def __call__(self, *arg):
r"""
Redefinition of :meth:`TensorField.__call__` to allow for a single
vector argument.
"""
if len(arg) > 1:
# the endomorphism acting as a type (1,1) tensor on a pair
# (1-form, vector), returning a scalar:
return TensorField.__call__(self, *arg)
# the endomorphism acting as such, on a vector, returning a vector:
vector = arg[0]
if not isinstance(vector, VectorField):
raise TypeError("The argument must be a vector field.")
frame = self.common_frame(vector)
t = self.components[frame]
v = vector.components[frame]
manif = self.manifold
result = VectorField(self.domain)
n = manif.dim
si = manif.sindex
for i in range(si, si + n):
res = 0
for j in range(si, si + n):
res += t[[i, j]] * v[[j]]
result.set_comp(frame)[i] = res
# Name of the output:
result.name = None
if self.name is not None and vector.name is not None:
result.name = self.name + "(" + vector.name + ")"
# LaTeX symbol for the output:
result.latex_name = None
if self.latex_name is not None and vector.latex_name is not None:
result.latex_name = self.latex_name + r"\left(" + \
vector.latex_name + r"\right)"
return result
def __call__(self, *arg):
r"""
Redefinition of
:meth:`~sage.geometry.manifolds.tensorfield.TensorField.__call__`
to allow for a proper
treatment of the identity map and of the call with a single argument
"""
if self._is_identity:
if len(arg) == 1:
# The identity map acting as such, on a vector field:
vector = arg[0]
if vector._tensor_type != (1,0):
raise TypeError("the argument must be a vector field")
dom = self._domain.intersection(vector._domain)
return vector.restrict(dom)
elif len(arg) == 2:
# self acting as a type-(1,1) tensor on a pair
# (1-form, vector field), returning a scalar field:
oneform = arg[0]
vector = arg[1]
dom = self._domain.intersection(
oneform._domain).intersection(vector._domain)
return oneform.restrict(dom)(vector.restrict(dom))
else:
raise TypeError("wrong number of arguments")
# Generic case
if len(arg) == 1:
raise NotImplementedError("__call__ with 1 arg not implemented yet")
return TensorField.__call__(self, *arg)
def __call__(self, *arg):
r"""
Redefinition of :meth:`TensorField.__call__` to allow for a single
vector argument.
"""
if len(arg) > 1:
# the endomorphism acting as a type (1,1) tensor on a pair
# (1-form, vector), returning a scalar:
return TensorField.__call__(self, *arg)
# the endomorphism acting as such, on a vector, returning a vector:
vector = arg[0]
if not isinstance(vector, VectorField):
raise TypeError("The argument must be a vector field.")
frame_name = self.common_frame(vector)
t = self.components[frame_name]
v = vector.components[frame_name]
manif = self.manifold
result = VectorField(self.domain)
n = manif.dim
si = manif.sindex
for i in range(si, si+n):
res = 0
for j in range(si, si+n):
res += t[[i,j]]*v[[j]]
result.set_comp(frame_name)[i] = res
# Name of the output:
result.name = None
if self.name is not None and vector.name is not None:
result.name = self.name + "(" + vector.name + ")"
# LaTeX symbol for the output:
result.latex_name = None
if self.latex_name is not None and vector.latex_name is not None:
result.latex_name = self.latex_name + r"\left(" + \
vector.latex_name + r"\right)"
return result
def __call__(self, *arg):
r"""
Redefinition of
:meth:`~sage.geometry.manifolds.tensorfield.TensorField.__call__`
to allow for a proper
treatment of the identity map and of the call with a single argument
"""
if self._is_identity:
if len(arg) == 1:
# The identity map acting as such, on a vector field:
vector = arg[0]
if vector._tensor_type != (1, 0):
raise TypeError("the argument must be a vector field")
dom = self._domain.intersection(vector._domain)
return vector.restrict(dom)
elif len(arg) == 2:
# self acting as a type-(1,1) tensor on a pair
# (1-form, vector field), returning a scalar field:
oneform = arg[0]
vector = arg[1]
dom = self._domain.intersection(oneform._domain).intersection(
vector._domain)
return oneform.restrict(dom)(vector.restrict(dom))
else:
raise TypeError("wrong number of arguments")
# Generic case
if len(arg) == 1:
raise NotImplementedError(
"__call__ with 1 arg not implemented yet")
return TensorField.__call__(self, *arg)