def __init__(self, chart1, chart2, *transformations):
r"""
Construct a transition map.
TESTS::
sage: M = Manifold(2, 'M')
sage: X.<x,y> = M.chart()
sage: Y.<u,v> = M.chart()
sage: X_to_Y = X.transition_map(Y, [x+y, x-y])
sage: X_to_Y
Change of coordinates from Chart (M, (x, y)) to Chart (M, (u, v))
sage: type(X_to_Y)
<class 'sage.manifolds.differentiable.chart.DiffCoordChange'>
sage: TestSuite(X_to_Y).run(skip='_test_pickling')
.. TODO::
fix _test_pickling
"""
CoordChange.__init__(self, chart1, chart2, *transformations)
# Jacobian matrix:
self._jacobian = self._transf.jacobian()
# Jacobian determinant:
if self._n1 == self._n2:
self._jacobian_det = self._transf.jacobian_det()
def __init__(self, chart1, chart2, *transformations):
r"""
Construct a transition map.
TESTS::
sage: M = Manifold(2, 'M')
sage: X.<x,y> = M.chart()
sage: Y.<u,v> = M.chart()
sage: X_to_Y = X.transition_map(Y, [x+y, x-y])
sage: X_to_Y
Change of coordinates from Chart (M, (x, y)) to Chart (M, (u, v))
sage: type(X_to_Y)
<class 'sage.manifolds.differentiable.chart.DiffCoordChange'>
sage: TestSuite(X_to_Y).run(skip='_test_pickling')
.. TODO::
fix _test_pickling
"""
CoordChange.__init__(self, chart1, chart2, *transformations)
# Jacobian matrix:
self._jacobian = self._transf.jacobian()
# Jacobian determinant:
if self._n1 == self._n2:
self._jacobian_det = self._transf.jacobian_det()
# If the two charts are on the same open subset, the Jacobian matrix is
# added to the dictionary of changes of frame:
if chart1._domain == chart2._domain:
domain = chart1._domain
frame1 = chart1._frame
frame2 = chart2._frame
vf_module = domain.vector_field_module()
ch_basis = vf_module.automorphism()
ch_basis.add_comp(frame1)[:, chart1] = self._jacobian
ch_basis.add_comp(frame2)[:, chart1] = self._jacobian
vf_module._basis_changes[(frame2, frame1)] = ch_basis
for sdom in domain._supersets:
sdom._frame_changes[(frame2, frame1)] = ch_basis
# The inverse is computed only if it does not exist already
# (because if it exists it may have a simpler expression than that
# obtained from the matrix inverse)
if (frame1, frame2) not in vf_module._basis_changes:
ch_basis_inv = ch_basis.inverse()
vf_module._basis_changes[(frame1, frame2)] = ch_basis_inv
for sdom in domain._supersets:
sdom._frame_changes[(frame1, frame2)] = ch_basis_inv
def __init__(self, chart1, chart2, *transformations):
r"""
Construct a transition map.
TESTS::
sage: M = Manifold(2, 'M')
sage: X.<x,y> = M.chart()
sage: Y.<u,v> = M.chart()
sage: X_to_Y = X.transition_map(Y, [x+y, x-y])
sage: X_to_Y
Change of coordinates from Chart (M, (x, y)) to Chart (M, (u, v))
sage: type(X_to_Y)
<class 'sage.manifolds.differentiable.chart.DiffCoordChange'>
sage: TestSuite(X_to_Y).run(skip='_test_pickling')
.. TODO::
fix _test_pickling
"""
CoordChange.__init__(self, chart1, chart2, *transformations)
# Jacobian matrix:
self._jacobian = self._transf.jacobian()
# If the two charts are on the same open subset, the Jacobian matrix is
# added to the dictionary of changes of frame:
if chart1._domain == chart2._domain:
domain = chart1._domain
frame1 = chart1._frame
frame2 = chart2._frame
vf_module = domain.vector_field_module()
ch_basis = vf_module.automorphism()
ch_basis.add_comp(frame1)[:, chart1] = self._jacobian
ch_basis.add_comp(frame2)[:, chart1] = self._jacobian
vf_module._basis_changes[(frame2, frame1)] = ch_basis
for sdom in domain._supersets:
sdom._frame_changes[(frame2, frame1)] = ch_basis
# The inverse is computed only if it does not exist already
# (because if it exists it may have a simpler expression than that
# obtained from the matrix inverse)
if (frame1, frame2) not in vf_module._basis_changes:
ch_basis_inv = ch_basis.inverse()
vf_module._basis_changes[(frame1, frame2)] = ch_basis_inv
for sdom in domain._supersets:
sdom._frame_changes[(frame1, frame2)] = ch_basis_inv