Minor changes in the zero and one treatment of tensor fields

src/sage/manifolds/differentiable/diff_form.py

@@ -529,7 +529,6 @@ def wedge(self, other):
         dest_map = self._vmodule._dest_map
         dest_map_resu = dest_map.restrict(dom_resu,
                                           subcodomain=ambient_dom_resu)
-        ###
         # Facilitate computations involving zero:
         if resu_degree > ambient_dom_resu._dim:
             return dom_resu.diff_form_module(resu_degree,
@@ -540,7 +539,6 @@ def wedge(self, other):
         if self is other and (self._tensor_rank % 2) == 1:
             return dom_resu.diff_form_module(resu_degree,
                                              dest_map=dest_map_resu).zero()
-        ###
         # Generic case:
         self_r = self.restrict(dom_resu)
         other_r = other.restrict(dom_resu)

src/sage/manifolds/differentiable/mixed_form.py

@@ -35,18 +35,18 @@ class MixedForm(AlgebraElement):
     `\varphi: M \to N` between two differentiable manifolds `M` and `N`. More
     precisely, a mixed form `a` along `\varphi: M \to N` can be considered as a
     differentiable map
-    
+
     .. MATH::
 
         a: M \longrightarrow \bigoplus^n_{k=0} T^{(0,k)}N,
-    
+
     where `T^{(0,k)}` denotes the tensor bundle of type `(0,k)`, `\bigoplus`
     the Whitney sum and `n` the dimension of `N`, such that
-    
+
     .. MATH::
 
         \forall x\in M, \quad a(x) \in \bigoplus^n_{k=0} \Lambda^k\left( T_{\varphi(x)}^* N \right),
-    
+
     where `\Lambda^k(T^*_{\varphi(x)} N)` is the `k`-th exterior power of the
     dual of the tangent space `T_{\varphi(x)} N`.
 
@@ -656,13 +656,11 @@ def _add_(self, other):
             True
 
         """
-        ###
         # Case zero:
         if self._is_zero:
             return other
         if other._is_zero:
             return self
-        ###
         # Generic case:
         resu_comp = [self[j] + other[j]
                      for j in range(self._max_deg + 1)]
@@ -730,13 +728,11 @@ def _sub_(self, other):
         True
 
         """
-        ###
         # Case zero:
         if self._is_zero:
             return -other
         if other._is_zero:
             return self
-        ###
         # Generic case:
         resu_comp = [self[j] - other[j]
                      for j in range(self._max_deg + 1)]
@@ -851,17 +847,14 @@ def wedge(self, other):
             A/\eta = [0] + [x*y dy] + [x*y dx/\dy] + [-y*z dx/\dy/\dz]
 
         """
-        ###
         # Case zero:
         if self._is_zero or other._is_zero:
             return self.parent().zero()
-        ###
         # Case one:
         if self is self.parent().one():
             return other
         if other is self.parent().one():
             return self
-        ###
         # Generic case:
         resu_comp = [None] * (self._max_deg + 1)
         resu_comp[0] = self[0] * other[0]
@@ -941,7 +934,7 @@ def exterior_derivative(self):
         `\Omega^*(M,\varphi)`:
 
         .. MATH::
-        
+
             \mathrm{d}: \Omega^*(M,\varphi) \to \Omega^*(M,\varphi).
 
         OUTPUT:

src/sage/manifolds/differentiable/multivector_module.py

@@ -390,8 +390,6 @@ def zero(self):
              manifold M
 
         """
-        zero = self.element_class(self._vmodule, self._degree,
-                                  name='zero', latex_name='0')
         zero = self._element_constructor_(name='zero', latex_name='0')
         for frame in self._domain._frames:
             if self._dest_map.restrict(frame._domain) == frame._dest_map:

src/sage/manifolds/differentiable/tangent_space.py

@@ -245,7 +245,7 @@ def __init__(self, point):
                             if frame is frame2:
                                 basis = basis2
                             if basis is not None:
-                                cauto = auto.add_comp(basis)
+                                cauto = auto.add_comp(basis=basis)
                                 for ind, val in comp._comp.items():
                                     cauto._comp[ind] = val(point)
                         except ValueError:

src/sage/manifolds/differentiable/tensorfield.py

@@ -1213,7 +1213,7 @@ def set_comp(self, basis=None):
             basis = self._domain._def_frame
         self._del_derived() # deletes the derived quantities
         rst = self.restrict(basis._domain, dest_map=basis._dest_map)
-        return rst.set_comp(basis)
+        return rst.set_comp(basis=basis)
 
     def _add_comp_unsafe(self, basis=None):
         r"""
@@ -1342,7 +1342,7 @@ def add_comp(self, basis=None):
             basis = self._domain._def_frame
         self._del_derived() # deletes the derived quantities
         rst = self.restrict(basis._domain, dest_map=basis._dest_map)
-        return rst.add_comp(basis)
+        return rst.add_comp(basis=basis)
 
     def add_comp_by_continuation(self, frame, subdomain, chart=None):
         r"""
@@ -2294,13 +2294,11 @@ def _add_(self, other):
             True
 
         """
-        ###
         # Case zero:
         if self._is_zero:
             return other
         if other._is_zero:
             return self
-        ###
         # Generic case:
         resu_rst = {}
         for dom in self._common_subdomains(other):
@@ -2365,13 +2363,11 @@ def _sub_(self, other):
             True
 
         """
-        ###
         # Case zero:
         if self._is_zero:
             return -other
         if other._is_zero:
             return self
-        ###
         # Generic case:
         resu_rst = {}
         for dom in self._common_subdomains(other):
@@ -2446,15 +2442,12 @@ def _rmul_(self, scalar):
             True
 
         """
-        ###
         # Case zero:
         if scalar._is_zero:
             return self.parent().zero()
-        ###
         # Case one:
         if scalar is self._domain._one_scalar_field:
             return self
-        ###
         # Generic case:
         resu = self._new_instance()
         for dom, rst in self._restrictions.items():

src/sage/manifolds/differentiable/tensorfield_paral.py

@@ -900,7 +900,7 @@ class :class:`~sage.tensor.modules.comp.Components`; if such
         # deleted by _del_derived):
         self._restrictions[basis._domain] = rst
         # The set_comp operation is performed on the subdomain:
-        return rst.set_comp(basis)
+        return rst.set_comp(basis=basis)
 
     def _add_comp_unsafe(self, basis=None):
         r"""
@@ -1077,7 +1077,7 @@ class :class:`~sage.tensor.modules.comp.Components`; if such
         # subdomains:
         self._del_derived(del_restrictions=False)
         # The add_comp operation is performed on the subdomain:
-        return rst.add_comp(basis)
+        return rst.add_comp(basis=basis)
 
     def comp(self, basis=None, from_basis=None):
         r"""

src/sage/manifolds/differentiable/vectorfield_module.py

@@ -1447,7 +1447,7 @@ def _element_constructor_(self, comp=[], basis=None, name=None,
                                  "to a vector field in {}".format(self))
         resu = self.element_class(self, name=name, latex_name=latex_name)
         if comp != []:
-            resu.set_comp(basis)[:] = comp
+            resu.set_comp(basis=basis)[:] = comp
         return resu
 
     # Rem: _an_element_ is declared in the superclass FiniteRankFreeModule

src/sage/manifolds/differentiable/vectorframe.py

@@ -710,7 +710,7 @@ def __init__(self, vector_field_module, symbol, latex_symbol=None,
                     xsd = sd._vector_field_modules[dest_map]
                     if not isinstance(xsd, FiniteRankFreeModule):
                         for t in xsd._tensor_modules.values():
-                            t(0)._add_comp_unsafe(self)
+                            t.zero()._add_comp_unsafe(self)
                             # (since new components are initialized to zero)
         if dest_map is self._domain.identity_map():
             # The frame is added to the list of the domain's covering frames:

src/sage/manifolds/scalarfield.py

@@ -1673,23 +1673,23 @@ def set_expr(self, coord_expression, chart=None):
             sage: f._express # the (u,v) expression has been lost:
             {Chart (M, (x, y)): 3*y}
 
-        Since zero and one are special elements, their components cannot be
+        Since zero and one are special elements, their expressions cannot be
         changed::
 
             sage: z = M.zero_scalar_field()
             sage: z.set_expr(3*y)
             Traceback (most recent call last):
             ...
-            AssertionError: the components of the element zero cannot be changed
+            AssertionError: the expressions of the element zero cannot be changed
             sage: one = M.one_scalar_field()
             sage: one.set_expr(3*y)
             Traceback (most recent call last):
             ...
-            AssertionError: the components of the element 1 cannot be changed
+            AssertionError: the expressions of the element 1 cannot be changed
 
         """
         if self is self.parent().one() or self is self.parent().zero():
-            raise AssertionError("the components of the element "
+            raise AssertionError("the expressions of the element "
                                  "{} cannot be changed".format(self._name))
         if chart is None:
             chart = self._domain._def_chart
@@ -1735,23 +1735,23 @@ def add_expr(self, coord_expression, chart=None):
             sage: f._express # random (dict. output); f has now 2 expressions:
             {Chart (M, (x, y)): 3*y, Chart (M, (u, v)): cos(u) - sin(v)}
 
-        Since zero and one are special elements, their components cannot be
+        Since zero and one are special elements, their expressions cannot be
         changed::
 
             sage: z = M.zero_scalar_field()
             sage: z.add_expr(cos(u)-sin(v), c_uv)
             Traceback (most recent call last):
             ...
-            AssertionError: the components of the element zero cannot be changed
+            AssertionError: the expressions of the element zero 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 components of the element 1 cannot be changed
+            AssertionError: the expressions of the element 1 cannot be changed
 
         """
         if self is self.parent().one() or self is self.parent().zero():
-            raise AssertionError("the components of the element "
+            raise AssertionError("the expressions of the element "
                                  "{} cannot be changed".format(self._name))
         if chart is None:
             chart = self._domain._def_chart

src/sage/tensor/modules/free_module_alt_form.py

@@ -614,15 +614,13 @@ def wedge(self, other):
             return self * other
         fmodule = self._fmodule
         rank_r = self._tensor_rank + other._tensor_rank
-        ###
         # Facilitate computations involving zero:
         if rank_r > fmodule._rank:
             return fmodule.dual_exterior_power(rank_r).zero()
         if self._is_zero or other._is_zero:
             return fmodule.dual_exterior_power(rank_r).zero()
         if self is other and (self._tensor_rank % 2) == 1:
             return fmodule.dual_exterior_power(rank_r).zero()
-        ###
         # Generic case:
         basis = self.common_basis(other)
         if basis is None:

src/sage/tensor/modules/free_module_basis.py

@@ -601,21 +601,21 @@ def __init__(self, fmodule, symbol, latex_symbol=None, indices=None,
         # base module itself, since it is considered as a type-(1,0) tensor
         # module):
         for t in fmodule._tensor_modules.values():
-            t(0)._add_comp_unsafe(self)
+            t.zero()._add_comp_unsafe(self)
             # (since new components are initialized to zero)
         # Initialization of the components w.r.t the current basis of the zero
         # elements of all exterior powers of the module and its dual
         # constructed up to now:
         for t in fmodule._exterior_powers.values():
-            t(0)._add_comp_unsafe(self)
+            t.zero()._add_comp_unsafe(self)
         for t in fmodule._dual_exterior_powers.values():
-            t(0)._add_comp_unsafe(self)
+            t.zero()._add_comp_unsafe(self)
         # Initialization of the components w.r.t. the current basis of the
         # identity map of the general linear group:
         if fmodule._general_linear_group is not None:
             from .comp import KroneckerDelta
             gl = fmodule._general_linear_group
-            gl(1)._components[self] = KroneckerDelta(fmodule._ring, self,
+            gl.one()._components[self] = KroneckerDelta(fmodule._ring, self,
                                     start_index=fmodule._sindex,
                                     output_formatter=fmodule._output_formatter)
         # The dual basis:

src/sage/tensor/modules/free_module_tensor.py

@@ -192,7 +192,6 @@ class being:
 # *****************************************************************************
 from __future__ import absolute_import
 
-from sage.misc.cachefunc import cached_method
 from sage.rings.integer import Integer
 from sage.structure.element import ModuleElement
 from sage.tensor.modules.comp import (Components, CompWithSym, CompFullySym,
@@ -2025,13 +2024,12 @@ def _add_(self, other):
         """
         # No need for consistency check since self and other are guaranteed
         # to belong to the same tensor module
-        ###
+        #
         # Case zero:
         if self._is_zero:
             return other
         if other._is_zero:
             return self
-        ###
         # Generic case:
         basis = self.common_basis(other)
         if basis is None:
@@ -2088,6 +2086,13 @@ def _sub_(self, other):
         """
         # No need for consistency check since self and other are guaranted
         # to belong to the same tensor module
+        #
+        # Case zero:
+        if self._is_zero:
+            return -other
+        if other._is_zero:
+            return self
+        # Generic case:
         basis = self.common_basis(other)
         if basis is None:
             raise ValueError("no common basis for the subtraction")