Singular

D.6.16.4 semiCMcod2

Usage:

semiCMcod2(M,t1[,s]); M matrix, t1 module, s any

Assume:

M is a presentation matrix of an ideal i, CM of codimension 2, and t1 is a presentation of the space of first order deformations of i ((M,t1) as returned by the procedure matrixT1)

Return:

new ring in which the ideal semi describing the semiuniversal deformation of i;
if the optional third argument is given, the perturbation matrix of the semiuniversal deformation is returned instead of the ideal.

Note:

The current basering should not contain any variables named A(j) where j is some integer!

LIB "spcurve.lib";
ring r=32003,(x(1),x(2),x(3)),ds;
ideal curve=x(1)*x(2),x(1)*x(3),x(2)*x(3);
matrix M=isCMcod2(curve);
list l=matrixT1(M,3);
def rneu=semiCMcod2(l[1],std(l[2]));
setring rneu;
semi;
==> semi[1]=A(2)*A(3)-x(2)*A(3)-x(1)*x(2)
==> semi[2]=A(1)*A(3)+x(1)*x(3)
==> semi[3]=-x(2)*A(1)-x(3)*A(2)+x(2)*x(3)