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 0.0232423 seconds Computing generators in degree 2 : -- used 0.0421872 seconds Computing generators in degree 3 : -- used 0.07726 seconds Computing generators in degree 4 : -- used 0.137102 seconds Finding easy relations : -- used 1.38195 seconds Computing relations in degree 1 : -- used 0.0831073 seconds Computing relations in degree 2 : -- used 0.0840004 seconds Computing relations in degree 3 : -- used 0.219048 seconds Computing relations in degree 4 : -- used 0.30156 seconds Computing relations in degree 5 : -- used 0.844587 seconds Computing relations in degree 6 : -- used 1.15772 seconds Computing relations in degree 7 : -- used 1.56139 seconds Computing relations in degree 8 : -- used 2.13039 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.