Copyright	(c) Immanuel Albrecht 2020-202x
License	BSD-3
Maintainer	mail@immanuel-albrecht.de
Stability	experimental
Portability	POSIX
Safe Haskell	Safe-Inferred
Language	Haskell2010

Data.Matroid.Uniform

Description

This module provides implementations of uniform matroids.

Synopsis

data UniformMatroid a
uniformOn :: Ord a => Set a -> Int -> UniformMatroid a
uniform :: Int -> Int -> UniformMatroid Int
data FreeMatroid a
freeOn :: Ord a => Set a -> FreeMatroid a

Documentation

data UniformMatroid a Source #

data type representing a uniform matroid over a given ground set

Instances

Instances details

(Ord a, Show a) => Matroid UniformMatroid a Source #
Instance details Defined in Data.Matroid.Uniform Methods groundset :: UniformMatroid a -> Set a Source # showName :: UniformMatroid a -> String Source # rk :: UniformMatroid a -> Set a -> Int Source # indep :: UniformMatroid a -> Set a -> Bool Source # basis :: UniformMatroid a -> Set a -> Set a Source # cl :: UniformMatroid a -> Set a -> Set a Source # abstract :: UniformMatroid a -> AMatroid a Source # dual :: UniformMatroid a -> AMatroid a Source # restriction :: UniformMatroid a -> Set a -> AMatroid a Source # contraction :: UniformMatroid a -> Set a -> AMatroid a Source # loops :: UniformMatroid a -> Set a Source # coRk :: UniformMatroid a -> Set a -> Int Source # coloops :: UniformMatroid a -> Set a Source #
Eq a => Eq (UniformMatroid a) Source #
Instance details Defined in Data.Matroid.Uniform Methods (==) :: UniformMatroid a -> UniformMatroid a -> Bool # (/=) :: UniformMatroid a -> UniformMatroid a -> Bool #
Ord a => Ord (UniformMatroid a) Source #
Instance details Defined in Data.Matroid.Uniform Methods compare :: UniformMatroid a -> UniformMatroid a -> Ordering # (<) :: UniformMatroid a -> UniformMatroid a -> Bool # (<=) :: UniformMatroid a -> UniformMatroid a -> Bool # (>) :: UniformMatroid a -> UniformMatroid a -> Bool # (>=) :: UniformMatroid a -> UniformMatroid a -> Bool # max :: UniformMatroid a -> UniformMatroid a -> UniformMatroid a # min :: UniformMatroid a -> UniformMatroid a -> UniformMatroid a #
Show a => Show (UniformMatroid a) Source #
Instance details Defined in Data.Matroid.Uniform Methods showsPrec :: Int -> UniformMatroid a -> ShowS # show :: UniformMatroid a -> String # showList :: [UniformMatroid a] -> ShowS #

uniformOn Source #

Arguments

:: Ord a
=> Set a	ground set of the uniform matroid
-> Int	rank of the uniform matroid (r)
-> UniformMatroid a

returns a uniform matroid on a given ground set of rank r

uniform Source #

Arguments

:: Int	size of the uniform matroid (number of edges, n)
-> Int	rank of the uniform matroid (r)
-> UniformMatroid Int

returns a uniform matroid on the intergers from 1..n of rank r

data FreeMatroid a Source #

data type that represents a free matroid over a given set (free matroids are of course uniform)

Instances

Instances details

(Ord a, Show a) => Matroid FreeMatroid a Source #
Instance details Defined in Data.Matroid.Uniform Methods groundset :: FreeMatroid a -> Set a Source # showName :: FreeMatroid a -> String Source # rk :: FreeMatroid a -> Set a -> Int Source # indep :: FreeMatroid a -> Set a -> Bool Source # basis :: FreeMatroid a -> Set a -> Set a Source # cl :: FreeMatroid a -> Set a -> Set a Source # abstract :: FreeMatroid a -> AMatroid a Source # dual :: FreeMatroid a -> AMatroid a Source # restriction :: FreeMatroid a -> Set a -> AMatroid a Source # contraction :: FreeMatroid a -> Set a -> AMatroid a Source # loops :: FreeMatroid a -> Set a Source # coRk :: FreeMatroid a -> Set a -> Int Source # coloops :: FreeMatroid a -> Set a Source #
Eq a => Eq (FreeMatroid a) Source #
Instance details Defined in Data.Matroid.Uniform Methods (==) :: FreeMatroid a -> FreeMatroid a -> Bool # (/=) :: FreeMatroid a -> FreeMatroid a -> Bool #
Ord a => Ord (FreeMatroid a) Source #
Instance details Defined in Data.Matroid.Uniform Methods compare :: FreeMatroid a -> FreeMatroid a -> Ordering # (<) :: FreeMatroid a -> FreeMatroid a -> Bool # (<=) :: FreeMatroid a -> FreeMatroid a -> Bool # (>) :: FreeMatroid a -> FreeMatroid a -> Bool # (>=) :: FreeMatroid a -> FreeMatroid a -> Bool # max :: FreeMatroid a -> FreeMatroid a -> FreeMatroid a # min :: FreeMatroid a -> FreeMatroid a -> FreeMatroid a #
Show a => Show (FreeMatroid a) Source #
Instance details Defined in Data.Matroid.Uniform Methods showsPrec :: Int -> FreeMatroid a -> ShowS # show :: FreeMatroid a -> String # showList :: [FreeMatroid a] -> ShowS #

freeOn Source #

Arguments

:: Ord a
=> Set a	ground set of the free matroid
-> FreeMatroid a

returns a free matroid on a given ground set (where every subset of the groundset is independent)