reduce method of polynomial ideals gives incorrect results

[lftabera]

Define the following polynomial ring, polynomial, and ideal:

sage: term_order = TermOrder('degrevlex', 2) + TermOrder('degrevlex', 2)
sage: K = PolynomialRing(QQ, 'x,y,a0,a1', order=term_order)
sage: x, y, a0, a1 = K.gens()
sage: f = x**3 + x**2*y
sage: m = Ideal(x**4, x**2*y, y**2)

Before #27508, we get an incorrect reduction:

sage: m.reduce(f) == f.reduce(m.groebner_basis())
False
sage: m.reduce(f)
x^3 + x^2*y
sage: f.reduce(m.groebner_basis())
x^3

Singular computes correctly the reduction as x^3.

The problem is we call singular via libsingular without asking for tail reduction.

This was fixed in #27508, after which we get correct results:

sage: m.reduce(f) == f.reduce(m.groebner_basis())
True
sage: m.reduce(f)
x^3
sage: f.reduce(m.groebner_basis())
x^3

[lftabera]

I am not able to debug this. For me, it seems that this is an error in libsingular and, probably, a duplicate of #12529

[vdelecroix]

update milestone 8.3 -> 8.4

[gh-mwageringel]

This works correctly in 9.2.beta10, possibly since #27508.

[dimpase]

indeed