HaskellForMaths-0.4.9: Combinatorics, group theory, commutative algebra, non-commutative algebra

Safe Haskell | None
Language | Haskell98

Math.Combinatorics.Hypergraph

Description

A module defining a type for hypergraphs.

Synopsis

- data Hypergraph a = H [a] [[a]]
- hypergraph :: Ord a => [a] -> [[a]] -> Hypergraph a
- toHypergraph :: Ord a => [a] -> [[a]] -> Hypergraph a
- isUniform :: Ord a => Hypergraph a -> Bool
- same :: Eq a => [a] -> Bool
- fromGraph :: Graph a -> Hypergraph a
- fromDesign :: Ord a => Design a -> Hypergraph a
- incidenceGraph :: Ord a => Hypergraph a -> Graph (Either a [a])
- incidenceMatrix :: (Eq a1, Num a2) => Hypergraph a1 -> [[a2]]
- fromIncidenceMatrix :: (Num a1, Enum a1, Ord a1, Num a2, Eq a2) => [[a2]] -> Hypergraph a1
- isPartialLinearSpace :: Ord a => Hypergraph a -> Bool
- isProjectivePlane :: Ord a => Hypergraph a -> Bool
- isProjectivePlaneTri :: Ord a => Hypergraph a -> Bool
- isProjectivePlaneQuad :: Ord a => Hypergraph a -> Bool
- isGeneralizedQuadrangle :: Ord a => Hypergraph a -> Bool
- grid :: (Ord a, Ord b, Num a, Num b, Enum a, Enum b) => a -> b -> Hypergraph (a, b)
- dualGrid :: Integral a => a -> a -> Hypergraph a
- isGenQuadrangle' :: Ord a => Hypergraph a -> Bool
- isConfiguration :: Ord a => Hypergraph a -> Bool
- fanoPlane :: Hypergraph Integer
- heawoodGraph :: Graph (Either Integer [Integer])
- desarguesConfiguration :: Hypergraph [Integer]
- desarguesGraph :: Graph (Either [Integer] [[Integer]])
- pappusConfiguration :: Hypergraph Integer
- pappusGraph :: Graph (Either Integer [Integer])
- coxeterGraph :: Graph [Integer]
- duads :: [[Integer]]
- synthemes :: [[[Integer]]]
- tutteCoxeterGraph :: Graph (Either [Integer] [[Integer]])
- intersectionGraph :: Ord a => Hypergraph a -> Graph [a]

# Documentation

data Hypergraph a Source #

Constructors

H [a] [[a]] |

#### Instances

Instances details

Eq a => Eq (Hypergraph a) Source # |
Instance details Defined in Math.Combinatorics.Hypergraph Methods (==) :: Hypergraph a -> Hypergraph a -> Bool (/=) :: Hypergraph a -> Hypergraph a -> Bool
Ord a => Ord (Hypergraph a) Source # |
Instance details Defined in Math.Combinatorics.Hypergraph Methods compare :: Hypergraph a -> Hypergraph a -> Ordering (<) :: Hypergraph a -> Hypergraph a -> Bool (<=) :: Hypergraph a -> Hypergraph a -> Bool (>) :: Hypergraph a -> Hypergraph a -> Bool (>=) :: Hypergraph a -> Hypergraph a -> Bool max :: Hypergraph a -> Hypergraph a -> Hypergraph a min :: Hypergraph a -> Hypergraph a -> Hypergraph a
Show a => Show (Hypergraph a) Source # |
Instance details Defined in Math.Combinatorics.Hypergraph Methods showsPrec :: Int -> Hypergraph a -> ShowS show :: Hypergraph a -> String showList :: [Hypergraph a] -> ShowS

hypergraph :: Ord a => [a] -> [[a]] -> Hypergraph a Source #

toHypergraph :: Ord a => [a] -> [[a]] -> Hypergraph a Source #

isUniform :: Ord a => Hypergraph a -> Bool Source #

Is this hypergraph uniform - meaning that all blocks are of the same size

same :: Eq a => [a] -> Bool Source #

fromGraph :: Graph a -> Hypergraph a Source #

fromDesign :: Ord a => Design a -> Hypergraph a Source #

incidenceGraph :: Ord a => Hypergraph a -> Graph (Either a [a]) Source #

incidenceMatrix :: (Eq a1, Num a2) => Hypergraph a1 -> [[a2]] Source #

fromIncidenceMatrix :: (Num a1, Enum a1, Ord a1, Num a2, Eq a2) => [[a2]] -> Hypergraph a1 Source #

isPartialLinearSpace :: Ord a => Hypergraph a -> Bool Source #

isProjectivePlane :: Ord a => Hypergraph a -> Bool Source #

Is this hypergraph a projective plane - meaning that any two lines meet in a unique point, and any two points lie on a unique line

isProjectivePlaneTri :: Ord a => Hypergraph a -> Bool Source #

Is this hypergraph a projective plane with a triangle. This is a weak non-degeneracy condition, which eliminates all points on the same line, or all lines through the same point.

isProjectivePlaneQuad :: Ord a => Hypergraph a -> Bool Source #

Is this hypergraph a projective plane with a quadrangle. This is a stronger non-degeneracy condition.

isGeneralizedQuadrangle :: Ord a => Hypergraph a -> Bool Source #

grid :: (Ord a, Ord b, Num a, Num b, Enum a, Enum b) => a -> b -> Hypergraph (a, b) Source #

dualGrid :: Integral a => a -> a -> Hypergraph a Source #

isGenQuadrangle' :: Ord a => Hypergraph a -> Bool Source #

isConfiguration :: Ord a => Hypergraph a -> Bool Source #

Is this hypergraph a (projective) configuration.

fanoPlane :: Hypergraph Integer Source #

heawoodGraph :: Graph (Either Integer [Integer]) Source #

The Heawood graph is the incidence graph of the Fano plane

desarguesConfiguration :: Hypergraph [Integer] Source #

desarguesGraph :: Graph (Either [Integer] [[Integer]]) Source #

pappusConfiguration :: Hypergraph Integer Source #

pappusGraph :: Graph (Either Integer [Integer]) Source #

coxeterGraph :: Graph [Integer] Source #

duads :: [[Integer]] Source #

synthemes :: [[[Integer]]] Source #

tutteCoxeterGraph :: Graph (Either [Integer] [[Integer]]) Source #

The Tutte-Coxeter graph, also called the Tutte 8-cage

intersectionGraph :: Ord a => Hypergraph a -> Graph [a] Source #