Singular

D.15.9.4 curveColengthDerivations

Usage:

curveColengthDerivations(I); I ideal

Assume:

I is a radical ideal

Return:

the colength of derivations of R/I

Remarks:

The procedure goes through all branches and computes the colength of derivations there. Then the d-dimension of the minimal primes is computed. After that, everything is summed up.

Note:

the optional parameter can be used if the normalization has already been computed. If a list L contains the output of the procedure normal (with options prim, wd and usering if the ring has a mixed ordering), apply curveColengthDerivations(I,L)

LIB "curveInv.lib";
///////////////////////////////////////
// colength of derivations of curves //
///////////////////////////////////////
// Example 1:
ring R = 0,(x,y,z),ds;
ideal I = x2-y4z,z3y2+xy2;
I = std(radical(I));
curveColengthDerivations(I);
==> 9
// Example 2:
ring S = 0,(x,y),ds;
ideal I = (x+y)*(x2-y3);
curveColengthDerivations(I);
==> 4
// Example 3:
ideal J = (x2-y3)*(x2+y2)*(x-y);
curveColengthDerivations(J);
==> 15