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D.5.2.3 lift_kbase
Procedure from library deform.lib (see deform_lib).
- Usage:
lift_kbase(N,M); N,M=poly/ideal/vector/module
- Return:
matrix A, coefficient matrix expressing N as linear combination of k-basis of M. Let the k-basis have k elements and size(N)=c columns. Then A satisfies:
matrix(reduce(N,std(M)),k,c) = matrix(kbase(std(M)))*A- Assume:
dim(M)=0 and the monomial ordering is a well ordering or the last block of the ordering is c or C
Example:
LIB "deform.lib"; ring R=0,(x,y),ds; module M=[x2,xy],[y2,xy],[0,xx],[0,yy]; module N=[x3+xy,x],[x,x+y2]; print(M); → x2,y2,0, 0, → xy,xy,x2,y2 module kb=kbase(std(M)); print(kb); → y2,xy,y,x,1,0,0,0, → 0, 0, 0,0,0,y,x,1 print(N); → xy+x3,x, → x, x+y2 matrix A=lift_kbase(N,M); print(A); → 0,0, → 1,0, → 0,0, → 0,1, → 0,0, → 0,0, → 1,1, → 0,0 matrix(reduce(N,std(M)),nrows(kb),ncols(A)) - matrix(kbase(std(M)))*A; → _[1,1]=0 → _[1,2]=0 → _[2,1]=0 → _[2,2]=0 |