Use R ::= Z/(32003)[a,b,c,d,e];
I := Ideal(a+b+c+d, ab+bc+cd+da, abc+bcd+cda, abcd-e^4);
I.DegTrunc := 3;
GB.Start_GBasis(I);
GB.Complete(I);
LT(I.GBasis);
[a, b^2, bc^2]
-------------------------------
I.DegTrunc := 6;
GB.Complete(I);
LT(I.GBasis);
[a, b^2, bc^2, bcd^2, c^2d^2, cd^4, be^4, d^2e^4]
-------------------------------
RESOLUTION TRUNCATION:
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Set Verbose;
Use R_Gen ::= Z/(5)[x,y,z,t];
M := 3; N := 4;
D := DensePoly(2);
P := Mat([ [ Randomized(D) | J In 1..N ] | I In 1.. M]);
I := Ideal(Minors(2,P));
GB.Start_Res(I);
GB.Complete(I);
-- text suppressed --
Betti numbers: 17 48 48 18
318 steps of computation
I := Ideal(Minors(2,P));
GB.Start_Res(I);
I.RegTrunc := 6; -- here we store the Castelnuovo Regularity
GB.Complete(I);
...
Betti numbers: 17 48 48 18
281 steps of computation
GB.GetBettiMatrix(I);
-------------------
0 0 0 0
0 0 0 0
0 0 0 0
0 0 0 18
0 0 16 0
0 0 32 0
0 48 0 0
17 0 0 0
-------------------
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