Bug in computing the Hilbert series of an ideal of minors in a matrix

[Christian Stump]

Hi,

if I compute the Hilbert series of the ideal generated by all 2x2 minors in a 4x10 matrix of variables, everything works well. But if I increase the number of columns to 11, the outcome is false. I created a ticket at http://trac.sagemath.org/ticket/20145 -- I would appreciate if someone would have a look!

Thanks, Christian

[luisfe]

Looks like a Singular error, the first Hilbert series and second Hilbert series returned are not consistent:

{{{

sage: gb = I.groebner_basis()
sage: h1=hilb(gb,1)
// ** _ is no standard basis
sage: h2=hilb(gb,2)
// ** _ is no standard basis
sage: Zt=ZZ['t']
sage: f1=Zt(list(h1));f1.degree()
33
sage: f2=Zt(list(h2));f2.degree()
3
sage: f1-(1-t)**30*f2
4294967296*t^22 - 4294967296*t^21 + 4294967296*t^20 - 4294967296*t^19 + 4294967296*t^18

}}}

[Dima Pasechnik]

On Wednesday, March 2, 2016 at 9:36:20 AM UTC, luisfe wrote:

Looks like a Singular error, the first Hilbert series and second Hilbert series returned are not consistent:

indeed.