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D.4.11.7 fitting
Procedure from library homolog.lib (see homolog_lib).
- Usage:
- fitting (M,n); M module, n int
- Return:
- ideal, (standard basis of) n-th Fitting ideal of M'=coker(M).
Example:
| | LIB "homolog.lib";
ring R=0,x(0..4),dp;
matrix M[2][4]=x(0),x(1),x(2),x(3),x(1),x(2),x(3),x(4);
print(M);
==> x(0),x(1),x(2),x(3),
==> x(1),x(2),x(3),x(4)
fitting(M,-1);
==> _[1]=0
fitting(M,0);
==> _[1]=x(3)^2-x(2)*x(4)
==> _[2]=x(2)*x(3)-x(1)*x(4)
==> _[3]=x(1)*x(3)-x(0)*x(4)
==> _[4]=x(2)^2-x(0)*x(4)
==> _[5]=x(1)*x(2)-x(0)*x(3)
==> _[6]=x(1)^2-x(0)*x(2)
fitting(M,1);
==> _[1]=x(4)
==> _[2]=x(3)
==> _[3]=x(2)
==> _[4]=x(1)
==> _[5]=x(0)
fitting(M,2);
==> _[1]=1
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