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7.8.8 syz (letterplace)
Syntax:
syz ( ideal_expression )
syz ( module_expression )
Type:
- module
Purpose:
- computes the first syzygy (i.e., the module of relations of the given
generators) bimodule of the ideal, resp. module.
If option(returnSB) is set, a Groebner basis is returned, otherwise a generating set.
Example:
| | LIB "freegb.lib";
ring r = 0,(x,y),(c,Dp);
ring R = freeAlgebra(r, 7, 2);
ideal I = twostd(x*y*x + 1);
I;
==> I[1]=x*y-y*x
==> I[2]=y*x*x+1
module S = syz(I);
print(S);
==> ncgen(1)*x*x,S[1,2],S[1,3],S[1,4],S[1,5],
==> S[2,1], S[2,2],S[2,3],S[2,4],S[2,5]
testSyz(I,S);
==> _[1]=0
==> _[2]=0
==> _[3]=0
==> _[4]=0
==> _[5]=0
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See
ideal;
lift (letterplace);
liftstd (letterplace);
module;
ncgen;
option.
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