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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)
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