Minimal associated primes for polynomial ideals can hang unexpectedly

[kedlaya]

This might be an upstream issue. I don't know if finding a more minimal example would help to isolate this, but note that this is only in two variables over a quadratic field, and the degrees are not absurdly large.

sage: L.<zeta3> = CyclotomicField(3)                                                        
sage: Q.<x5,x6> = L[] 
sage: I = Q.ideal((x5*x6^16 - 3*x5*x6^15 + 3*x5*x6^14 + x5*x6^13 - 6*x5*x6^12 + 7*x5*x6^11 - 3*x5*x6^10 - 3*x5*x6^9 + 7*x5*x6^8 - 6*x5*x6^7 + x5*x6^6 + 3*x5*x6^5 - 3*x5*x6^4 + x5*x6^3 + (-zeta3)*x6^13 + (3*zeta3)*x6^12 + (-3*zeta3)*x6^11 + (-zeta3)*x6^10 + (6*zeta3)*x6^9 + (-7*zeta3)*x6^8 + (3*zeta3)*x6^7 + (3*zeta3)*x6^6 + (-7*zeta3)*x6^5 + (6*zeta3)*x6^4 + (-zeta3)*x6^3 + (-3*zeta3)*x6^2 + (3*zeta3)*x6 + (-zeta3), x5^2*x6^5 - x5^2*x6^3 + (3*zeta3)*x5*x6^15 + (-7*zeta3)*x5*x6^14 + (4*zeta3)*x5*x6^13 + (7*zeta3)*x5*x6^12 + (-14*zeta3)*x5*x6^11 + (10*zeta3)*x5*x6^10 + (-10*zeta3)*x5*x6^8 + (14*zeta3)*x5*x6^7 + (-8*zeta3)*x5*x6^6 + (-4*zeta3)*x5*x6^5 + (8*zeta3)*x5*x6^4 + (-3*zeta3)*x5*x6^3 + (-zeta3)*x5*x6^2 + (zeta3)*x5 + (3*zeta3 + 3)*x6^12 + (-7*zeta3 - 7)*x6^11 + (4*zeta3 + 4)*x6^10 + (7*zeta3 + 7)*x6^9 + (-14*zeta3 - 14)*x6^8 + (10*zeta3 + 10)*x6^7 + (-10*zeta3 - 10)*x6^5 + (14*zeta3 + 14)*x6^4 + (-8*zeta3 - 8)*x6^3 + (-4*zeta3 - 4)*x6^2 + (8*zeta3 + 8)*x6 + (-3*zeta3 - 3), x5^4*x6^4 - x5^4*x6^3 + (2*zeta3)*x5^3*x6^4 + (-2*zeta3)*x5^3*x6^3 + (-zeta3)*x5^3*x6 + (zeta3)*x5^3 + (-2*zeta3 - 2)*x5^2*x6^4 + (2*zeta3 + 2)*x5^2*x6^3 + (2*zeta3 + 2)*x5^2*x6 + (-2*zeta3 - 2)*x5^2 + 7*x5*x6^15 - 18*x5*x6^14 + 11*x5*x6^13 + 18*x5*x6^12 - 36*x5*x6^11 + 25*x5*x6^10 - 25*x5*x6^8 + 35*x5*x6^7 - 19*x5*x6^6 - 11*x5*x6^5 + 20*x5*x6^4 - 7*x5*x6^3 - 2*x5*x6 + 2*x5 + (-7*zeta3)*x6^12 + (18*zeta3)*x6^11 + (-11*zeta3)*x6^10 + (-18*zeta3)*x6^9 + (36*zeta3)*x6^8 + (-25*zeta3)*x6^7 + (25*zeta3)*x6^5 + (-35*zeta3)*x6^4 + (19*zeta3)*x6^3 + (11*zeta3)*x6^2 + (-20*zeta3)*x6 + (7*zeta3)))

Now lots of things behave normally and run instantly:

sage: gb = I.groebner_basis()
sage: l = I.associated_primes()

But try:

sage: l = I.minimal_associated_primes()

and Sage hangs, apparently within sage.libs.singular.function_factory.ff.primdec__lib.minAssGTZ. (Sage reports that the Singular version is 4.1.1p2.p0.)

Upstream: Reported upstream. No feedback yet.

Component: commutative algebra

Keywords: minimal associated primes, singular

Issue created by migration from https://trac.sagemath.org/ticket/29671

[kedlaya]

comment:1

Looks like this is an upstream issue:

sage: singular(I).minAssGTZ()

also hangs, whereas similar commands like

sage: singular(I).primdecGTZ()

work just fine.

[kedlaya]

Changed keywords from minimal associated primes to minimal associated primes, singular

[kedlaya]

Upstream: Reported upstream. No feedback yet.

[mkoeppe]

comment:5

Moving to 9.4, as 9.3 has been released.