The modules M and N should be graded (homogeneous) modules over the same ring.
If M and/or N are ideals or rings, they are regarded as modules in the evident way.
Computes the components in degree ≤d of Tori(M,N). The method computes the homogeneous component up to the chosen degree d of the i-th homology of the complex Fi+1⊗N →Fi⊗N →Fi-1⊗N, obtained by applying .⊗N to the resolution F• of M: 0←M ←F0 ←...←Fi ←Fi+1.
Example: Failure of the minimal resolution conjecture for 11 points in P6.
i1 : kk = ZZ/10007; |
i2 : R = kk[x_0..x_6]; |
i3 : gamma = 11; |
i4 : I = intersect(apply(gamma,i->(ideal random(R^6,R^{1:-1}))));
o4 : Ideal of R
|
i5 : betti res I
0 1 2 3 4 5 6
o5 = total: 1 17 46 46 30 18 4
0: 1 . . . . . .
1: . 17 46 45 5 . .
2: . . . 1 25 18 4
o5 : BettiTally
|
i6 : apply(0..2,i-> time rank source basis(7-i,(TorDegreeLimit(6-i,R^1/ideal(vars R),R^1/I,7-i))))
-- used 0.176132 seconds
-- used 0.969883 seconds
-- used 2.72517 seconds
o6 = (0, 0, 5)
o6 : Sequence
|