def __init__(self, parent, coord_functions=None, name=None,
latex_name=None, is_isomorphism=False, is_identity=False):
r"""
Construct a differentiable map.
TESTS::
sage: M = Manifold(2, 'M')
sage: X.<x,y> = M.chart()
sage: N = Manifold(3, 'N')
sage: Y.<u,v,w> = N.chart()
sage: f = Hom(M,N)({(X,Y): (x+y, x*y, x-y)}, name='f') ; f
Differentiable map f from the 2-dimensional differentiable manifold
M to the 3-dimensional differentiable manifold N
sage: f.display()
f: M --> N
(x, y) |--> (u, v, w) = (x + y, x*y, x - y)
sage: TestSuite(f).run()
The identity map::
sage: f = Hom(M,M)({}, is_identity=True) ; f
Identity map Id_M of the 2-dimensional differentiable manifold M
sage: f.display()
Id_M: M --> M
(x, y) |--> (x, y)
sage: TestSuite(f).run()
"""
ContinuousMap.__init__(self, parent, coord_functions=coord_functions,
name=name, latex_name=latex_name,
is_isomorphism=is_isomorphism,
is_identity=is_identity)
def __init__(self, parent, coord_functions=None, name=None,
latex_name=None, is_isomorphism=False, is_identity=False):
r"""
Construct a differentiable map.
TESTS::
sage: M = Manifold(2, 'M')
sage: X.<x,y> = M.chart()
sage: N = Manifold(3, 'N')
sage: Y.<u,v,w> = N.chart()
sage: f = Hom(M,N)({(X,Y): (x+y, x*y, x-y)}, name='f') ; f
Differentiable map f from the 2-dimensional differentiable manifold
M to the 3-dimensional differentiable manifold N
sage: f.display()
f: M --> N
(x, y) |--> (u, v, w) = (x + y, x*y, x - y)
sage: TestSuite(f).run()
The identity map::
sage: f = Hom(M,M)({}, is_identity=True) ; f
Identity map Id_M of the 2-dimensional differentiable manifold M
sage: f.display()
Id_M: M --> M
(x, y) |--> (x, y)
sage: TestSuite(f).run()
"""
ContinuousMap.__init__(self, parent, coord_functions=coord_functions,
name=name, latex_name=latex_name,
is_isomorphism=is_isomorphism,
is_identity=is_identity)
def _init_derived(self):
r"""
Initialize the derived quantities.
TESTS::
sage: M = Manifold(2, 'M')
sage: X.<x,y> = M.chart()
sage: f = M.diffeomorphism(M, [x+y, x-y])
sage: f._init_derived()
sage: f._restrictions
{}
sage: f._inverse
"""
ContinuousMap._init_derived(self) # derived quantities of the mother
# class
self._diff = {} # dict. of the coord. expressions of the differential
def _init_derived(self):
r"""
Initialize the derived quantities.
TESTS::
sage: M = Manifold(2, 'M')
sage: X.<x,y> = M.chart()
sage: f = M.diffeomorphism(M, [x+y, x-y])
sage: f._init_derived()
sage: f._restrictions
{}
sage: f._inverse
"""
ContinuousMap._init_derived(self) # derived quantities of the mother
# class
self._diff = {} # dict. of the coord. expressions of the differential
def _del_derived(self):
r"""
Delete the derived quantities.
TESTS::
sage: M = Manifold(2, 'M')
sage: X.<x,y> = M.chart()
sage: f = M.diffeomorphism(M, [x+y, x-y])
sage: f^(-1)
Diffeomorphism of the 2-dimensional differentiable manifold M
sage: f._inverse # was set by f^(-1)
Diffeomorphism of the 2-dimensional differentiable manifold M
sage: f._del_derived()
sage: f._inverse # has been set to None by _del_derived()
"""
ContinuousMap._del_derived(self) # derived quantities of the mother
# class
self._diff.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.diffeomorphism(M, [x+y, x-y])
sage: f^(-1)
Diffeomorphism of the 2-dimensional differentiable manifold M
sage: f._inverse # was set by f^(-1)
Diffeomorphism of the 2-dimensional differentiable manifold M
sage: f._del_derived()
sage: f._inverse # has been set to None by _del_derived()
"""
ContinuousMap._del_derived(self) # derived quantities of the mother
# class
self._diff.clear()
