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, 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