Trac #30266: make scalarfields immutable

src/sage/manifolds/scalarfield.py

@@ -40,12 +40,13 @@
 #                  https://www.gnu.org/licenses/
 # *****************************************************************************
 
-from sage.structure.element import CommutativeAlgebraElement
+from sage.structure.element import (CommutativeAlgebraElement,
+                                    ModuleElementWithMutability)
 from sage.symbolic.expression import Expression
 from sage.manifolds.chart_func import ChartFunction
+from sage.misc.cachefunc import cached_method
 
-
-class ScalarField(CommutativeAlgebraElement):
+class ScalarField(CommutativeAlgebraElement, ModuleElementWithMutability):
     r"""
     Scalar field on a topological manifold.
 
@@ -277,6 +278,48 @@ class ScalarField(CommutativeAlgebraElement):
         sage: zer is M.scalar_field_algebra().zero()
         True
 
+    The constant scalar fields zero and one are immutable, and therefore
+    their expressions cannot be changed::
+
+        sage: zer.is_immutable()
+        True
+        sage: zer.set_expr(x)
+        Traceback (most recent call last):
+        ...
+        AssertionError: the expressions of an immutable element cannot be
+         changed
+        sage: one = M.one_scalar_field()
+        sage: one.is_immutable()
+        True
+        sage: one.set_expr(x)
+        Traceback (most recent call last):
+        ...
+        AssertionError: the expressions of an immutable element cannot be
+         changed
+
+    Other scalar fields can be declared immutable, too::
+
+        sage: c.is_immutable()
+        False
+        sage: c.set_immutable()
+        sage: c.is_immutable()
+        True
+        sage: c.set_expr(y^2)
+        Traceback (most recent call last):
+        ...
+        AssertionError: the expressions of an immutable element cannot be
+         changed
+        sage: c.set_name('b')
+        Traceback (most recent call last):
+        ...
+        AssertionError: the name of an immutable element cannot be changed
+
+    Immutable elements are hashable and can therefore be used as keys for
+    dictionaries::
+
+        sage: {c: 1}[c]
+        1
+
     By definition, a scalar field acts on the manifold's points, sending
     them to elements of the manifold's base field (real numbers in the
     present case)::
@@ -1077,7 +1120,7 @@ def __init__(self, parent, coord_expression=None, chart=None, name=None,
             sage: TestSuite(f).run()
 
         """
-        CommutativeAlgebraElement.__init__(self, parent)
+        super().__init__(parent)  # both super classes have same signature
         domain = parent._domain
         self._domain = domain
         self._manifold = domain.manifold()
@@ -1442,6 +1485,9 @@ def set_name(self, name=None, latex_name=None):
             \Phi
 
         """
+        if self.is_immutable():
+            raise AssertionError("the name of an immutable element "
+                                 "cannot be changed")
         if name is not None:
             self._name = name
             if latex_name is None:
@@ -1723,17 +1769,19 @@ def set_expr(self, coord_expression, chart=None):
             sage: z.set_expr(3*y)
             Traceback (most recent call last):
             ...
-            AssertionError: the expressions of the element zero cannot be changed
+            AssertionError: the expressions of an immutable element cannot be
+             changed
             sage: one = M.one_scalar_field()
             sage: one.set_expr(3*y)
             Traceback (most recent call last):
             ...
-            AssertionError: the expressions of the element 1 cannot be changed
+            AssertionError: the expressions of an immutable element cannot be
+             changed
 
         """
-        if self is self.parent().one() or self is self.parent().zero():
-            raise AssertionError("the expressions of the element "
-                                 "{} cannot be changed".format(self._name))
+        if self.is_immutable():
+            raise AssertionError("the expressions of an immutable element "
+                                 "cannot be changed")
         if chart is None:
             chart = self._domain._def_chart
         self._express.clear()
@@ -1785,17 +1833,19 @@ def add_expr(self, coord_expression, chart=None):
             sage: z.add_expr(cos(u)-sin(v), c_uv)
             Traceback (most recent call last):
             ...
-            AssertionError: the expressions of the element zero cannot be changed
+            AssertionError: the expressions of an immutable element cannot be
+             changed
             sage: one = M.one_scalar_field()
             sage: one.add_expr(cos(u)-sin(v), c_uv)
             Traceback (most recent call last):
             ...
-            AssertionError: the expressions of the element 1 cannot be changed
+            AssertionError: the expressions of an immutable element cannot be
+             changed
 
         """
-        if self is self.parent().one() or self is self.parent().zero():
-            raise AssertionError("the expressions of the element "
-                                 "{} cannot be changed".format(self._name))
+        if self.is_immutable():
+            raise AssertionError("the expressions of an immutable element "
+                                 "cannot be changed")
         if chart is None:
             chart = self._domain._def_chart
         self._express[chart] = chart.function(coord_expression)
@@ -1863,6 +1913,9 @@ def add_expr_by_continuation(self, chart, subdomain):
             on V: (u, v) |--> arctan(1/(u^2 + v^2))
 
         """
+        if self.is_immutable():
+            raise AssertionError("the expressions of an immutable element "
+                                 "cannot be changed")
         if not chart._domain.is_subset(self._domain):
             raise ValueError("the chart is not defined on a subset of " +
                              "the scalar field domain")
@@ -1898,6 +1951,9 @@ def set_restriction(self, rst):
             True
 
         """
+        if self.is_immutable():
+            raise AssertionError("the expressions of an immutable element "
+                                 "cannot be changed")
         if not isinstance(rst, ScalarField):
             raise TypeError("the argument must be a scalar field")
         if not rst._domain.is_subset(self._domain):
@@ -3459,3 +3515,28 @@ def set_calc_order(self, symbol, order, truncate=False):
             if truncate:
                 expr.simplify()
         self._del_derived()
+
+    @cached_method
+    def __hash__(self):
+        r"""
+        Hash function.
+
+        TESTS::
+
+            sage: M = Manifold(2, 'M')
+            sage: X.<x,y> = M.chart()
+            sage: f = M.scalar_field(x^2, name='f')
+            sage: f.set_immutable()
+            sage: hash(f) == f.__hash__()
+            True
+
+        Let us check that ``f`` can be used as a dictionary key::
+
+            sage: {f: 1}[f]
+            1
+
+        """
+        if self.is_mutable():
+            raise ValueError('element must be immutable in order to be '
+                             'hashable')
+        return hash((self._domain, repr(self)))

src/sage/manifolds/scalarfield_algebra.py

@@ -596,6 +596,7 @@ def zero(self):
                                   coord_expression=coord_express,
                                   name='zero', latex_name='0')
         zero._is_zero = True
+        zero.set_immutable()
         return zero
 
     @cached_method
@@ -625,6 +626,7 @@ def one(self):
         """
         coord_express = {chart: chart.one_function()
                          for chart in self._domain.atlas()}
-        return self.element_class(self,
-                                  coord_expression=coord_express,
-                                  name='1', latex_name='1')
+        one = self.element_class(self, coord_expression=coord_express,
+                                 name='1', latex_name='1')
+        one.set_immutable()
+        return one