Use R ::= QQ[x,y,z];
Syz([x^2-y, xy-z, xy]);
Module([0, xy, -xy + z], [z, x^2 - y, -x^2 + y], [yz, -y^2, y^2 - xz],
[xy, 0, -x^2 + y])
-------------------------------
I := Ideal(x, x, y);
Syz(Gens(I)); SyzOfGens(I); Syz(I, 1);
Module([[1, -1, 0], [0, y, -x]])
-------------------------------
Module([[1, -1, 0], [0, y, -x]])
-------------------------------
Module([[x, -y]])
-------------------------------
I := Ideal(x^2-yz, xy-z^2, xyz);
Syz(I,0);
Module([x^2 - yz], [xy - z^2], [xyz])
-------------------------------
Syz(I,1);
Module([-x^2 + yz, xy - z^2, 0], [xz^2, -yz^2, -y^2 + xz], [z^3, 0,
-xy + z^2], [0, z^3, -x^2 + yz])
-------------------------------
Syz(I,2);
Module([0, z, -x, y], [-z^2, -x, y, -z])
-------------------------------
Syz(I,3);
Module([[0]])
-------------------------------
Res(I);
0 --> R^2(-6) --> R(-4)(+)R^3(-5) --> R^2(-2)(+)R(-3)
-------------------------------
|