 LIB "elim.lib";
ring r=0,(x,y,u,v,w),dp;
ideal i=xu,yu2,wu3,vx+y3;
elim(i,3..4);
==> _[1]=y2xw
==> _[2]=xyw
==> _[3]=x2y
elim(i,uv);
==> _[1]=y2xw
==> _[2]=xyw
==> _[3]=x2y
int p = printlevel;
printlevel = 2;
elim(i,uv,"withWeights","slimgb");
==> // result is a SB in the following ring:
==> // coefficients: QQ
==> // number of vars : 5
==> // block 1 : ordering a
==> // : names u v x y w
==> // : weights 5 21 0 0 0
==> // block 2 : ordering wp
==> // : names u v x y w
==> // : weights 5 7 5 21 15
==> // block 3 : ordering C
==> _[1]=x3w
==> _[2]=x2+y
printlevel = p;
ring S = (0,a),(x,y,z,u,v),ws(1,2,3,4,5);
minpoly = a2+1;
qring T = std(ideal(ax+y2+v3,(x+v)^2));
ideal i=xu,yu2,azu3,vx+ay3;
module m=i*gen(1)+i*gen(2);
m=elim(m,xy);
show(m);
==> // module, 6 generator(s)
==> [0,uv+(4a)*u3v3+(3a)*u2v4]
==> [0,z+(a)*u3]
==> [z+(a)*u3]
==> [uv+(4a)*u3v3+(3a)*u2v4]
==> [0,v]
==> [v]
