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

## Synopsis

• Usage:
regStats(List)
• Inputs:
• 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:
• , 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.