Singular

D.8.2.5 fastelim

Usage:

fastelim(i,p[h,o,a,b,e,m]); i=ideal, p=polynomial; h,o,a,b,e=integers
p: product of variables to be eliminated;
Optional parameters:

- h !=0: use Hilbert-series driven std-basis computation - o !=0: use proc valvars for a - hopefully - optimal ordering of vars - a !=0: order vars to be eliminated w.r.t. increasing complexity - b !=0: order vars not to be eliminated w.r.t. increasing complexity - e !=0: use elimpart first to eliminate easy part - m !=0: compute a minimal system of generators

(default: h,o,a,b,e,m = 0,1,0,0,0,0)

Return:

ideal obtained from i by eliminating those variables, which occur in p

LIB "presolve.lib";
ring s=31991,(e,f,x,y,z,t,u,v,w,a,b,c,d),dp;
ideal i = w2+f2-1, x2+t2+a2-1,  y2+u2+b2-1, z2+v2+c2-1,
d2+e2-1, f4+2u, wa+tf, xy+tu+ab;
fastelim(i,xytua,1,1);       //with hilb,valvars
==> _[1]=z2+v2+c2-1
==> _[2]=f2+w2-1
==> _[3]=e2+d2-1
fastelim(i,xytua,1,0,1);     //with hilb,minbase
==> _[1]=z2+v2+c2-1
==> _[2]=f2+w2-1
==> _[3]=e2+d2-1