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RandomMonomialIdeals :: degStats

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

Synopsis

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 :

For the programmer

The object degStats is a method function with options.