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D.4.13.3 satiety

Procedure from library mregular.lib (see mregular_lib).

Usage:
satiety (i[,e]); i ideal, e integer

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

Assume:
i is a homogeneous ideal of the basering S=K[x(0)..x(n)]. e=0: (default)
The satiety is computed determining the fresh elements in the socle of i. It works over arbitrary fields.
e=1: Makes random changes of coordinates to find a monomial ideal with same satiety. It works over infinite fields only. If K is finite, it works if it terminates, but may result in an infinite loop. After 30 loops, a warning message is displayed and -1 is returned.

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:
If printlevel > 0 (default = 0), dim(S/i) is also displayed.

Example:
 


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