Singular

It is often faster to avoid parameters:
instead of the ring r=(0,p1, p2, x, y ), (u1, u2, u3, u4 ), lp;
define ring R=0,(u1,u2,u3,u4, p1,p2,x,y),(lp(4),dp);
do your groebner calculation in that ring R and simplify
the result (i.e. remove all but one element with the same leading
monomial w.r.t. u1..u4.

Hans Schoenemann

Hi,

I'm trying to make computations with Singular like the following one. They are very very long (after two days I'm still waiting...). Is there something that I can do to speed the computation?

Thanks, Nicola

**********************

ring r = ( 0, p1, p2, x, y ), (u1, u2, u3, u4 ), lp;


// For every generator n/d of your field you construct a polynomial
// n(u1,u2,u3,u4)-n(p1,p2,x,y)/d(p1,p2,x,y)*d(u1,u2,u3,u4). The u1,
// u2,u3,u4 are new variables whereas the p1,p2,x,y are parameters
// (meaning we calculate these polynomials over Q(p1,p2,x,y)[u1,u2,u3,u4].


poly F = (2*u1*u2+u4*u3^3+u4^3*u3)*(u4*u1+u2*u3)-(2*p1*p2+y*x^3+y^3*x)*(y*p1+p2*x) ;


poly G = (u3*u1+u4*u2)*(2*u1*u2+u4*u3^3+u4^3*u3)^2-(x*p1+y*p2)*(2*p1*p2+y*x^3+y^3*x)^2 ;


poly H1 = 1/2*u1^2+1/2*u2^2+1/8*u3^4+3/4*u3^2*u4^2+1/8*u4^4-1/2*p1^2-1/2*p2^2-1/8*x^4-3/4*x^2*y^2-1/8*y^4 ;


poly H2 = (u1*u2+1/2*u3*u4*(u3^2+u4^2))^2-(p1*p2+1/2*x*y*(x^2+y^2))^2 ;


poly FF = 2*(u4*u3^5+4*u4^3*u3^3+2*u1*u2*u3^2+u4^5*u3+2*u1*u2*u4^2)*(2*u1*u2+u4*u3^3+u4^3*u3)-2*(y*x^5+4*y^3*x^3+2*p1*p2*x^2+y^5*x+2*p1*p2*y^2)*(2*p1*p2+y*x^3+y^3*x) ;


ideal H = H1, H2, F, G ;

ideal J = groebner( H );

reduce( FF, J);