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SyzOfGens

syzygy module for a given set of generators

Syntax
SyzOfGens(M: IDEAL|MODULE): MODULE

Description
If M is an ideal or submodule, this function calculates the syzygy module for the given set of generators of M.

If M is a quotient of a ring by an ideal I or a quotient of a free module by a submodule N, then this function calculates the syzygy module for the given set of generators of I or N, respectively.

SyzOfGens(I) is the same as Syz(gens(I)) .

The coefficient ring must be a field.

Example
/**/  use R ::= QQ[x,y,z];
/**/  I := ideal(x, y, x+y);
/**/  indent(SyzOfGens(I));
SubmoduleRows(F, matrix([
  [1, 1, -1],
  [0, x +y, -y]
]))

/**/  R3 := NewFreeModule(R, 3);
/**/  MGens := matrix(R,[[x,y,z], [x-y,0,z], [y^2,y^2,0]]);
/**/  indent(SyzOfGens(SubmoduleRows(R3, MGens)));
SubmoduleRows(F, matrix([
  [1, -1, -1]
]))

See Also