def __init__(self, ring, gens, coerce=True):
"""
Initialize this ideal.
INPUT:
- ``ring`` -- A ring
- ``gens`` -- The generators for this ideal
- ``coerce`` -- (default: ``True``) If ``gens`` needs to be coerced
into ``ring``.
EXAMPLES::
sage: R, x = PolynomialRing(ZZ, 'x').objgen()
sage: I = R.ideal([4 + 3*x + x^2, 1 + x^2])
sage: I
Ideal (x^2 + 3*x + 4, x^2 + 1) of Univariate Polynomial Ring in x over Integer Ring
"""
self.__ring = ring
if not isinstance(gens, (list, tuple)):
gens = [gens]
if coerce:
gens = [ring(x) for x in gens]
gens = tuple(gens)
if len(gens) == 0: gens = (ring.zero_element(), )
self.__gens = gens
MonoidElement.__init__(self, ring.ideal_monoid())
def __init__(self, ring, gens, coerce=True):
"""
Initialize this ideal.
INPUT:
- ``ring`` -- A ring
- ``gens`` -- The generators for this ideal
- ``coerce`` -- (default: ``True``) If ``gens`` needs to be coerced
into ``ring``.
EXAMPLES::
sage: R, x = PolynomialRing(ZZ, 'x').objgen()
sage: I = R.ideal([4 + 3*x + x^2, 1 + x^2])
sage: I
Ideal (x^2 + 3*x + 4, x^2 + 1) of Univariate Polynomial Ring in x over Integer Ring
"""
self.__ring = ring
if not isinstance(gens, (list, tuple)):
gens = [gens]
if coerce:
gens = [ring(x) for x in gens]
gens = tuple(gens)
if len(gens)==0: gens=(ring.zero_element(),)
self.__gens = gens
MonoidElement.__init__(self, ring.ideal_monoid())
def __init__(self, ring, gens, coerce=True):
self.__ring = ring
if not isinstance(gens, (list, tuple)):
gens = [gens]
if coerce:
gens = [ring(x) for x in gens]
gens = tuple(gens)
if len(gens)==0: gens=(ring.zero_element(),)
self.__gens = gens
MonoidElement.__init__(self, ring.ideal_monoid())