def gen(self, i=0):
"""
Return the `i^{th}` generator of ``self``. This is a one-form,
more precisely the exterior derivative of the i-th coordinate.
INPUT:
- ``i`` - integer (optional, default 0)
EXAMPLES::
sage: x, y, z = var('x, y, z')
sage: U = CoordinatePatch((x, y, z)); U
Open subset of R^3 with coordinates x, y, z
sage: F = DifferentialForms(U); F
Algebra of differential forms in the variables x, y, z
sage: F.gen(0)
dx
sage: F.gen(1)
dy
sage: F.gen(2)
dz
"""
form = DifferentialForm(self, 0, self._patch.coordinate(i))
return form.diff()
def gen(self, i=0):
"""
Return the `i^{th}` generator of ``self``. This is a one-form,
more precisely the exterior derivative of the i-th coordinate.
INPUT:
- ``i`` - integer (optional, default 0)
EXAMPLES::
sage: x, y, z = var('x, y, z')
sage: U = CoordinatePatch((x, y, z)); U
Open subset of R^3 with coordinates x, y, z
sage: F = DifferentialForms(U); F
Algebra of differential forms in the variables x, y, z
sage: F.gen(0)
dx
sage: F.gen(1)
dy
sage: F.gen(2)
dz
"""
form = DifferentialForm(self, 0, self._patch.coordinate(i))
return form.diff()
def gen(self, i=0):
"""
Return the `i^{th}` generator of ``self``. This is a one-form,
more precisely the exterior derivative of the i-th coordinate.
INPUT:
- ``i`` - integer (optional, default 0)
EXAMPLES::
sage: x, y, z = var('x, y, z')
sage: U = CoordinatePatch((x, y, z)); U
doctest:...: DeprecationWarning: Use Manifold instead.
See http://trac.sagemath.org/24444 for details.
Open subset of R^3 with coordinates x, y, z
sage: F = DifferentialForms(U); F
doctest:...: DeprecationWarning: For the set of differential forms of
degree p, use U.diff_form_module(p), where U is the base manifold
(type U.diff_form_module? for details).
See http://trac.sagemath.org/24444 for details.
Algebra of differential forms in the variables x, y, z
sage: F.gen(0)
doctest:...: DeprecationWarning: Use U.diff_form(degree) instead,
where U is the base manifold (type U.diff_form? for details).
See http://trac.sagemath.org/24444 for details.
dx
sage: F.gen(1)
dy
sage: F.gen(2)
dz
"""
form = DifferentialForm(self, 0, self._patch.coordinate(i))
return form.diff()