# minimalCurveBetti -- computes the Betti diagram of the minimal curve

## 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:
• M,
• Outputs:
• T,
 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, , 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