Singular

D.4.6.4 elim1

Usage:

elim1(id,arg); id ideal/module, arg can be either an intvec v or a product p of variables (type poly)

Return:

ideal/module obtained from id by eliminating either the variables with indices appearing in v or the variables appearing in p

Method:

elim1 calls eliminate but in a ring with ordering dp (resp. ls) if the first var not to be eliminated belongs to a -p (resp. -s) ordering.

Note:

no special monomial ordering is required.
This proc uses 'execute' or calls a procedure using 'execute'.

LIB "elim.lib";
ring r=0,(x,y,t,s,z),dp;
ideal i=x-t,y-t2,z-t3,s-x+y3;
elim1(i,ts);
==> _[1]=y2-xz
==> _[2]=xy-z
==> _[3]=x2-y
module m=i*gen(1)+i*gen(2);
m=elim1(m,3..4); show(m);
==> // module, 6 generator(s)
==> [y2-xz]
==> [0,y2-xz]
==> [xy-z]
==> [0,xy-z]
==> [x2-y]
==> [0,x2-y]