D.2.4.17 mod2id

Procedure from library poly.lib (see poly_lib).

Usage:

mod2id(M,vpos); M matrix, vpos intvec

Assume:

vpos is an integer vector such that gen(i) corresponds to var(vpos[i]).
The basering contains variables var(vpos[i]) which do not occur in M.

Return:

ideal I in which each gen(i) from the module is replaced by var(vpos[i]) and all monomials var(vpos[i])*var(vpos[j]) have been added to the generating set of I.

Note:

This procedure should be used in the following situation: one wants to pass to a ring with new variables, say e(1),..,e(s), which correspond to the components gen(1),..,gen(s) of the module M such that e(i)*e(j)=0 for all i,j.
The new ring should already exist and be the current ring

Example:

LIB "poly.lib";
ring r=0,(e(1),e(2),x,y,z),(dp(2),ds(3));
module mo=x*gen(1)+y*gen(2);
intvec iv=2,1;
mod2id(mo,iv);
→ _[1]=e(2)^2
→ _[2]=e(1)*e(2)
→ _[3]=e(1)^2
→ _[4]=e(1)*y+e(2)*x