Safe Haskell	Safe-Inferred
Language	Haskell2010

GRType

Description

This module represents group presentation and its sub-types.

Synopsis

Documentation

This is a data type of GR generators.

A_Y is a generators witch obtain from alphabet letters Y of S-machine.

A_K is a generators witch forms the hubRelation.

A_R is a generators witch obtain from rules SRule of S-machine.

A_Q is a generators witch obtain from states State of S-machine.

Constructors

Instances details

Eq A Source #
Instance details Defined in GRType Methods (==) :: A -> A -> Bool # (/=) :: A -> A -> Bool #
Ord A Source #
Instance details Defined in GRType Methods compare :: A -> A -> Ordering # (<) :: A -> A -> Bool # (<=) :: A -> A -> Bool # (>) :: A -> A -> Bool # (>=) :: A -> A -> Bool # max :: A -> A -> A # min :: A -> A -> A #
Show A Source #
Instance details Defined in GRType Methods showsPrec :: Int -> A -> ShowS # show :: A -> String # showList :: [A] -> ShowS #

This is a data type of symbols in GrRelation.

Symbols can represent generators A and its invertions.

SmbA represents generators.

SmbA' represents invertions of generators.

Constructors

SmbA A
SmbA' A

Instances details

Eq SmbR Source #
Instance details Defined in GRType Methods (==) :: SmbR -> SmbR -> Bool # (/=) :: SmbR -> SmbR -> Bool #
Ord SmbR Source #
Instance details Defined in GRType Methods compare :: SmbR -> SmbR -> Ordering # (<) :: SmbR -> SmbR -> Bool # (<=) :: SmbR -> SmbR -> Bool # (>) :: SmbR -> SmbR -> Bool # (>=) :: SmbR -> SmbR -> Bool # max :: SmbR -> SmbR -> SmbR # min :: SmbR -> SmbR -> SmbR #
Show SmbR Source #
Instance details Defined in GRType Methods showsPrec :: Int -> SmbR -> ShowS # show :: SmbR -> String # showList :: [SmbR] -> ShowS #

This is a data type of GR relations.

Relation represents relation beetwen right and left symbols SmbR.

For example, relation ab=ba will coded like

>>> Relation ([a, b], [b, a])

where a, b are SmbR

Relator is relation in witch one part is identity.

For example, ab=1 is

>>> Relator [a,b]

Constructors

Relation ([SmbR], [SmbR])
Relator [SmbR]

Instances details

Eq GrRelation Source #
Instance details Defined in GRType Methods (==) :: GrRelation -> GrRelation -> Bool # (/=) :: GrRelation -> GrRelation -> Bool #
Ord GrRelation Source #
Instance details Defined in GRType Methods compare :: GrRelation -> GrRelation -> Ordering # (<) :: GrRelation -> GrRelation -> Bool # (<=) :: GrRelation -> GrRelation -> Bool # (>) :: GrRelation -> GrRelation -> Bool # (>=) :: GrRelation -> GrRelation -> Bool # max :: GrRelation -> GrRelation -> GrRelation # min :: GrRelation -> GrRelation -> GrRelation #
Show GrRelation Source #
Instance details Defined in GRType Methods showsPrec :: Int -> GrRelation -> ShowS # show :: GrRelation -> String # showList :: [GrRelation] -> ShowS #

newtype GR Source #

GR is a group presentation type.

It consists of set of generators A and set of relations GrRelation.

Constructors

Instances details

Eq GR Source #
Instance details Defined in GRType Methods (==) :: GR -> GR -> Bool # (/=) :: GR -> GR -> Bool #
Ord GR Source #
Instance details Defined in GRType Methods compare :: GR -> GR -> Ordering # (<) :: GR -> GR -> Bool # (<=) :: GR -> GR -> Bool # (>) :: GR -> GR -> Bool # (>=) :: GR -> GR -> Bool # max :: GR -> GR -> GR # min :: GR -> GR -> GR #
Show GR Source #
Instance details Defined in GRType Methods showsPrec :: Int -> GR -> ShowS # show :: GR -> String # showList :: [GR] -> ShowS #
ShowInfo GR Source #
Instance details Defined in ShowInfo Methods showTitle :: GR -> Title Source # showInfo :: GR -> String Source # showTitleAndInfo :: GR -> String Source # showListTitle :: [GR] -> Title Source # showListInfo :: [GR] -> String Source #