Gröbner Bases
Syzygies
Resolutions
Quantum Alg.
Left Maximality
Max. Twosided
Syzygies
Now we compute the first of Suppose we have the ideal I , generated by e2, f . Let us compare its first module of syzygies, computed directly from the original set of generators and from the Gröbner basis of I .

ideal i=e2,f;
module Fi=syz(i);
print(matrix(Fi));
==>
-ef-2h+6,-f3,                     -ef2-fh+4f,  -e2f2+7ef+2h2-18, 
e3, e2f2-6efh-6ef+6h2+18h+12,e3f-3e2h-6e2,e4f-4e3h-15e3
ideal j=std(i);
j;
==> j[1]=f
j[2]=h2+h
j[3]=eh+e
j[4]=e2
module Sj=syz(j);
print(matrix(Sj));
==>
0,   0,   h2+5h+6,eh+3e,e2,0, 
e, 0, -f, -1, 0, e2,
-h+2,e, 0, -f, -2,0,
0, -h+3,0, 0, -f,-h2+7h-12
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KL, 06/03 http://www.singular.uni-kl.de