D.5.2.4 lift_rel_kb

Procedure from library deform.lib (see deform_lib).

Usage:

lift_rel_kb(N,M[,kbaseM,p]);

Assume:

[p a monomial ] or the product of all variables
N, M modules of same rank, M depending only on variables not in p and vdim(M) is finite in this ring,
[ kbaseM the kbase of M in the subring given by variables not in p ]
warning: these assumptions are not checked by the procedure

Return:

matrix A, whose j-th columns present the coeff’s of N[j] in kbaseM, i.e. kbaseM*A = reduce(N,std(M))

Example:

LIB "deform.lib";
ring r=0,(A,B,x,y),dp;
module M      = [x2,xy],[xy,y3],[y2],[0,x];
module kbaseM = [1],[x],[xy],[y],[0,1],[0,y],[0,y2];
poly f=xy;
module N = [AB,BBy],[A3xy+x4,AB*(1+y2)];
matrix A = lift_rel_kb(N,M,kbaseM,f);
print(A);
→ AB,0, 
→ 0, 0, 
→ 0, A3,
→ 0, 0, 
→ 0, AB,
→ B2,0, 
→ 0, AB 
"TEST:";
→ TEST:
print(matrix(kbaseM)*A-matrix(reduce(N,std(M))));
→ 0,0,
→ 0,0