3.2 Solvability

Lemma 3..1   The set of polynomials F is solvable iff $\{1\} \neq std(F)$. (See lemma 2.19.)

SINGULAR example:

// consider two parallel lines:
ring R=0,(x,y),dp;
poly l1=x+y-3;
poly l2=x+y-500;
ideal F=l1,l2;
std(F);
// consider a circle and a line
poly c=x^2+y^2-4;
F=c,l1;
std(F);
F=c,l2;
std(F);
// solvable means: solvable in the algebaric closure !