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
|