preimage versus eliminate

[Wolfram Decker]

I am worried about the timings when comparing preimage and eliminate:

ring SS = 0, (u,v,z), dp;

poly f = -2*u*v^4*z4+u^4*v5+12*u^4*v3*z^2+12*u2*v^4*z3-u^3*v*z5+11*u^3*v2*z^4-21*u3*v^3*z3-4*u^4*v*z4+2*u^4*v2*z^3-6*u4*v^4*z+u5*z^4-3*u5*v^2*z2+u^5*v3*z-3*u*v^5*z3-2*u^2*v3*z^4+u3*v^4*z2+v^5*z4; f = subst(f,z,u+v+z);

ideal IC = f; ideal AI; AI[1]=v7+4v6z+6v5z2+4v4z3+v3z4; AI[2]=uv6+3uv5z+v6z+3uv4z2+3v5z2+uv3z3+3v4z3+v3z4; AI[3]=u2v5+3u2v4z+uv5z+3u2v3z2+3uv4z2+u2v2z3+3uv3z3+uv2z4; AI[4]=u3v4+2u3v3z+2u2v4z+u3v2z2+4u2v3z2+uv4z2+2u2v2z3+2uv3z3+uv2z4; AI[5]=u4v3+2u4v2z+2u3v3z+u4vz2+4u3v2z2+u2v3z2+2u3vz3+2u2v2z3+u2vz4; AI[6]=u5v2+u5vz+3u4v2z+3u4vz2+3u3v2z2+3u3vz3+u2v2z3+u2vz4; AI[7]=u6v+u6z+3u5vz+3u5z2+3u4vz2+3u4z3+u3vz3+u3z4; AI[8]=u7+4u6z+6u5z2+4u4z3+u3z4;

int aa = timer;

ring Rtarget = 0, (y(1..8)), dp; setring Rtarget; ideal RNC = preimage(SS, AI, IC);

timer-aa;

68

aa = timer;

def Rbig = Rtarget + SS; setring Rbig; ideal IC = imap(SS,IC); ideal AI = imap(SS,AI);

ideal J; J = IC; int k; for(k=1;k<=8;k++)

{

J=J,var(k)-AI[k];

}

ideal RNC = eliminate(J,uvz);

1

[hannes]

preimage and eliminate are internally the nearly same: preimage has a little bit more freedom in chosing an eliminataion ordering, yielding in general a little faster results