def __init__(self, parent, degree, fun = None):
r"""
Construct a differential form.
INPUT:
- ``parent`` -- Parent algebra of differential forms.
- ``degree`` -- Degree of the differential form.
- ``fun`` (default: None) -- Initialize this differential form with the given function. If the degree is not zero, this argument is silently ignored.
EXAMPLES::
sage: x, y, z = var('x, y, z')
sage: F = DifferentialForms(); F
Algebra of differential forms in the variables x, y, z
sage: f = DifferentialForm(F, 0, sin(z)); f
sin(z)
"""
from sage.tensor.differential_forms import DifferentialForms
if not isinstance(parent, DifferentialForms):
raise TypeError("Parent not an algebra of differential forms.")
RingElement.__init__(self, parent)
self._degree = degree
self._components = {}
if degree == 0 and fun is not None:
self.__setitem__([], fun)
def __init__(self, parent, degree, fun=None):
r"""
Construct a differential form.
INPUT:
- ``parent`` -- Parent algebra of differential forms.
- ``degree`` -- Degree of the differential form.
- ``fun`` (default: None) -- Initialize this differential form with the given function. If the degree is not zero, this argument is silently ignored.
EXAMPLES::
sage: x, y, z = var('x, y, z')
sage: F = DifferentialForms(); F
Algebra of differential forms in the variables x, y, z
sage: f = DifferentialForm(F, 0, sin(z)); f
sin(z)
"""
from sage.tensor.differential_forms import DifferentialForms
if not isinstance(parent, DifferentialForms):
raise TypeError("Parent not an algebra of differential forms.")
RingElement.__init__(self, parent)
self._degree = degree
self._components = {}
if degree == 0 and fun is not None:
self.__setitem__([], fun)
def __init__(self, parent=UnsignedInfinityRing):
"""
EXAMPLES::
sage: sage.rings.infinity.LessThanInfinity() is UnsignedInfinityRing(5)
True
"""
RingElement.__init__(self, parent)
def __init__(self, parent=UnsignedInfinityRing):
"""
EXAMPLES::
sage: sage.rings.infinity.LessThanInfinity() is UnsignedInfinityRing(5)
True
"""
RingElement.__init__(self, parent)
def __init__(self, parent, x):
"""
TESTS::
sage: sage.rings.infinity.FiniteNumber(InfinityRing, 1)
A positive finite number
sage: sage.rings.infinity.FiniteNumber(InfinityRing, -1)
A negative finite number
sage: sage.rings.infinity.FiniteNumber(InfinityRing, 0)
Zero
"""
RingElement.__init__(self, parent)
self.value = x
def __init__(self, parent, x):
"""
TESTS::
sage: sage.rings.infinity.FiniteNumber(InfinityRing, 1)
A positive finite number
sage: sage.rings.infinity.FiniteNumber(InfinityRing, -1)
A negative finite number
sage: sage.rings.infinity.FiniteNumber(InfinityRing, 0)
Zero
"""
RingElement.__init__(self, parent)
self.value = x
