Singular

D.4.18.6 modsatiety

Usage:

modsatiety(i); i ideal,

Return:

an integer, the satiety of i.
(returns -1 if i is not homogeneous)

Assume:

i is a homogeneous ideal of the basering R=K[x(0)..x(n)].

Theory:

The satiety, or saturation index, of a homogeneous ideal i is the least integer s such that, for all d>=s, the degree d part of the ideals i and isat=sat(i,maxideal(1))[1] coincide.

Note:

This is a probabilistic procedure, and it computes the initial of the ideal modulo the prime number 2147483647 (the biggest prime less than 2^31).

LIB "noether.lib";
ring r=0,(t,a,b,c,d),dp;
ideal i=b4-a3d, ab3-a3c, bc4-ac3d-bcd3+ad4, c6-bc3d2-c3d3+bd5, ac5-b2c3d-ac2d3+b2d4, a2c4-a3d3+b3d3-a2cd3, b3c3-a3d3, ab2c3-a3cd2+b3cd2-ab2d3, a2bc3-a3c2d+b3c2d-a2bd3, a3c3-a3bd2, a4c2-a3b2d;
modsatiety(i);
==> // WARNING: The characteristic of base field must be zero.
==> // The procedure is probabilistic and  it computes the
==> //initial ideals modulo the prime number 2147483647.
==> msat(i)=0 and the time of this computation: 1/100sec.