UserFunction Syzygies

Syzygies(u:DPOLID(C,v,O))

The single argument $u$ has the type $DPOLID$ which abbreviates Distributive Polynomial Ideal.
The meaning of its parameters is as follows.

$C$: Coefficient type

$v=\{v_1,v_2,\ldots \}$: Distibutive variables in decreasing order.

$O:LEX|GRLEX|GREVLEX$: Term ordering.

Specification. Generators for the syzygy module are returned.

Examples. The input for the examples is given in Reduce algebraic mode syntax.
The output for each minisession is returned in a separate window.

I:={x**2+3*x+y,x*y+2*x-3,y**2+3*x+2*y+9};

Syzygies(I|DPOLID(Q,{x,y},GRLEX)|);

The given ideal:
$<x^2+3x+y,xy+2x-3,y^2+3x+2y+9>$
Generators of Syzygies Module:
$\left(\begin{array}{c}-y-2\\[1mm]x+3\\[1mm]1\\[1mm]\end{array}\right) \left(\begin{array}{c}-3\\[1mm]-y\\[1mm]x\\[1mm]\end{array}\right)$

Related Functions.FreeResolution, HilbertFunction.

References.

W.W. Adams, P. Loustaunau, An Introduction to Groebner Bases, American Mathematical Society, 1994.

D. Cox, J. Little, D. O'Shea, Ideals, Varieties and Algorithms Using Algebraic Geometry,
Undergraduate Texts in Mathematics, Springer, 1992 and 1998.

G.M. Greuel, G. Pfister, A Singular Introduction to Commutative Algebra, Springer, 2002.

M. Kreuzer, L. Robbiano, Using Computational Commutative Algebra I and II, Springer, 2000.