def _del_derived(self):
r"""
Delete the derived quantities.
TESTS::
sage: M = Manifold(2, 'M')
sage: X.<x,y> = M.chart()
sage: f = M.scalar_field({X: x+y})
sage: U = M.open_subset('U', coord_def={X: x>0})
sage: f.restrict(U)
Scalar field on the Open subset U of the 2-dimensional
differentiable manifold M
sage: f._restrictions
{Open subset U of the 2-dimensional differentiable manifold M:
Scalar field on the Open subset U of the 2-dimensional
differentiable manifold M}
sage: f._del_derived()
sage: f._restrictions # restrictions are derived quantities
{}
"""
ScalarField._del_derived(
self) # derived quantities of the mother class
self._differential = None # reset of the differential
# First deletes any reference to self in the vectors' dictionaries:
for vid, val in self._lie_derivatives.items():
del val[0]._lie_der_along_self[id(self)]
# Then clears the dictionary of Lie derivatives
self._lie_derivatives.clear()
def _del_derived(self):
r"""
Delete the derived quantities.
TESTS::
sage: M = Manifold(2, 'M')
sage: X.<x,y> = M.chart()
sage: f = M.scalar_field({X: x+y})
sage: U = M.open_subset('U', coord_def={X: x>0})
sage: f.restrict(U)
Scalar field on the Open subset U of the 2-dimensional
differentiable manifold M
sage: f._restrictions
{Open subset U of the 2-dimensional differentiable manifold M:
Scalar field on the Open subset U of the 2-dimensional
differentiable manifold M}
sage: f._del_derived()
sage: f._restrictions # restrictions are derived quantities
{}
"""
ScalarField._del_derived(self) # derived quantities of the mother class
self._differential = None # reset of the differential
# First deletes any reference to self in the vectors' dictionaries:
for vid, val in self._lie_derivatives.items():
del val[0]._lie_der_along_self[id(self)]
# Then clears the dictionary of Lie derivatives
self._lie_derivatives.clear()
def __init__(self,
parent,
coord_expression=None,
chart=None,
name=None,
latex_name=None):
r"""
Construct a scalar field.
TESTS::
sage: M = Manifold(2, 'M')
sage: X.<x,y> = M.chart()
sage: f = M.scalar_field({X: x+y}, name='f') ; f
Scalar field f on the 2-dimensional differentiable manifold M
sage: from sage.manifolds.scalarfield import ScalarField
sage: isinstance(f, ScalarField)
True
sage: f.parent()
Algebra of differentiable scalar fields on the 2-dimensional
differentiable manifold M
sage: TestSuite(f).run()
"""
ScalarField.__init__(self,
parent,
coord_expression=coord_expression,
chart=chart,
name=name,
latex_name=latex_name)
self._tensor_type = (0, 0)
def _init_derived(self):
r"""
Initialize the derived quantities.
TEST::
sage: M = Manifold(2, 'M')
sage: X.<x,y> = M.chart()
sage: f = M.scalar_field({X: x+y})
sage: f._init_derived()
"""
ScalarField._init_derived(
self) # derived quantities of the mother class
def _init_derived(self):
r"""
Initialize the derived quantities.
TESTS::
sage: M = Manifold(2, 'M')
sage: X.<x,y> = M.chart()
sage: f = M.scalar_field({X: x+y})
sage: f._init_derived()
"""
ScalarField._init_derived(self) # derived quantities of the parent class
self._differential = None # differential 1-form of the scalar field
self._lie_derivatives = {} # dict. of Lie derivatives of self, (keys: id(vector))
def _init_derived(self):
r"""
Initialize the derived quantities.
TESTS::
sage: M = Manifold(2, 'M')
sage: X.<x,y> = M.chart()
sage: f = M.scalar_field({X: x+y})
sage: f._init_derived()
"""
ScalarField._init_derived(self) # derived quantities of the parent class
self._differential = None # differential 1-form of the scalar field
self._lie_derivatives = {} # dict. of Lie derivatives of self, (keys: id(vector))
def __init__(self, parent, coord_expression=None, chart=None, name=None,
latex_name=None):
r"""
Construct a scalar field.
TESTS::
sage: M = Manifold(2, 'M')
sage: X.<x,y> = M.chart()
sage: f = M.scalar_field({X: x+y}, name='f') ; f
Scalar field f on the 2-dimensional differentiable manifold M
sage: from sage.manifolds.scalarfield import ScalarField
sage: isinstance(f, ScalarField)
True
sage: f.parent()
Algebra of differentiable scalar fields on the 2-dimensional
differentiable manifold M
sage: TestSuite(f).run()
"""
ScalarField.__init__(self, parent, coord_expression=coord_expression,
chart=chart, name=name, latex_name=latex_name)
self._tensor_type = (0,0)
def _del_derived(self):
r"""
Delete the derived quantities.
TEST::
sage: M = Manifold(2, 'M')
sage: X.<x,y> = M.chart()
sage: f = M.scalar_field({X: x+y})
sage: U = M.open_subset('U', coord_def={X: x>0})
sage: f.restrict(U)
Scalar field on the Open subset U of the 2-dimensional
differentiable manifold M
sage: f._restrictions
{Open subset U of the 2-dimensional differentiable manifold M:
Scalar field on the Open subset U of the 2-dimensional
differentiable manifold M}
sage: f._del_derived()
sage: f._restrictions # restrictions are derived quantities
{}
"""
ScalarField._del_derived(
self) # derived quantities of the mother class