2.4.2 Euclidian algorithm

Lemma 2..13   If < is a wellordering and $I=\{f,g\}\subseteq K[x]$ then the computation of the standard basis of I yields the greatest common divisor of f and g.

SINGULAR example:

ring R=32003,x,dp;
poly f=(x^3+5)^2*(x-2)*(x^2+x+2)^4;
poly g=(x^3+5)*(x^2-3)*(x^2+x+2);
ideal I=f,g;
std(I);
// and the expected result:
(x^3+5)*(x^2+x+2);