| LIB "rootsmr.lib";
ring r = 0,(x,y,z),lp;
ideal i = (x-1)*(x-2),(y-1)^3*(x-y),(z-1)*(z-2)*(z-3)^2;
nrRootsProbab(i); //no of real roots (using internally std)
==> 9
i = groebner(i); //using the hilbert driven GB computation
int pr = printlevel;
printlevel = 2;
nrRootsProbab(i);
==> //ideal has 32 complex solutions, counted with multiplicity
==> *********************************************************************
==> * WARNING: This polynomial was obtained using pseudorandom numbers.*
==> * If you want to verify the result, please use the command *
==> * *
==> * verify(p,b,i) *
==> * *
==> * where p is the polynomial I returned, b is the monomial basis *
==> * used, and i the Groebner basis of the ideal *
==> *********************************************************************
==> 9
printlevel = pr;
|