HaskellForMaths-0.4.1: Combinatorics, group theory, commutative algebra, non-commutative algebra

Math.Combinatorics.FiniteGeometry

Description

Constructions of the finite geometries AG(n,Fq) and PG(n,Fq), their points, lines and flats, together with the incidence graphs between points and lines.

Synopsis

# Documentation

ptsAG :: Int -> [a] -> [[a]]Source

ptsAG n fq returns the points of the affine geometry AG(n,Fq), where fq are the elements of Fq

ptsPG :: Num a => Int -> [a] -> [[a]]Source

ptsPG n fq returns the points of the projective geometry PG(n,Fq), where fq are the elements of Fq

closureAG :: (Ord a, FiniteField a) => [[a]] -> [[a]]Source

Given a list of points in AG(n,Fq), return their closure, the smallest flat containing them

closurePG :: (Ord a, FiniteField a) => [[a]] -> [[a]]Source

Given a set of points in PG(n,Fq), return their closure, the smallest flat containing them

Constructors

 Zero One Star

Instances

 Eq ZeroOneStar Show ZeroOneStar

flatsPG :: Num a => Int -> [a] -> Int -> [[[a]]]Source

`flatsPG n fq k` returns the k-flats in PG(n,Fq), where fq are the elements of Fq. The returned flats are represented as matrices in reduced row echelon form, the rows of which are the points that generate the flat. The full set of points in the flat can be recovered by calling `closurePG`

flatsAG :: Num a => Int -> [a] -> Int -> [[[a]]]Source

flatsAG n fq k returns the k-flats in AG(n,Fq), where fq are the elements of Fq.

linesPG :: Num a => Int -> [a] -> [[[a]]]Source

The lines (1-flats) in PG(n,fq)

linesAG :: Num a => Int -> [a] -> [[[a]]]Source

The lines (1-flats) in AG(n,fq)

incidenceGraphPG :: (Ord a, FiniteField a) => Int -> [a] -> Graph (Either [a] [[a]])Source

Incidence graph of PG(n,fq), considered as an incidence structure between points and lines

incidenceGraphAG :: (Ord a, FiniteField a) => Int -> [a] -> Graph (Either [a] [[a]])Source

Incidence graph of AG(n,fq), considered as an incidence structure between points and lines