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D.5.9.3 matrixT1
Procedure from library spcurve.lib (see section 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)
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