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12529 libsingular reduces polynomials incompletely SimonKing malb "Condensed version of a report by Oleksandr Kazymyrov [http://groups.google.com/group/sage-support/browse_thread/thread/b90fbb622ddb55ab on sage-support].
Define `g` by modding out in a multivariate polynomial ring:
{{{
sage: gens = 'y a0 a1 a2 b0 b1 b2 c1 c2 d0 d1 d2 d3 d4 d5 d6 d7'.split()
sage: R = PolynomialRing(GF(8), 17, gens)
sage: R.inject_variables(verbose=False)
sage: A, B, C = a0 + a1*y + a2*y^2, b0 + b1*y + b2*y^2, c1*y + c2*y^2
sage: D = d0 + d1*y + d2*y^2 + d3*y^3 + d4*y^4 + d5*y^5 + d6*y^6 + d7*y^7
sage: F = D.subs({y: B})
sage: G = A.subs({y: F}) + C
sage: g = G.mod(y^8 + y)
}}}
After modding out by a polynomial of degree 8 in `y`,
the degree of `g` in `y` should be at most 7.
Up to Sage 9.1.rc1:
{{{
sage: g.degree(y)
14
}}}
After #27508 (Force tail reduction in polynomial quotient ring),
merged in Sage 9.1.rc2:
{{{
sage: g.degree(y)
7
}}}
The problem was libsingular not doing tail reduction
when calling Singular.
This ticket adds the above example as a doctest." defect positive_review major sage-9.2 commutative algebra multivariate polynomial reduction malb Samuel Lelièvre Kiran Kedlaya N/A public/12529 5b3253a14e46a97e783d5800cc20898bd1bb6957 todo