D.5.9.8 posweight

Procedure from library spcurve.lib (see spcurve_lib).

Usage:

posweight(M,t1,n[,s]); M matrix, t1 module, n int, s string
n=0 : all deformations of non-negative weight
n=1 : only non-constant deformations of non-negative weight
n=2 : all deformations of positive weight
As an optional parameter the name of a new ring may be specified.

Assume:

M is a presentation matrix of a Cohen-Macaulay codimension 2 ideal and t1 is its T1 space in matrix notation

Create:

new basering (default name: rneu); a different name for this ring may be given as a 4th parameter

Return:

list, consisting of a presentation matrix describing the deformation given by the generators of T1 of non-negative/positive weight and the weight vector for the new variables

Note:

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

Example:

LIB "spcurve.lib";
ring r=32003,(x(1),x(2),x(3)),ds;
ideal curve=(x(3)-x(1)^2)*x(3),(x(3)-x(1)^2)*x(2),x(2)^2-x(1)^7*x(3);
matrix M=isCMcod2(curve);
list l=matrixT1(M,3);
list li=posweight(l[1],std(l[2]),0);
pmat(li[1]);
→ T(2)+x(1)*T(1), -x(3)+x(1)^2, 
→ -x(3),          x(2),         
→ x(2),           -x(1)^7
li[2];
→ 3,1