0 →P →M →N →0
has finite projective dimension. Current implementation works only in case no free summand is needed.i1 : kk=ZZ/10007;S=kk[x_0..x_4] o2 = S o2 : PolynomialRing |
i3 : N=constructEx1(S);E=annihilator N; o4 : Ideal of S |
i5 : X=ideal(gens E*random(source gens E,S^{ -3}));SX=S/X; o5 : Ideal of S |
i7 : NX=N**SX; |
i8 : phi=MCMapproximation NX; o8 : Matrix |
i9 : M=source phi; |
i10 : P=ker phi; |
i11 : betti res NX 0 1 2 3 4 5 6 o11 = total: 6 13 18 18 18 18 18 0: 6 13 3 . . . . 1: . . 15 18 3 . . 2: . . . . 15 18 3 3: . . . . . . 15 o11 : BettiTally |
i12 : betti res M 0 1 2 3 4 5 6 o12 = total: 18 18 18 18 18 18 18 -1: 3 . . . . . . 0: 15 18 3 . . . . 1: . . 15 18 3 . . 2: . . . . 15 18 3 3: . . . . . . 15 o12 : BettiTally |
i13 : betti res P 0 1 o13 = total: 25 18 -1: 3 . 0: 9 18 1: 13 . o13 : BettiTally |