# degStats -- statistics on the degrees of a list of objects

## Synopsis

• Usage:
degStats(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 average degree of a list of monomial ideals, second entry is the standard deviation of the degree, and third entry (if option turned on) is the degree tally

## Description

This function computes the degree of $R/I$ for each ideal $I$ in the list and computes the mean and standard deviation of the degrees.

 i1 : R=ZZ/101[a,b,c]; i2 : ideals = {monomialIdeal"a3,b,c2", monomialIdeal"a3,b,ac"} 3 2 3 o2 = {monomialIdeal (a , b, c ), monomialIdeal (a , b, a*c)} o2 : List i3 : degStats(ideals) o3 = (3.5, 2.5) o3 : Sequence

The following examples use the existing functions randomMonomialSets and idealsFromGeneratingSets or randomMonomialIdeals to automatically generate a list of ideals, rather than creating the list manually:

 i4 : ideals = idealsFromGeneratingSets(randomMonomialSets(4,3,1.0,3)) o4 = {monomialIdeal (x , x , x , x ), monomialIdeal (x , x , x , x ), 1 2 3 4 1 2 3 4 ------------------------------------------------------------------------ monomialIdeal (x , x , x , x )} 1 2 3 4 o4 : List i5 : degStats(ideals) o5 = (1, 0) o5 : Sequence
 i6 : ideals = randomMonomialIdeals(4,3,1.0,3) o6 = {monomialIdeal (x , x , x , x ), monomialIdeal (x , x , x , x ), 1 2 3 4 1 2 3 4 ------------------------------------------------------------------------ monomialIdeal (x , x , x , x )} 1 2 3 4 o6 : List i7 : degStats(ideals) o7 = (1, 0) o7 : Sequence

Note that this function can be run with a list of any objects to which degree can be applied.

## Ways to use degStats :

• "degStats(List)"

## For the programmer

The object degStats is .