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permgroup

represent a permutation group

 

Calling Sequence

Parameters

Description

Examples

Calling Sequence

permgroup(deg, gens)

Parameters

deg

-

degree of the permutation group

gens

-

set of generators for the permutation group

Description

• 

The function permgroup is used as a procedure and an unevaluated procedure call. As a procedure, permgroup checks its arguments and then either exits with an error or returns the unevaluated permgroup call.

• 

The first argument is the degree of the group, and should be an integer. The second argument is a set of group generators. Each generator is represented in disjoint cycle notation. The generators may be named or unnamed. A named generator is an equation; the left operand is the generator's name, the right operand is the permutation in disjoint cycle notation.

• 

A permutation in disjoint cycle notation is a list of lists. Each sub-list represents a cycle; the permutation is the product of these cycles. The cycle [a1,a2,...,an] represents the permutation which maps a1 to a2, a2 to a3, ..., an1 to an, and an to a1. The identity element is represented by the empty list .

• 

The permgroup function follows the convention that ``permutations act on the right''. In other words, if p1 and p2 are permutations, then the product of p1 and p2, p1 &* p2 is defined such that p1 &* p2i=p2p1i for i=1..deg.

Examples

permgroup5,a=1,2,4,5,b=5,4,3,2,1

permgroup5,a=1,2,4,5,b=5,4,3,2,1

(1)

permgroup6,1,2,1,2,3,4,5,6

permgroup6,1,2,1,2,3,4,5,6

(2)

the following is not legal:

permgroup5,x=3,4,y=7,2

Error, (in permgroup) generators must represent products of disjoint cycles, but [[7, 2]] does not

See Also

grelgroup

subgrel

 


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