/**/ use R ::= QQ[x,y,z];
/**/ indent(syz([x^2-y-1, y^3-z, x^2-y, y^3-z]));
SubmoduleRows(F, matrix(
[y^3 -z, 0, 0, -x^2 +y +1],
[0, 1, 0, -1],
[x^2 -y, 0, -x^2 +y +1, 0],
[0, 0, y^3 -z, -x^2 +y]
))
-------------------------------
/**/ I := ideal(x, x, y);
/**/ syz(gens(I));
submodule(FreeModule(..), [[1, -1, 0], [0, y, -x]])
/**/ SyzOfGens(I);
submodule(FreeModule(..), [[1, -1, 0], [0, y, -x]])
syz(I, 1); -- NOT YET IMPLEMENTED
Module([[x, -y]])
-------------------------------
I := ideal(x^2-yz, xy-z^2, xyz); -- NOT YET IMPLEMENTED
syz(I,0);
Module([x^2 - yz], [xy - z^2], [xyz])
-------------------------------
syz(I,1); -- NOT YET IMPLEMENTED
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(-6)^2 --> R(-4)(+)R(-5)^3 --> R(-2)^2(+)R(-3)
-------------------------------
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