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D.4.3.6 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 |