Module: sage.rings.quotient_ring_element
Author: William Stein
Class: QuotientRingElement
sage: R, x = PolynomialRing(Z).objgen() sage: S = R/(4 + 3*x + x^2, 1 + x^2); S Quotient of Univariate Polynomial Ring in x over Integer Ring by the ideal (x^2 + 1, x^2 + 3*x + 4) sage: v = S.gens(); v (x,)
sage: loads(v[0].dumps()) == v[0] # todo: not implemented True
sage: R, (x,y) = PolynomialRing(Z, 2, 'xy').objgens() sage: S = R/(x^2 + y^2); S Quotient of Polynomial Ring in x, y over Integer Ring by the ideal (y^2 + x^2) sage: S.gens() (x, y)
We name each of the generators.
sage: S, (a,b) = (R/(x^2 + y^2)).objgens('ab') sage: a a sage: b b sage: b.lift() y sage: (a^3 + b^2).lift() y^2 + x^3
self, parent, rep, [reduce=True]) |
Functions: copy,
is_unit,
is_zero,
lift
Special Functions: __float__,
__int__,
__invert__,
__long__,
__neg__,
__pos__,
__pow__,
__rdiv__,
_add_,
_cmp_,
_div_,
_integer_,
_mul_,
_rational_,
_reduce_,
_repr_,
_sub_
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