Singular

LIB "multigrading.lib";
ring r = 0,(x,y,z),dp;
// Setting degrees for preimage ring.;
intmat grad[3][3] =
1,0,0,
0,1,0,
0,0,1;
setBaseMultigrading(grad);
// grading on r:
getVariableWeights();
==> 1,0,0,
==> 0,1,0,
==> 0,0,1 
getLattice();
==> 0,0,0
// only for the purpose of this example
if( voice > 1 ){ /*keepring(r);*/ export(r); }
ring R = 0,(a,b),dp;
ideal i = a2-b2+a6-b5+ab3,a7b+b15-ab6+a6b6;
// The quotient ring by this ideal will become our image ring.;
qring Q = std(i);
listvar();
==> // Q                              [0]  *ring
==> // R                              [0]  ring
==> // grad                           [0]  intmat 3 x 3
==> // r                              [0]  ring
map f = r,-a2b6+b5+a3b+a2+ab,-a2b7-3a2b5+b4+a,a6-b6-b3+a2; f;
==> f[1]=-a2b6+b5+a3b+a2+ab
==> f[2]=-a2b7-3a2b5+b4+a
==> f[3]=a6-b6-b3+a2
// TODO: Unfortunately this is not a very spectacular example...:
// Pushing forward f:
pushForward(f);
// due to pushForward we have got new grading on Q
getVariableWeights();
==> 0,0,
==> 0,0,
==> 0,0,
==> 1,0,
==> 0,1 
getLattice();
==> 1,0,0,0,0,
==> 0,1,0,0,0,
==> 0,0,1,0,0,
==> 1,1,1,1,0,
==> 1,1,1,1,1 
// only for the purpose of this example
if( voice > 1 ){ kill r; }