Merge #32102

Author: Matthias Koeppe

src/sage/manifolds/chart.py

@@ -1066,7 +1066,7 @@ def derivative(self, coord):
             # NB: for efficiency, we access directly to the "private" attributes
             # of other classes. A more conventional OOP writing would be
             # coordsi = coord - self._chart.domain().start_index()
-            coordsi = coord - self._chart._domain._sindex
+            coordsi = coord - self._chart.domain()._sindex
             if coordsi < 0 or coordsi >= self._nc:
                 raise ValueError("coordinate index out of range")
             return self._der[coordsi]

src/sage/manifolds/chart_func.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.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/continuous_map_image.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='', names=None, calc_method=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='', names=None, calc_method=None):
             sage: TestSuite(X).run()
 
         """
-        Chart.__init__(self, domain, coordinates=coordinates, names=names,
-                       calc_method=calc_method)
+        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
@@ -391,8 +408,8 @@ def transition_map(self, other, transformations, intersection_name=None,
             [Chart (R^2, (x, y)), Chart (U, (r, phi)), Chart (U, (x, y))]
 
         """
-        dom1 = self._domain
-        dom2 = other._domain
+        dom1 = self.domain()
+        dom2 = other.domain()
         dom = dom1.intersection(dom2, name=intersection_name)
         if dom is dom1:
             chart1 = self
@@ -548,7 +565,7 @@ def restrict(self, subset, restrictions=None):
             Chart (B, (z1, z2))
 
         """
-        if subset == self._domain:
+        if subset == self.domain():
             return self
         if subset not in self._dom_restrict:
             resu = Chart.restrict(self, subset, restrictions=restrictions)
@@ -558,8 +575,8 @@ def restrict(self, subset, restrictions=None):
                 sframe._subframes.add(resu._frame)
                 sframe._restrictions[subset] = resu._frame
             # The subchart frame is not a "top frame" in the supersets
-            # (including self._domain):
-            for dom in self._domain.open_supersets():
+            # (including self.domain()):
+            for dom in self.domain().open_supersets():
                 if resu._frame in dom._top_frames:
                     # it was added by the Chart constructor invoked in
                     # Chart.restrict above
@@ -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='', names=None, calc_method=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='', names=None, calc_method=None):
             sage: TestSuite(X).run()
 
         """
-        RealChart.__init__(self, domain, coordinates=coordinates, names=names,
-                           calc_method = calc_method)
+        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
@@ -1031,7 +1066,7 @@ def restrict(self, subset, restrictions=None):
             True
 
         """
-        if subset == self._domain:
+        if subset == self.domain():
             return self
         if subset not in self._dom_restrict:
             resu = RealChart.restrict(self, subset, restrictions=restrictions)
@@ -1041,8 +1076,8 @@ def restrict(self, subset, restrictions=None):
                 sframe._subframes.add(resu._frame)
                 sframe._restrictions[subset] = resu._frame
             # The subchart frame is not a "top frame" in the supersets
-            # (including self._domain):
-            for dom in self._domain.open_supersets():
+            # (including self.domain()):
+            for dom in self.domain().open_supersets():
                 if resu._frame in dom._top_frames:
                     # it was added by the Chart constructor invoked in
                     # Chart.restrict above
@@ -1125,8 +1160,8 @@ def __init__(self, chart1, chart2, *transformations):
         self._jacobian  = self._transf.jacobian()
         # If the two charts are on the same open subset, the Jacobian matrix is
         # added to the dictionary of changes of frame:
-        if chart1._domain == chart2._domain:
-            domain = chart1._domain
+        if chart1.domain() == chart2.domain():
+            domain = chart1.domain()
             frame1 = chart1._frame
             frame2 = chart2._frame
             vf_module = domain.vector_field_module()

src/sage/manifolds/differentiable/chart.py

@@ -1080,9 +1080,9 @@ def paral_comp(tcomp, chart1, chart2, coord2_1, jacob,
                         coord1 = chart1._xx
                         ff = tensor._express[chart2]
                         resu_fc.append( chart1.function(ff(*(phi(*coord1)))) )
-            dom_resu = resu_fc[0].parent()._chart._domain
+            dom_resu = resu_fc[0].parent()._chart.domain()
             for fc in resu_fc[1:]:
-                dom_resu = dom_resu.union(fc.parent()._chart._domain)
+                dom_resu = dom_resu.union(fc.parent()._chart.domain())
             resu = dom_resu.scalar_field(name=resu_name,
                                          latex_name=resu_latex_name)
             for fc in resu_fc:

src/sage/manifolds/differentiable/diff_map.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/examples/real_line.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/integrated_curve.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/levi_civita_connection.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)],