i1 : R = ZZ/101[a,b,c,d]/ideal{a^4,b^4,c^4,d^4} o1 = R o1 : QuotientRing |
i2 : M = coker matrix {{a^3*b^3*c^3*d^3}}; |
i3 : S = R/ideal{a^3*b^3*c^3*d^3} o3 = S o3 : QuotientRing |
i4 : HB = torAlgebra(R,S,GenDegreeLimit=>4,RelDegreeLimit=>8) Computing generators in degree 1 : -- used 0.00660901 seconds Computing generators in degree 2 : -- used 0.012112 seconds Computing generators in degree 3 : -- used 0.0298512 seconds Computing generators in degree 4 : -- used 0.0208811 seconds Finding easy relations : -- used 0.476178 seconds Computing relations in degree 1 : -- used 0.0331612 seconds Computing relations in degree 2 : -- used 0.0347357 seconds Computing relations in degree 3 : -- used 0.0579462 seconds Computing relations in degree 4 : -- used 0.0649328 seconds Computing relations in degree 5 : -- used 0.202907 seconds Computing relations in degree 6 : -- used 0.27776 seconds Computing relations in degree 7 : -- used 0.368849 seconds Computing relations in degree 8 : -- used 0.585488 seconds o4 = HB o4 : QuotientRing |
i5 : numgens HB o5 = 35 |
i6 : apply(5,i -> #(flatten entries getBasis(i,HB))) o6 = {1, 1, 4, 10, 20} o6 : List |
i7 : Mres = res(M, LengthLimit=>8) 1 1 4 10 20 35 56 84 120 o7 = R <-- R <-- R <-- R <-- R <-- R <-- R <-- R <-- R 0 1 2 3 4 5 6 7 8 o7 : ChainComplex |
Note that in this example, Tor*R(S,k) has trivial multiplication, since the map from R to S is a Golod homomorphism by a theorem of Levin and Avramov.