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D.5.9.3 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) |