coordinate, the argument ``coordinates`` can be omitted when the shortcut
       operator ``<,>`` is used to declare the chart (see examples below).
-    - ``names`` -- (default: ``None``) unused argument, except if
-      ``coordinates`` is not provided; it must then be a tuple containing
-      the coordinate symbols (this is guaranteed if the shortcut operator
-      ``<,>`` is used).
     - ``calc_method`` -- (default: ``None``) string defining the calculus
       method for computations involving coordinates of the chart; must be
       one of
@@ -722,6 +735,27 @@ class RealDiffChart(DiffChart, RealChart):
       - ``None``: the default of
         :class:`~sage.manifolds.calculus_method.CalculusMethod` will be
         used
+    - ``names`` -- (default: ``None``) unused argument, except if
+      ``coordinates`` is not provided; it must then be a tuple containing
+      the coordinate symbols (this is guaranteed if the shortcut operator
+      ``<,>`` is used).
+    - ``coord_restrictions``: Additional restrictions on the coordinates.
+      A restriction can be any symbolic equality or inequality involving
+      the coordinates, such as ``x > y`` or ``x^2 + y^2 != 0``. The items
+      of the list (or set or frozenset) ``coord_restrictions`` are combined
+      with the ``and`` operator; if some restrictions are to be combined with
+      the ``or`` operator instead, they have to be passed as a tuple in some
+      single item of the list (or set or frozenset) ``coord_restrictions``.
+      For example::
+
+        coord_restrictions=[x > y, (x != 0, y != 0), z^2 < x]
+
+      means ``(x > y) and ((x != 0) or (y != 0)) and (z^2 < x)``.
+      If the list ``coord_restrictions`` contains only one item, this
+      item can be passed as such, i.e. writing ``x > y`` instead
+      of the single element list ``[x > y]``.  If the chart variables have
+      not been declared as variables yet, ``coord_restrictions`` must
+      be ``lambda``-quoted.
 
     EXAMPLES:
 
@@ -908,9 +942,9 @@ class RealDiffChart(DiffChart, RealChart):
     `\{y=0, x\geq 0\}`, we must have `y\not=0` or `x<0` on U. Accordingly,
     we set::
 
-        sage: c_cartU.<x,y,z> = U.chart()
-        sage: c_cartU.add_restrictions((y!=0, x<0)) # the tuple (y!=0, x<0) means y!=0 or x<0
-        sage: # c_cartU.add_restrictions([y!=0, x<0]) would have meant y!=0 AND x<0
+        sage: c_cartU.<x,y,z> = U.chart(coord_restrictions=lambda x,y,z: (y!=0, x<0))
+        ....:    # the tuple (y!=0, x<0) means y!=0 or x<0
+        ....:    #           [y!=0, x<0] would have meant y!=0 AND x<0
         sage: U.atlas()
         [Chart (U, (r, th, ph)), Chart (U, (x, y, z))]
         sage: M.atlas()
@@ -942,7 +976,8 @@ class RealDiffChart(DiffChart, RealChart):
     :meth:`~sage.manifolds.chart.RealChart.plot`.
 
     """
-    def __init__(self, domain, coordinates, calc_method=None, bounds=None, periods=None):
+    def __init__(self, domain, coordinates, calc_method=None,
+                 bounds=None, periods=None, coord_restrictions=None):
         r"""
         Construct a chart on a real differentiable manifold.
 
@@ -960,8 +995,8 @@ def __init__(self, domain, coordinates, calc_method=None, bounds=None, periods=N
             sage: TestSuite(X).run()
 
         """
-        RealChart.__init__(self, domain, coordinates,
-                           calc_method=calc_method, bounds=bounds, periods=periods)
+        RealChart.__init__(self, domain, coordinates, calc_method=calc_method,
+                           bounds=bounds, periods=periods, coord_restrictions=coord_restrictions)
         # Construction of the coordinate frame associated to the chart:
         self._frame = CoordFrame(self)
         self._coframe = self._frame._coframe

src/sage/manifolds/differentiable/examples/real_line.py

@@ -368,8 +368,6 @@ def __init__(self, lower, upper, ambient_interval=None,
                     coordinate = 't'
                 else:
                     coordinate = names[0]
-            self._canon_chart = self.chart(coordinates=coordinate)
-            t = self._canon_chart[start_index]
         else:
             if lower < ambient_interval.lower_bound():
                 raise ValueError("the lower bound is smaller than that of "
@@ -379,20 +377,19 @@ def __init__(self, lower, upper, ambient_interval=None,
                                  + "the containing interval")
             self.declare_subset(ambient_interval)
             ambient_interval._top_subsets.add(self)
-            t = ambient_interval.canonical_coordinate()
         if lower != minus_infinity:
             if upper != infinity:
-                restrictions = [t > lower, t < upper]
+                restrictions = lambda t: [t > lower, t < upper]
             else:
-                restrictions = t > lower
+                restrictions = lambda t: t > lower
         else:
             if upper != infinity:
-                restrictions = t < upper
+                restrictions = lambda t: t < upper
             else:
                 restrictions = None
         if ambient_interval is None:
-            if restrictions is not None:
-                self._canon_chart.add_restrictions(restrictions)
+            self._canon_chart = self.chart(coordinates=coordinate,
+                                           coord_restrictions=restrictions)
         else:
             self._canon_chart = ambient_interval.canonical_chart().restrict(self,
                                                                             restrictions=restrictions)

src/sage/manifolds/differentiable/integrated_curve.py

@@ -1469,17 +1469,13 @@ def solve_across_charts(self, charts=None, step=None, solution_key=None,
         maps::
 
             sage: M = Manifold(2, 'M', structure="Riemannian")
-            sage: C.<x,y> = M.chart()
-            sage: P.<r,th> = M.chart()
+            sage: C.<x,y> = M.chart(coord_restrictions=lambda x,y: x**2+y**2 < 3**2)
+            sage: P.<r,th> = M.chart(coord_restrictions=lambda r, th: r > 2)
             sage: P_to_C = P.transition_map(C,(r*cos(th), r*sin(th)))
             sage: C_to_P = C.transition_map(P,(sqrt(x**2+y**2), atan2(y,x)))
 
-        Let us also add restrictions on those charts, to avoid any
-        singularity. We have to make sure that the charts still intersect.
-        Here the intersection is the donut region `2 < r < 3`::
-
-            sage: P.add_restrictions(r > 2)
-            sage: C.add_restrictions(x**2+y**2 < 3**2)
+        Here we added restrictions on those charts, to avoid any
+        singularity.  The intersection is the donut region `2 < r < 3`.
 
         We still have to define the metric. This is done in the Cartesian
         frame. The metric in the polar frame is computed automatically::
@@ -1574,14 +1570,12 @@ def solve_across_charts(self, charts=None, step=None, solution_key=None,
         .. PLOT::
 
             M = Manifold(2, 'M', structure="Riemannian")
-            C= M.chart(names = ("x", "y"))
+            C= M.chart(names = ("x", "y"), coord_restrictions=lambda x,y: x**2+y**2 < 3**2)
             x, y = C[:]
-            P = M.chart(names = ("r", "ph"))
+            P = M.chart(names = ("r", "th"), coord_restrictions=lambda r,th: r > 2)
             r, th = P[:]
             P_to_C = P.transition_map(C,(r*cos(th), r*sin(th)))
             C_to_P = C.transition_map(P,(sqrt(x**2+y**2), atan2(y,x)))
-            P.add_restrictions(r > 2)
-            C.add_restrictions(x**2+y**2 < 3**2)
             g = M.metric()
             g[0,0,C] = 1
             g[1,1,C] = 1

src/sage/manifolds/differentiable/levi_civita_connection.py

@@ -628,8 +628,8 @@ def riemann(self, name=None, latex_name=None):
         metric of the hyperbolic plane (Poincaré disk model)::
 
             sage: M = Manifold(2, 'M', start_index=1)
-            sage: X.<x,y> = M.chart('x:(-1,1) y:(-1,1)')  # Cartesian coord. on the Poincaré disk
-            sage: X.add_restrictions(x^2+y^2<1)
+            sage: X.<x,y> = M.chart('x:(-1,1) y:(-1,1)', coord_restrictions=lambda x,y: x^2+y^2<1)
+            ....:   # Cartesian coord. on the Poincaré disk
             sage: g = M.metric('g')
             sage: g[1,1], g[2,2] = 4/(1-x^2-y^2)^2, 4/(1-x^2-y^2)^2
             sage: nab = g.connection()

src/sage/manifolds/differentiable/manifold.py

@@ -1017,8 +1017,8 @@ def diffeomorphism(self, codomain=None, coord_functions=None, chart1=None,
 
             sage: M = Manifold(2, 'M')  # the open unit disk
             sage: forget()  # for doctests only
-            sage: c_xy.<x,y> = M.chart('x:(-1,1) y:(-1,1)')  # Cartesian coord on M
-            sage: c_xy.add_restrictions(x^2+y^2<1)
+            sage: c_xy.<x,y> = M.chart('x:(-1,1) y:(-1,1)', coord_restrictions=lambda x,y: x^2+y^2<1)
+            ....:    # Cartesian coord on M
             sage: N = Manifold(2, 'N')  # R^2
             sage: c_XY.<X,Y> = N.chart()  # canonical coordinates on R^2
             sage: Phi = M.diffeomorphism(N, [x/sqrt(1-x^2-y^2), y/sqrt(1-x^2-y^2)],

src/sage/manifolds/manifold.py

@@ -669,7 +669,7 @@ def _an_element_(self):
             sage: p in V
             True
             sage: p.coord()
-            (-pi - 1, 2)
+            (-pi - 1, 0)
 
         """
         from sage.rings.infinity import Infinity
@@ -1429,7 +1429,8 @@ def is_manifestly_coordinate_domain(self):
         """
         return bool(self._covering_charts)
 
-    def chart(self, coordinates='', names=None, calc_method=None):
+    def chart(self, coordinates='', names=None, calc_method=None,
+              coord_restrictions=None):
         r"""
         Define a chart, the domain of which is the manifold.
 
@@ -1461,6 +1462,8 @@ def chart(self, coordinates='', names=None, calc_method=None):
           - ``'sympy'``: SymPy
           - ``None``: the current calculus method defined on the manifold is
             used (cf. :meth:`set_calculus_method`)
+        - ``coord_restrictions``: Additional restrictions on the coordinates.
+          See below.
 
         The coordinates declared in the string ``coordinates`` are
         separated by ``' '`` (whitespace) and each coordinate has at most four
@@ -1493,6 +1496,26 @@ def chart(self, coordinates='', names=None, calc_method=None):
         omitted when the shortcut operator ``<,>`` is used to declare the
         chart (see examples below).
 
+        Additional restrictions on the coordinates can be set using the
+        argument ``coord_restrictions``.
+
+        A restriction can be any symbolic equality or inequality involving
+        the coordinates, such as ``x > y`` or ``x^2 + y^2 != 0``. The items
+        of the list (or set or frozenset) ``coord_restrictions`` are combined
+        with the ``and`` operator; if some restrictions are to be combined with
+        the ``or`` operator instead, they have to be passed as a tuple in some
+        single item of the list (or set or frozenset) ``coord_restrictions``.
+        For example::
+
+          coord_restrictions=[x > y, (x != 0, y != 0), z^2 < x]
+
+        means ``(x > y) and ((x != 0) or (y != 0)) and (z^2 < x)``.
+        If the list ``coord_restrictions`` contains only one item, this
+        item can be passed as such, i.e. writing ``x > y`` instead
+        of the single element list ``[x > y]``.  If the chart variables have
+        not been declared as variables yet, ``coord_restrictions`` must
+        be ``lambda``-quoted.
+
         OUTPUT:
 
         - the created chart, as an instance of
@@ -1560,6 +1583,16 @@ def chart(self, coordinates='', names=None, calc_method=None):
             sage: latex(P)
             \left(U,(r, {\phi})\right)
 
+        Using ``coord_restrictions``::
+
+            sage: D = Manifold(2, 'D', structure='topological')
+            sage: X.<x,y> = D.chart(coord_restrictions=lambda x,y: [x^2+y^2<1, x>0]); X
+            Chart (D, (x, y))
+            sage: X.valid_coordinates(0, 0)
+            False
+            sage: X.valid_coordinates(1/2, 0)
+            True
+
         See the documentation of classes
         :class:`~sage.manifolds.chart.Chart` and
         :class:`~sage.manifolds.chart.RealChart` for more examples,
@@ -1569,7 +1602,8 @@ def chart(self, coordinates='', names=None, calc_method=None):
         if calc_method is None:
             calc_method = self._calculus_method
         return self._structure.chart(self, coordinates=coordinates,
-                                     names=names, calc_method=calc_method)
+                                     names=names, calc_method=calc_method,
+                                     coord_restrictions=coord_restrictions)
 
     def is_open(self):
         """
@@ -2347,8 +2381,8 @@ def homeomorphism(self, codomain, coord_functions=None, chart1=None,
 
             sage: forget()  # for doctests only
             sage: M = Manifold(2, 'M', structure='topological')  # the open unit disk
-            sage: c_xy.<x,y> = M.chart('x:(-1,1) y:(-1,1)')  # Cartesian coord on M
-            sage: c_xy.add_restrictions(x^2+y^2<1)
+            sage: c_xy.<x,y> = M.chart('x:(-1,1) y:(-1,1)', coord_restrictions=lambda x,y: x^2+y^2<1)
+            ....:    # Cartesian coord on M
             sage: N = Manifold(2, 'N', structure='topological')  # R^2
             sage: c_XY.<X,Y> = N.chart()  # canonical coordinates on R^2
             sage: Phi = M.homeomorphism(N, [x/sqrt(1-x^2-y^2), y/sqrt(1-x^2-y^2)],

src/sage/manifolds/topological_submanifold.py

@@ -881,8 +881,7 @@ def as_subset(self):
             sage: M = Manifold(2, 'M', structure="topological")
             sage: N = Manifold(1, 'N', ambient=M, structure="topological")
             sage: CM.<x,y> = M.chart()
-            sage: CN.<u> = N.chart()
-            sage: CN.add_restrictions([u > -1, u < 1])
+            sage: CN.<u> = N.chart(coord_restrictions=lambda u: [u > -1, u < 1])
             sage: phi = N.continuous_map(M, {(CN,CM): [u, u^2]})
             sage: N.set_embedding(phi)
             sage: N