Description
A finite length module M determines a unique biliaison class. Curves of minimal degrees in this class are called minimal curves. Given the ideal of a curve J, this function returns the Betti tally of any minimal curve of J. Given a finite length module M, this function returns the Betti tally of any minimal curve in the biliaison class specified by M.
Synopsis
-
- Usage:
T = minimalCurveBetti(M)
-
Inputs:
-
Outputs:
i1 : R = ZZ/101[x,y,z,w];
|
i2 : M = coker vars R;
|
i3 : I = minimalCurveBetti M
0 1 2 3
o3 = total: 1 4 4 1
0: 1 . . .
1: . 4 4 1
o3 : BettiTally
|
Synopsis
-
- Usage:
T = minimalCurve(J)
-
Inputs:
-
J, an ideal, of a pure dimension one subscheme
-
Outputs:
-
T, a Betti tally, of a minimal curve in the biliaison class
i4 : R = ZZ/101[x,y,z,w];
|
i5 : J = monomialCurveIdeal(R,{1,3,4});
o5 : Ideal of R
|
i6 : I = minimalCurveBetti J
0 1 2 3
o6 = total: 1 4 4 1
0: 1 . . .
1: . 4 4 1
o6 : BettiTally
|