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Magma

 

Calling Sequence

Description

List of Magma Package Commands

Magma representation

Accessing the Magma Package Commands

Examples

Compatibility

Calling Sequence

Magma[command](arguments)

command(arguments)

Description

• 

The Magma package is a collection of routines for working with small, finite magmas. A magma (sometimes also called a groupoid or a general binary system) is simply a set, together with a binary operation defined on that set.

List of Magma Package Commands

• 

The following is a list of the commands in the main Magma package.

AreIsomorphic

CayleyColorTable

Center

Centralizer

Commutant

CountIdempotents

CountSquares

DirectProduct

Enumerate

Format

GetIsomorphism

HasIdentity

HasLeftIdentity

HasLeftZero

HasRightIdentity

HasRightZero

HasZero

IdempotentElements

Identity

IsAlternative

IsAntiCommutative

IsAssociative

IsBand

IsCommutative

IsCrossedSet

IsDiassociative

IsDistributive

IsExtra

IsFlexible

IsGroup

IsIdempotent

IsIdentity

IsJordan

IsKei

IsLeftAlternative

IsLeftBol

IsLeftDistributive

IsLeftIdentity

IsLeftInvertible

IsLeftInvolutary

IsLeftQuasigroup

IsLeftSemimedial

IsLeftZero

IsLoop

IsMedial

IsMonoid

IsomorphicCopy

IsomorphismClasses

IsomorphismClassRepresentatives

IsParamedial

IsPower3Associative

IsPowerAssociative

IsQuandle

IsQuasigroup

IsQuasitrivial

IsRack

IsRightAlternative

IsRightBol

IsRightDistributive

IsRightIdentity

IsRightInvertible

IsRightInvolutary

IsRightQuasigroup

IsRightSemimedial

IsRightZero

IsSemigroup

IsSimple

IsSquag

IsSteiner

IsSubMagma

IsSzasz

IsZero

IsZeropotent

LeftIdentity

Nucleus

RandomMagma

Rank

RightIdentity

Squares

SubMagmaCayleyTable

SubMagmaClosure

TransportStructure

Unrank

Zero

Magma representation

• 

A magma is a set together with a binary operation.  Since, by transport of structure,  every finite magma of order n is isomorphic to a magma on the set of integers from 1 to n, magmas are represented uniformly throughout the package by their Cayley tables as Arrays with entries from 1 to n. Thus, the (i,j) entry of the Cayley table is the result of multiplying the elements i and j.

• 

Arrays representing Cayley tables of magmas are stored in row-major order (C_order) and have datatype integer[4].

Accessing the Magma Package Commands

• 

Each command in the Magma package can be accessed by using either the long form or the short form of the command name in the command calling sequence.  For example, if M is a magma you may use either Magma[IsAssociative](M) or with(Magma); then IsAssociative(M).

• 

Because the underlying implementation of the Magma package is a module, it is possible to use the form Magma:-command to access a command from the package. For more information, see Module Members.

Examples

withMagma:

Enumerate4,'associative','commutative'

58

(1)

Enumerate4,'associative','commutative','identity'

19

(2)

Q4Enumerate4,'quandle','output'='list'

Q41111222233334444,1111222234334344,1111222244333344,1111224334324324,1111322243332444,1122221144333344,1342421324313124

(3)

selectIsAssociative,Q4

1111222233334444

(4)

Compatibility

• 

The Magma package was introduced in Maple 15.

• 

For more information on Maple 15 changes, see Updates in Maple 15.