7.8.13 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