Eliminate direct use of Chart._domain

src/sage/manifolds/chart.py

@@ -320,7 +320,7 @@ def __init__(self, domain, coordinates='', names=None, calc_method=None):
         # The chart is added to the domain's atlas, as well as to all the
         # atlases of the domain's supersets; moreover the first defined chart
         # is considered as the default chart
-        for sd in self._domain.open_supersets():
+        for sd in domain.open_supersets():
             # the chart is added in the top charts only if its coordinates have
             # not been used:
             for chart in sd._atlas:
@@ -332,7 +332,7 @@ def __init__(self, domain, coordinates='', names=None, calc_method=None):
             if sd._def_chart is None:
                 sd._def_chart = self
         # The chart is added to the list of the domain's covering charts:
-        self._domain._covering_charts.append(self)
+        domain._covering_charts.append(self)
         # Initialization of the set of charts that are restrictions of the
         # current chart to subsets of the chart domain:
         self._subcharts = set([self])
@@ -346,7 +346,7 @@ def __init__(self, domain, coordinates='', names=None, calc_method=None):
         # The null and one functions of the coordinates:
         # Expression in self of the zero and one scalar fields of open sets
         # containing the domain of self:
-        for dom in self._domain.open_supersets():
+        for dom in domain.open_supersets():
             dom._zero_scalar_field._express[self] = self.function_ring().zero()
             dom._one_scalar_field._express[self] = self.function_ring().one()
 
@@ -386,10 +386,10 @@ def _init_coordinates(self, coord_list):
             for prop in coord_properties[1:]:
                 prop1 = prop.strip()
                 if prop1[0:6] == 'period':
-                    if self._manifold.base_field_type() in ['real', 'complex']:
+                    if domain.base_field_type() in ['real', 'complex']:
                         period = SR(prop1[7:])
                     else:
-                        period = self._manifold.base_field()(prop1[7:])
+                        period = domain.base_field()(prop1[7:])
                     self._periods[coord_index + self._sindex] = period
                 else:
                     # prop1 is the coordinate's LaTeX symbol
@@ -411,7 +411,7 @@ def _repr_(self):
             Chart (M, (x, y))
 
         """
-        return 'Chart ({}, {})'.format(self._domain._name, self._xx)
+        return 'Chart ({}, {})'.format(self.domain()._name, self._xx)
 
     def _latex_(self):
         r"""
@@ -430,7 +430,7 @@ def _latex_(self):
             \left(M,({\zeta_1}, {\zeta2})\right)
 
         """
-        description = r'\left(' + latex(self._domain).strip() + ',('
+        description = r'\left(' + latex(self.domain()).strip() + ',('
         n = len(self._xx)
         for i in range(n-1):
             description += latex(self._xx[i]).strip() + ', '
@@ -712,10 +712,10 @@ 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:
-            if not subset.is_subset(self._domain):
+            if not subset.is_subset(self.domain()):
                 raise ValueError("the specified subset is not a subset " +
                                  "of the domain of definition of the chart")
             coordinates = ""
@@ -784,7 +784,7 @@ def valid_coordinates(self, *coordinates, **kwds):
             False
 
         """
-        if len(coordinates) != self._domain._dim:
+        if len(coordinates) != self.domain()._dim:
             return False
         if 'parameters' in kwds:
             parameters = kwds['parameters']
@@ -966,8 +966,8 @@ 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
@@ -2028,10 +2028,10 @@ def restrict(self, subset, restrictions=None):
             True
 
         """
-        if subset == self._domain:
+        if subset == self.domain():
             return self
         if subset not in self._dom_restrict:
-            if not subset.is_subset(self._domain):
+            if not subset.is_subset(self.domain()):
                 raise ValueError("the specified subset is not a subset " +
                                  "of the domain of definition of the chart")
             coordinates = ""
@@ -2723,10 +2723,10 @@ def _plot_xx_list(xx_list, rem_coords, ranges, steps, number_values):
             transf = None # to be the MultiCoordFunction object relating self
                           # to the ambient chart
             if mapping is None:
-                if not self._domain.is_subset(chart._domain):
+                if not self.domain().is_subset(chart.domain()):
                     raise ValueError("the domain of {} is not ".format(self) +
                                      "included in that of {}".format(chart))
-                coord_changes = chart._domain._coord_changes
+                coord_changes = chart.domain()._coord_changes
                 for chart_pair in coord_changes:
                     if chart_pair == (self, chart):
                         transf = coord_changes[chart_pair]._transf
@@ -2741,10 +2741,10 @@ def _plot_xx_list(xx_list, rem_coords, ranges, steps, number_values):
                 if not isinstance(mapping, ContinuousMap):
                     raise TypeError("the argument 'mapping' must be a "
                                     "continuous manifold map")
-                if not self._domain.is_subset(mapping._domain):
+                if not self.domain().is_subset(mapping.domain()):
                     raise ValueError("the domain of {} is not ".format(self) +
                                      "included in that of {}".format(mapping))
-                if not chart._domain.is_subset(mapping._codomain):
+                if not chart.domain().is_subset(mapping._codomain):
                     raise ValueError("the domain of {} is not ".format(chart) +
                                      "included in the codomain of {}".format(
                                                                       mapping))
@@ -3004,8 +3004,8 @@ def __init__(self, chart1, chart2, *transformations):
         self._inverse = None
         # If the two charts are on the same open subset, the coordinate change
         # is added to the subset (and supersets) dictionary:
-        if chart1._domain == chart2._domain:
-            domain = chart1._domain
+        if chart1.domain() == chart2.domain():
+            domain = chart1.domain()
             for sdom in domain.open_supersets():
                 sdom._coord_changes[(chart1, chart2)] = self
 

src/sage/manifolds/chart_func.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/differentiable/chart.py

@@ -395,8 +395,8 @@ 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
@@ -552,7 +552,7 @@ 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)
@@ -562,8 +562,8 @@ 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
@@ -1035,7 +1035,7 @@ 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)
@@ -1045,8 +1045,8 @@ 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
@@ -1129,8 +1129,8 @@ 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/diff_map.py

@@ -1071,9 +1071,9 @@ 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/scalarfield_algebra.py

@@ -426,7 +426,7 @@ def _coerce_map_from_(self, other):
         elif isinstance(other, DiffScalarFieldAlgebra):
             return self._domain.is_subset(other._domain)
         elif isinstance(other, ChartFunctionRing):
-            return self._domain.is_subset(other._chart._domain)
+            return self._domain.is_subset(other._chart.domain())
         else:
             return False
 

src/sage/manifolds/manifold.py

@@ -1727,7 +1727,7 @@ def orientation(self):
                     # Try the default chart:
                     def_chart = self._def_chart
                     if def_chart is not None:
-                        if def_chart._domain is self:
+                        if def_chart.domain() is self:
                             self._orientation = [self._def_chart]
                     # Still no orientation? Choose arbitrary chart:
                     if not self._orientation:
@@ -1967,7 +1967,7 @@ def scalar_field(self, coord_expression=None, chart=None, name=None,
         if isinstance(coord_expression, dict):
             # check validity of entry
             for chart in coord_expression:
-                if not chart._domain.is_subset(self):
+                if not chart.domain().is_subset(self):
                     raise ValueError("the {} is not defined ".format(chart) +
                                      "on some subset of the " + str(self))
         alg = self.scalar_field_algebra()

src/sage/manifolds/point.py

@@ -371,7 +371,7 @@ def coordinates(self, chart=None, old_chart=None):
             chart = dom._def_chart
             def_chart = chart
         else:
-            dom = chart._domain
+            dom = chart.domain()
             def_chart = dom._def_chart
             if self not in dom:
                 raise ValueError("the point does not belong to the domain " +

src/sage/manifolds/scalarfield.py

@@ -2027,7 +2027,7 @@ def add_expr_by_continuation(self, chart, subdomain):
         if self.is_immutable():
             raise ValueError("the expressions of an immutable element "
                                  "cannot be changed")
-        if not chart._domain.is_subset(self._domain):
+        if not chart.domain().is_subset(self._domain):
             raise ValueError("the chart is not defined on a subset of " +
                              "the scalar field domain")
         schart = chart.restrict(subdomain)
@@ -2074,7 +2074,7 @@ def set_restriction(self, rst):
         self._restrictions[rst._domain].set_name(name=self._name,
                                                  latex_name=self._latex_name)
         for chart, expr in rst._express.items():
-            intersection = chart._domain.intersection(rst._domain)
+            intersection = chart.domain().intersection(rst._domain)
             self._express[chart.restrict(intersection)] = expr
         self._is_zero = False  # a priori
 
@@ -2150,13 +2150,13 @@ def _display_expression(self, chart, result):
             coords = chart[:]
             if len(coords) == 1:
                 coords = coords[0]
-            if chart._domain == self._domain:
+            if chart.domain() == self._domain:
                 if self._name is not None:
                     result._txt += "   "
                 result._latex += " & "
             else:
-                result._txt += "on " + chart._domain._name + ": "
-                result._latex += r"\mbox{on}\ " + latex(chart._domain) + \
+                result._txt += "on " + chart.domain()._name + ": "
+                result._latex += r"\mbox{on}\ " + latex(chart.domain()) + \
                                  r": & "
             result._txt += repr(coords) + " |--> " + repr(expression) + "\n"
             result._latex += latex(coords) + r"& \longmapsto & " + \
@@ -2198,13 +2198,13 @@ def _display_expression(self, chart, result):
                     if max_dom is None:
                         try:
                             self.coord_function(sch)
-                            max_dom = sch._domain
+                            max_dom = sch.domain()
                         except (TypeError, ValueError):
                             pass
-                    elif max_dom.is_subset(sch._domain):
+                    elif max_dom.is_subset(sch.domain()):
                         try:
                             self.coord_function(sch)
-                            max_dom = sch._domain
+                            max_dom = sch.domain()
                         except (TypeError, ValueError):
                             pass
                 if max_dom is not None:

src/sage/manifolds/scalarfield_algebra.py

@@ -527,7 +527,7 @@ def _coerce_map_from_(self, other):
         elif isinstance(other, ScalarFieldAlgebra):
             return self._domain.is_subset(other._domain)
         elif isinstance(other, ChartFunctionRing):
-            return self._domain.is_subset(other._chart._domain)
+            return self._domain.is_subset(other._chart.domain())
         else:
             return False