Betti numbers over quotient rings

[Thomas Kahle]

Hello,

Does M2 compute minimal free resolutions over quotient rings? Here is a
an example where a non-minimal resolution is produced. Is there some
command to trim it (I tried 'trim' (not defined) and 'prune' (does
nothing))?

R = QQ[a,b,c,d]/(a*b-c*d)
J = ideal (a*b*c, c^2*d)

-- The rewriting works

2 2
o24 = ideal (c d, c d)

i26 : mingens J

o26 = | c2d |

-- mingens also works but

i27 : betti res J

0 1 2
o27 = total: 1 2 1
0: 1 . .
1: . . 1
2: . 2 .

-- The resolution is not minimized:

i35 : (res J).dd#2

o35 = {3} | -1 |
{3} | 1 |

Cheers,
Thomas



--
Thomas Kahle