# mingenStats -- statistics on the minimal generators of a list of ideals: number and degree complexity

## Synopsis

• Usage:
mingenStats(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:
• , with the following entries: the average number of minimal generators, the standard deviation of the number of minimal generators, the average degree complexity, and the standard deviation of the degree complexity. If the option ShowTally is turned on, then the output sequence also includes the tallies of the two numbers following their standard deviation.

## Description

This function removes zero ideals from the list of ideals, then calculates the average and the standard deviation for the number of minimal generators and degree complexity of the list of nonzero ideals.

 i1 : n=4; D=3; p={0.0,1.0,0.0}; N=3; i5 : B=randomMonomialIdeals(n,D,p,N); i6 : mingenStats(B) o6 = (10, 0, 2, 0) o6 : Sequence

If the list given is a list of all zero ideals, mingenStats returns -infinity for the mean number of minimal generators and mean degree complexity.

 i7 : B=randomMonomialIdeals(3,3,0.0,1); i8 : mingenStats(B) o8 = (-infinity, 0, -infinity, 0) o8 : Sequence

## Caveat

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

## Ways to use mingenStats :

• "mingenStats(List)"

## For the programmer

The object mingenStats is .