| Safe Haskell | None |
|---|---|
| Language | Haskell98 |
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.
- ptsAG :: Int -> [a] -> [[a]]
- ptsPG :: Num a => Int -> [a] -> [[a]]
- pnf :: (Fractional a, Eq a) => [a] -> [a]
- ispnf :: (Num t, Eq t) => [t] -> Bool
- closureAG :: (Num a, Ord a, FinSet a) => [[a]] -> [[a]]
- lineAG :: (FinSet a, Ord a, Num a) => [[a]] -> [[a]]
- closurePG :: (Num a, Ord a, FinSet a) => [[a]] -> [[a]]
- linePG :: (FinSet t, Ord t, Num t) => [[t]] -> [[t]]
- qtorial :: (Integral b, Integral a) => b -> a -> a
- qnomial :: (Integral b, Integral a) => b -> b -> a -> a
- numFlatsPG :: (Integral b, Integral a) => b -> a -> b -> a
- numFlatsAG :: (Integral b, Integral a) => b -> a -> b -> a
- qtorials :: Integral a => a -> [a]
- qnomials :: Num d => d -> [[d]]
- data ZeroOneStar
- rrefs :: Int -> Int -> [[[ZeroOneStar]]]
- flatsPG :: (Eq a, Num a) => Int -> [a] -> Int -> [[[a]]]
- flatsAG :: (Eq a, Num a) => Int -> [a] -> Int -> [[[a]]]
- linesPG :: (Eq a, Num a) => Int -> [a] -> [[[a]]]
- linesAG :: (Eq a, Num a) => Int -> [a] -> [[[a]]]
- linesAG1 :: (FinSet a, Ord a, Num a) => Int -> [a] -> [[[a]]]
- linesAG2 :: (FinSet a, Ord a, Num a) => Int -> [a] -> [[[a]]]
- incidenceGraphPG :: (Num a, Ord a, FinSet a) => Int -> [a] -> Graph (Either [a] [[a]])
- incidenceGraphAG :: (Num a, Ord a, FinSet a) => Int -> [a] -> Graph (Either [a] [[a]])
- orderGL :: (Num a, Integral b) => b -> a -> a
- orderAff :: (Num a, Integral b) => b -> a -> a
- orderPGL :: (Integral b, Integral a) => b -> a -> a
- heawood :: Graph Integer
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
pnf :: (Fractional a, Eq a) => [a] -> [a] Source
closureAG :: (Num a, Ord a, FinSet a) => [[a]] -> [[a]] Source
Given a list of points in AG(n,Fq), return their closure, the smallest flat containing them
closurePG :: (Num a, Ord a, FinSet a) => [[a]] -> [[a]] Source
Given a set of points in PG(n,Fq), return their closure, the smallest flat containing them
numFlatsPG :: (Integral b, Integral a) => b -> a -> b -> a Source
numFlatsAG :: (Integral b, Integral a) => b -> a -> b -> a Source
rrefs :: Int -> Int -> [[[ZeroOneStar]]] Source
flatsPG :: (Eq a, 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 :: (Eq a, 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.
incidenceGraphPG :: (Num a, Ord a, FinSet a) => Int -> [a] -> Graph (Either [a] [[a]]) Source
Incidence graph of PG(n,fq), considered as an incidence structure between points and lines