The dual of a complex C is by definition Hom(C, R), where R is the ring of C.
i1 : S = ZZ/101[a..d] o1 = S o1 : PolynomialRing |
i2 : B = intersect(ideal(a,c),ideal(b,d)) o2 = ideal (c*d, a*d, b*c, a*b) o2 : Ideal of S |
i3 : C1 = freeResolution B 1 4 4 1 o3 = S <-- S <-- S <-- S 0 1 2 3 o3 : Complex |
i4 : C2 = dual C1 1 4 4 1 o4 = S <-- S <-- S <-- S -3 -2 -1 0 o4 : Complex |
i5 : prune HH C2 o5 = cokernel {-4} | d c b a | <-- cokernel {-2} | c a 0 0 | {-2} | 0 0 d b | -3 -2 o5 : Complex |
i6 : Ext^2(S^1/B, S) o6 = cokernel {-2} | c a 0 0 | {-2} | 0 0 d b | 2 o6 : S-module, quotient of S |
i7 : Ext^3(S^1/B, S) o7 = cokernel {-4} | d c b a | 1 o7 : S-module, quotient of S |