Data.Matroid.Ops

This module provides implementations of common operations on matroids and an abstract matroid data type.

Documentation

data AMatroid a

abstract matroid data type with elements of a given type

Its purpose is to hide the underlying type from the type system. The records resemble the typeclass Matroid, where everything except for the groundset has been placed inside the Maybe-Monad. A value of Nothing indicates that the default implementation of the typeclass should be used.

Constructors

WMatroid

Fields

• w_groundset :: Set a
• w_showName :: Maybe String
• w_rk :: Maybe (Set a -> Int)
• w_indep :: Maybe (Set a -> Bool)
• w_basis :: Maybe (Set a -> Set a)
• w_cl :: Maybe (Set a -> Set a)
• w_abstract :: Maybe (AMatroid a)
• w_dual :: Maybe (AMatroid a)
• w_restriction :: Maybe (Set a -> AMatroid a)
• w_contraction :: Maybe (Set a -> AMatroid a)
• w_loops :: Maybe (Set a)
• w_coRk :: Maybe (Set a -> Int)
• w_coloops :: Maybe (Set a)

Instances

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

This instance contains the default implementations of the members of the Matroid typeclass.

Defined in Data.Matroid.Typeclass

Methods

groundset :: AMatroid a -> Set a

showName :: AMatroid a -> String

rk :: AMatroid a -> Set a -> Int

indep :: AMatroid a -> Set a -> Bool

basis :: AMatroid a -> Set a -> Set a

cl :: AMatroid a -> Set a -> Set a

abstract :: AMatroid a -> AMatroid a

dual :: AMatroid a -> AMatroid a

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

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

loops :: AMatroid a -> Set a

coRk :: AMatroid a -> Set a -> Int

coloops :: AMatroid a -> Set a

Show a => Show (AMatroid a)

Defined in Data.Matroid.Ops

Methods

showsPrec :: Int -> AMatroid a -> ShowS

show :: AMatroid a -> String

showList :: [AMatroid a] -> ShowS

wrappedMatroid :: AMatroid a

defaults for WMatroid

a_restriction

Arguments

:: (Show a, Ord a)

=> AMatroid a

input matroid

-> Set a

restriction of ground set

-> AMatroid a

returns the restriction of a given matroid

Note that this routine implements the correct routines provided that the prerequisite members in the input matroid are defined. Routines which have missing prerequisite members in the input matroid will be left to Nothing. Data.Matroid.Typeclass.wrapUp fills all AMatroid record members.

a_namedRestriction

Arguments

:: Ord a

=> String

name

-> AMatroid a

input matroid

-> Set a

restriction of ground set

-> AMatroid a

returns the restriction of a given matroid, named

Note that this routine implements the correct routines provided that the prerequisite members in the input matroid are defined. Routines which have missing prerequisite members in the input matroid will be left to Nothing. Data.Matroid.Typeclass.wrapUp fills all AMatroid record members.

a_contraction

Arguments

:: (Show a, Ord a)

=> AMatroid a

input matroid

-> Set a

contract the ground set onto this set

-> AMatroid a

returns the contraction of a given matroid

Note that this routine implements the correct routines provided that the prerequisite members in the input matroid are defined. Routines which have missing prerequisite members in the input matroid will be left to Nothing. Data.Matroid.Typeclass.wrapUp fills all AMatroid record members.

a_namedContraction

Arguments

:: Ord a

=> String

name

-> AMatroid a

input matroid

-> Set a

contract the ground set onto this set

-> AMatroid a

returns the contraction of a given matroid, named

Note that this routine implements the correct routines provided that the prerequisite members in the input matroid are defined. Routines which have missing prerequisite members in the input matroid will be left to Nothing. Data.Matroid.Typeclass.wrapUp fills all AMatroid record members.

a_dual

Arguments

:: (Show a, Ord a)

=> AMatroid a

input matroid

-> AMatroid a

returns the contraction of a given matroid

Note that this routine implements the correct routines provided that the prerequisite members in the input matroid are defined. Routines which have missing prerequisite members in the input matroid will be left to Nothing. Data.Matroid.Typeclass.wrapUp fills all AMatroid record members.

a_namedDual

Arguments

:: Ord a

=> String

name

-> AMatroid a

input matroid

-> AMatroid a

returns the contraction of a given matroid, named

Note that this routine implements the correct routines provided that the prerequisite members in the input matroid are defined. Routines which have missing prerequisite members in the input matroid will be left to Nothing. Data.Matroid.Typeclass.wrapUp fills all AMatroid record members.