Data.Matroid.Uniform

This module provides implementations of uniform matroids.

Documentation

data UniformMatroid a

data type representing a uniform matroid over a given ground set

Instances

(Ord a, Show a) => Matroid UniformMatroid a

Defined in Data.Matroid.Uniform

Methods

groundset :: UniformMatroid a -> Set a

showName :: UniformMatroid a -> String

rk :: UniformMatroid a -> Set a -> Int

indep :: UniformMatroid a -> Set a -> Bool

basis :: UniformMatroid a -> Set a -> Set a

cl :: UniformMatroid a -> Set a -> Set a

abstract :: UniformMatroid a -> AMatroid a

dual :: UniformMatroid a -> AMatroid a

restriction :: UniformMatroid a -> Set a -> AMatroid a

contraction :: UniformMatroid a -> Set a -> AMatroid a

loops :: UniformMatroid a -> Set a

coRk :: UniformMatroid a -> Set a -> Int

coloops :: UniformMatroid a -> Set a

Eq a => Eq (UniformMatroid a)

Defined in Data.Matroid.Uniform

Methods

(==) :: UniformMatroid a -> UniformMatroid a -> Bool

(/=) :: UniformMatroid a -> UniformMatroid a -> Bool

Ord a => Ord (UniformMatroid a)

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)

Defined in Data.Matroid.Uniform

Methods

showsPrec :: Int -> UniformMatroid a -> ShowS

show :: UniformMatroid a -> String

showList :: [UniformMatroid a] -> ShowS

uniformOn

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

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

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

Instances

(Ord a, Show a) => Matroid FreeMatroid a

Defined in Data.Matroid.Uniform

Methods

groundset :: FreeMatroid a -> Set a

showName :: FreeMatroid a -> String

rk :: FreeMatroid a -> Set a -> Int

indep :: FreeMatroid a -> Set a -> Bool

basis :: FreeMatroid a -> Set a -> Set a

cl :: FreeMatroid a -> Set a -> Set a

abstract :: FreeMatroid a -> AMatroid a

dual :: FreeMatroid a -> AMatroid a

restriction :: FreeMatroid a -> Set a -> AMatroid a

contraction :: FreeMatroid a -> Set a -> AMatroid a

loops :: FreeMatroid a -> Set a

coRk :: FreeMatroid a -> Set a -> Int

coloops :: FreeMatroid a -> Set a

Eq a => Eq (FreeMatroid a)

Defined in Data.Matroid.Uniform

Methods

(==) :: FreeMatroid a -> FreeMatroid a -> Bool

(/=) :: FreeMatroid a -> FreeMatroid a -> Bool

Ord a => Ord (FreeMatroid a)

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)

Defined in Data.Matroid.Uniform

Methods

showsPrec :: Int -> FreeMatroid a -> ShowS

show :: FreeMatroid a -> String

showList :: [FreeMatroid a] -> ShowS

freeOn

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)