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D.4.13.1 regIdeal

Procedure from library mregular.lib (see mregular_lib).

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

Return:
an integer, the Castelnuovo-Mumford regularity 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)
If K is an infinite field, makes random changes of coordinates. If K is a finite field, works over a transcendental extension. e=1: Makes random changes of coordinates even when 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.

Note:
If printlevel > 0 (default = 0), additional info is displayed: dim(S/i), depth(S/i) and end(H^(depth(S/i))(S/i)) are computed, and an upper bound for the a-invariant of S/i is given. The algorithm also determines whether the regularity is attained or not at the last step of a minimal graded free resolution of i, and if the answer is positive, the regularity of the Hilbert function of S/i is given.

Example:
 


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