Singular Manual: modsatiety

| #### D.4.23.6 modsatiety Procedure from library `noether.lib` (see noether_lib). 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)) 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). Example:
    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: 7/100sec.

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