Procedure from library presolve.lib (see presolve_lib).
presolve.lib
idealSimplify(id); id ideal
ideal I = eliminate(Id,m) m is a product of variables which are only linearly involved in the generators of id
Example:
LIB "presolve.lib"; ring r=0,(x,y,z,w,t),dp; ideal i= t, x3+y2+2z, x2+3y, x2+y2+z2, w2+z; ideal j=idealSimplify(i); ideal k=eliminate(i,zyt); reduce(k,std(j)); → _[1]=0 → _[2]=0 reduce(j,std(k)); → _[1]=0 → _[2]=0