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Dom::SymmetricGroup -- symmetric groups

Introduction

Dom::SymmetricGroup(n) creates the symmetric group of order n, that is, the domain of all the permutations of {1,...,n} elements.

Domain


Dom::SymmetricGroup(n)

Parameters

n- positive integer

Details

Introduction

The domain element Dom::SymmetricGroup(n)(l) represents the bijective mapping of the first n positive integers that maps the integer i to l[i], for 1 ≤i ≤n.

Creating Elements


Dom::SymmetricGroup(n)(l)

Parameters

l- list or array consisting of the first n integers in some order.

Categories

Cat::Group

Related Domains

Dom::PermutationGroup

Entries

one

the identical mapping of the set {1, ..., n } to itself.

Method _mult: product of permutations

Method _invert: inverse of a permutation

Method func_call: function value of a permutation at a point

Method cycles: cycle representation of a permutation

Method order: order of a permutation

Method inversions: number of inversions

Method sign: sign of a permutation

Method random: random permutation

Method allElements: return all elements of the group

Method size: return the size of the group

Method convert: conversion of an object into a permutation

Method convert_to: conversion of a permutation into another type

Method expr: convert a permutation into a list

Example 1

Consider the group of permutations of the first seven positive integers:

>> G := Dom::SymmetricGroup(7)
     
                          Dom::SymmetricGroup(7)
        

We create an element of G by providing the image of 1, 2, etc.:

>> a:=G([2,4,6,1,3,5,7])
     
                           [2, 4, 6, 1, 3, 5, 7]
        
>> a(3)
     
                                     6
        

Super-Domain

Dom::PermutationGroup

Axioms

Ax::canonicalRep

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