regStats -- statistics on the regularities of a list of objects

Synopsis

Usage:

regStats(List)
Inputs:
- a list, of objects of type MonomialIdeal or any type to which regularity can be applied.
Optional inputs:
- ShowTally => ..., default value false, optional input to choose if the tally is to be returned
- Verbose => ..., default value false, optional input to request verbose feedback
Outputs:
- a sequence, whose first entry is the mean regularity of a list of monomial ideals, second entry is the standard deviation of the regularities, and third entry (if option is turned on) is the regularity tally.

Description

This function removes zero ideals from the list of ideals, then calculates the average and the standard deviation of the regularity of the list of nonzero ideals.

i1 : R=ZZ/101[a,b,c];

i2 : ideals = {monomialIdeal(a^3,b,c^2), monomialIdeal(a^3,b,a*c)}

                      3      2                   3
o2 = {monomialIdeal (a , b, c ), monomialIdeal (a , b, a*c)}

o2 : List

i3 : regStats(ideals)

o3 = (3.5, .5)

o3 : Sequence

If the list given is a list of all zero ideals, regStats returns -infinity for the mean regularity.

i4 : B=randomMonomialIdeals(3,3,0.0,1)

o4 = {monomialIdeal ()}

o4 : List

i5 : regStats(B)

o5 = (-infinity, 0)

o5 : Sequence

Caveat

The function removes zero ideals from the list of ideals before computing the two values.

Ways to use `regStats` :

"regStats(List)"

For the programmer

The object regStats is a method function with options.