2.4.3 Gaussian algorithm

Lemma 2..14   If < is a wellordering and the generators of I are linear then the computation of the standard basis of I is a Gaussian algorithm with the columns of matrix(I).

SINGULAR example:

ring R=32003,(x,y,z),dp;
ideal I=22*x+77*y+z-3,
         0*x+ 1*y+z-77,
         1*x+ 0*y+z+11;
std(I);