def _init_derived(self):
r"""
Initialize the derived quantities.
TESTS::
sage: M = Manifold(2, 'M')
sage: a = M.automorphism_field(name='a')
sage: a._init_derived()
"""
TensorField._init_derived(self)
self._inverse = None # inverse not set yet
def _init_derived(self):
r"""
Initialize the derived quantities.
TESTS::
sage: M = Manifold(2, 'M')
sage: a = M.automorphism_field(name='a')
sage: a._init_derived()
"""
TensorField._init_derived(self)
self._inverse = None # inverse not set yet
def __init__(self, vector_field_module, name=None, latex_name=None):
r"""
Construct a vector field with values on a non-parallelizable manifold.
TESTS:
Construction via ``parent.element_class``, and not via a direct call
to ``VectorField``, to fit with the category framework::
sage: M = Manifold(2, 'M') # the 2-dimensional sphere S^2
sage: U = M.open_subset('U') # complement of the North pole
sage: c_xy.<x,y> = U.chart() # stereographic coordinates from the North pole
sage: V = M.open_subset('V') # complement of the South pole
sage: c_uv.<u,v> = V.chart() # stereographic coordinates from the South pole
sage: M.declare_union(U,V) # S^2 is the union of U and V
sage: XM = M.vector_field_module()
sage: a = XM.element_class(XM, name='a'); a
Vector field a on the 2-dimensional differentiable manifold M
sage: a[c_xy.frame(),:] = [x, y]
sage: a[c_uv.frame(),:] = [-u, -v]
sage: TestSuite(a).run(skip='_test_pickling')
Construction with ``DifferentiableManifold.vector_field``::
sage: a1 = M.vector_field(name='a'); a1
Vector field a on the 2-dimensional differentiable manifold M
sage: type(a1) == type(a)
True
.. TODO::
Fix ``_test_pickling`` (in the superclass :class:`TensorField`).
"""
TensorField.__init__(self,
vector_field_module, (1, 0),
name=name,
latex_name=latex_name)
# Initialization of derived quantities:
TensorField._init_derived(self)
# Initialization of list of quantities depending on self:
self._init_dependencies()
def __init__(self, vector_field_module, name=None, latex_name=None):
r"""
Construct a vector field with values on a non-parallelizable manifold.
TESTS:
Construction via ``parent.element_class``, and not via a direct call
to ``VectorField``, to fit with the category framework::
sage: M = Manifold(2, 'M') # the 2-dimensional sphere S^2
sage: U = M.open_subset('U') # complement of the North pole
sage: c_xy.<x,y> = U.chart() # stereographic coordinates from the North pole
sage: V = M.open_subset('V') # complement of the South pole
sage: c_uv.<u,v> = V.chart() # stereographic coordinates from the South pole
sage: M.declare_union(U,V) # S^2 is the union of U and V
sage: XM = M.vector_field_module()
sage: a = XM.element_class(XM, name='a'); a
Vector field a on the 2-dimensional differentiable manifold M
sage: a[c_xy.frame(),:] = [x, y]
sage: a[c_uv.frame(),:] = [-u, -v]
sage: TestSuite(a).run(skip='_test_pickling')
Construction with ``DifferentiableManifold.vector_field``::
sage: a1 = M.vector_field(name='a'); a1
Vector field a on the 2-dimensional differentiable manifold M
sage: type(a1) == type(a)
True
.. TODO::
Fix ``_test_pickling`` (in the superclass :class:`TensorField`).
"""
TensorField.__init__(self, vector_field_module, (1,0), name=name,
latex_name=latex_name)
# Initialization of derived quantities:
TensorField._init_derived(self)
# Initialization of list of quantities depending on self:
self._init_dependencies()