id summary reporter owner description type status priority milestone component resolution keywords cc merged author reviewer upstream work_issues branch commit dependencies stopgaps
23621 Fix quotients of univariate polynomial rings over ZZ mderickx "The quotient of `ZZ[x]` by the ideal `(x, 2)`
works fine using a multivariate polynomial ring:
{{{
sage: R. = PolynomialRing(ZZ, 1)
sage: I = R.ideal([x, 2])
sage: I
Ideal (x, 2) of Multivariate Polynomial Ring in x over Integer Ring
sage: S = R.quo(I)
sage: [[S(a) == S(b) for b in (0, 2, x)] for a in (0, 2, x)]
[[True, True, True], [True, True, True], [True, True, True]]
}}}
but it fails using a univariate polynomial ring,
returning mathematically wrong answers:
{{{
sage: R. = ZZ[]
sage: I = R.ideal([x, 2])
sage: I
Ideal (x, 2) of Univariate Polynomial Ring in x over Integer Ring
sage: S = R.quo(I)
sage:
sage: [[S(a) == S(b) for b in (0, 2, x)] for a in (0, 2, x)]
[[True, False, False], [False, True, False], [False, False, True]]
}}}
Expected:
{{{
[[True, True, True], [True, True, True], [True, True, True]]
}}}
" defect new critical sage-9.7 commutative algebra ideal slelievre N/A