I have a system of equations over Q(rootof(z^3-2)) that if I give in maple I get solutions with different branches and some of them are given as algebraic numbers. The code in maple looks like this:
Code : Tout sélectionner
p1 := 2*RootOf(_Z^3-2)^2*z*x^2+8*RootOf(_Z^3-2)^2*z^2*x+2*x^3*RootOf(_Z^3-2)+8*x^2*RootOf(_Z^3-2)*z-2*w^2*x-14*w^2*z+126*w*x*z+28*x^3-42*x^2*z+3*x*y^2-42*x*y*z-296*x*z^2-294*y*z^2-700*z^3;
p2 := 2*RootOf(_Z^3-2)^2*x^3+22*RootOf(_Z^3-2)^2*z*x^2+56*RootOf(_Z^3-2)^2*z^2*x+6*x^3*RootOf(_Z^3-2)+24*x^2*RootOf(_Z^3-2)*z+2*w^2*z-42*w*x*z-10*x^3+2*x^2*z-x*y^2+28*x*z^2+42*y*z^2+100*z^3;
p3 := 2*w*RootOf(_Z^3-2)^2*x^2+8*x*w*RootOf(_Z^3-2)^2*z+2*y*RootOf(_Z^3-2)*x^2+8*x*y*RootOf(_Z^3-2)*z+42*x^2*z+168*x*z^2;
f := p1^2+p2^2+p3^2;
solve({p1 = 0, p2 = 0, p3 = 0});
Code : Tout sélectionner
r:=rootof(x^3-2);
p1 := 2*r^2*z*x^2+8*r^2*z^2*x+2*x^3*r+8*x^2*r*z-2*w^2*x-14*w^2*z+126*w*x*z+28*x^3-42*x^2*z+3*x*y^2-42*x*y*z-296*x*z^2-294*y*z^2-700*z^3;
p2 := 2*r^2*x^3+22*r^2*z*x^2+56*r^2*z^2*x+6*x^3*r+24*x^2*r*z+2*w^2*z-42*w*x*z-10*x^3+2*x^2*z-x*y^2+28*x*z^2+42*y*z^2+100*z^3;
p3 := 2*w*r^2*x^2+8*x*w*r^2*z+2*y*r*x^2+8*x*y*r*z+42*x^2*z+168*x*z^2;
f := p1^2 + p2^2 + p3^2;
solve([p1,p2,p3])
Am I already encountering a giac limitation? Is there a way to get the solution similar to maple? Maple provides the following solutionAlgebraic extensions not allowed in a rootof Error: Bad Argument Value