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

[christian.stump@…]

I wrote a long bug report, but it was killed as spam. The problem is that the Hilbert series of 2x2 minors of 4x11 matrix of variables is not computed correctly. Please see trac.sagemath.org/ticket/20145 for details...

[hannes]

There seems to be a confusion what I.hilbert_series().numerator() in sage should return: In the naming of Singular, it is the "second Hilbert series" hilb(I,2). It may be an interface bug as the 4 x 10 example:

ring r=QQ,(x(0..39)),dp;
matrix M[4][10]=maxideal(1);
ideal i=std(minor(M,2));
hilb(i,2);
1,27,108,84,0

correctly uses hilb(i,2) (aka hSecondSeries), while the 4 x 11 example

ring r=QQ,(x(0..43)),dp;
matrix M[4][11]=maxideal(1);
ideal i=std(minor(M,2));
hilb(i,2);
1,30,135,120,0
hilb(i,1);
1,0,-330,5060,-39270,183744,-468930,-172260,7837830,-42299400,146679390,-382391100,786893250,-1294246800,1673936550,-1580830020,752776200,752776200,1806623746,-471656596,-8403314,-403422496,1372406746,1847488500,-987193350,445188744,-168384150,52832780,-13522410,2753520,-429374,48180,-3465,120,0

seems to use hFirstSeries?

But the results of Singular are correct.

[hannes]

The example has in 32-bit integer overflow, which results now in an error message