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

Synopsis

Usage:

degStats(List)
Inputs:
- ideals, a list, of objects of type MonomialIdeal, or any objects to which degree 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 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 a method function with options.