D.2.4.18 id2mod

Procedure from library poly.lib (see poly_lib).

Usage:

id2mod(I,vpos); I ideal, vpos intvec

Return:

module corresponding to the ideal by replacing var(vpos[i]) by gen(i) and omitting all generators var(vpos[i])*var(vpos[j])

Note:

* This procedure only makes sense if the ideal contains all var(vpos[i])*var(vpos[j]) as monomial generators and all other generators of I are linear combinations of the var(vpos[i]) over the ring in the other variables.
* This is the inverse procedure to mod2id and should be applied only to ideals created by mod2id using the same intvec vpos (possibly after a standard basis computation)

Example:

LIB "poly.lib";
ring r=0,(e(1),e(2),x,y,z),(dp(2),ds(3));
ideal i=e(2)^2,e(1)*e(2),e(1)^2,e(1)*y+e(2)*x;
intvec iv=2,1;
id2mod(i,iv);
→ _[1]=x*gen(1)+y*gen(2)