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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));
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==>
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-ef-2h+6,-f3, -ef2-fh+4f, -e2f2+7ef+2h2-18,
e3, e2f2-6efh-6ef+6h2+18h+12,e3f-3e2h-6e2,e4f-4e3h-15e3
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ideal j=std(i);
j;
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==>
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j[1]=f
j[2]=h2+h
j[3]=eh+e
j[4]=e2
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module Sj=syz(j);
print(matrix(Sj));
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==>
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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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