HaskellForMaths-0.3.2: 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 :: FiniteField a => 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 :: FiniteField 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

Constructors

 Zero One Star

Instances

 Eq ZeroOneStar Show ZeroOneStar

flatsPG :: FiniteField 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

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

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

linesAG :: FiniteField 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