The function pdimStats computes the mean and standard deviation of the projective dimension of elements in the list:
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 : pdimStats(ideals) o3 = (3, 0) o3 : Sequence |
The function can also output the projective dimension tally as follows:
i4 : R=ZZ/101[a,b,c]; |
i5 : ideals = {monomialIdeal(a,c),monomialIdeal(b),monomialIdeal(a^2*b,b^2)}
2 2
o5 = {monomialIdeal (a, c), monomialIdeal b, monomialIdeal (a b, b )}
o5 : List
|
i6 : pdimStats(ideals, ShowTally=>true)
o6 = (1.66667, .471405, Tally{1 => 1})
2 => 2
o6 : Sequence
|
The following examples use the existing functions randomMonomialIdeals to automatically generate a list of ideals, rather than creating the list manually:
i7 : ideals = randomMonomialIdeals(4,3,1.0,3)
o7 = {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
o7 : List
|
i8 : pdimStats(ideals) o8 = (4, 0) o8 : Sequence |
i9 : ideals = randomMonomialIdeals(4,6,0.01,10)
2 3 2 3
o9 = {monomialIdeal(x x x ), monomialIdeal (x x x , x x x ), monomialIdeal
2 3 4 1 2 4 1 3 4
------------------------------------------------------------------------
5 3 2 2 2
(), monomialIdeal (x x , x x , x x ), monomialIdeal(x x ),
2 3 2 3 1 4 2 3
------------------------------------------------------------------------
2 2 5 4 2 2
monomialIdeal(x x ), monomialIdeal (x x , x x x , x x x x ),
1 4 1 3 2 3 4 1 2 3 4
------------------------------------------------------------------------
2 3 2 2 2
monomialIdeal(x x ), monomialIdeal (x x x , x x x , x ),
2 3 1 3 4 1 3 4 4
------------------------------------------------------------------------
3
monomialIdeal(x x x )}
2 3 4
o9 : List
|
i10 : pdimStats(ideals) o10 = (1.6, 1.0198) o10 : Sequence |
The object pdimStats is a method function with options.