UserFunction Saturation

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

The arguments $u$ and $v$ have the type $DPOLID$ which abbreviates
Distributive Polynomial Ideal. The meaning of its parameters is as follows.

$C$: Coefficient type.

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

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

Specification. The saturation of $u$ w.r.t. $v$ is returned.

Examples. The input is given in Reduce algebraic mode syntax.

The first example is from Greuel and Pfister, page 83.

I:={x**5*z**3,x*y*z,y*z**4}; J:={z};

T==|DPOLID(Q,{x,y,z},GRLEX)|;

Saturation(I,J|T|);

The output is returned in a separate window.

The given ideals:
$<x^5z^3,xyz,yz^4>$
$<z>$
The saturation ideal:
$<y,x^5>$

 

Related Functions. Quotient.

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.