#### D.6.16.3 matrixT1

Procedure from library `spcurve.lib` (see spcurve_lib).

Usage:
  matrixT1(M,n); M matrix, n integer

Assume:
  M is a presentation matrix of an ideal i, CM of codimension 2; consider i as a family of ideals in a ring in the first n variables where the remaining variables are considered as parameters

Return:
  list consisting of the k x (k+1) matrix M and a module K_M such that T1=Mat(k,k+1;R)/K_M is the space of first order deformations of i

Example:

    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);
    matrixT1(M,3);
    ==> [1]:
    ==>    _[1,1]=0
    ==>    _[1,2]=-x(3)
    ==>    _[2,1]=-x(2)
    ==>    _[2,2]=x(2)
    ==>    _[3,1]=x(1)
    ==>    _[3,2]=0
    ==> [2]:
    ==>    _[1]=gen(5)
    ==>    _[2]=gen(4)-gen(3)
    ==>    _[3]=-gen(2)
    ==>    _[4]=x(1)*gen(5)-x(2)*gen(3)
    ==>    _[5]=x(1)*gen(6)-x(2)*gen(4)
    ==>    _[6]=x(2)*gen(3)-x(3)*gen(1)
    ==>    _[7]=x(2)*gen(4)-x(3)*gen(2)
    ==>    _[8]=-x(3)*gen(2)
    ==>    _[9]=x(2)*gen(2)-x(2)*gen(1)
    ==>    _[10]=x(1)*gen(1)
    ==>    _[11]=-x(3)*gen(4)
    ==>    _[12]=x(2)*gen(4)-x(2)*gen(3)
    ==>    _[13]=x(1)*gen(3)
    ==>    _[14]=-x(3)*gen(6)
    ==>    _[15]=x(2)*gen(6)-x(2)*gen(5)
    ==>    _[16]=x(1)*gen(5)

User manual for Singular version 4-0-3, 2016, generated by texi2html.