Module permutation_rs::group [−] [src]

The core of working with groups.

A group is a set G with an associated operation G * G -> G such that

The operation is associative. I.e. (a * b) * c = a * (b * c) for all a, b, c in G.
There exist an identity element. I.e. an e in G with e * g = g for all g in G.
For each element g in G there is an inverse. I.e. an element h in G such that g * h = e, the identity element in G.

Modules

calculation	A module that provides various group related calculations.
free	A free group are the sequence of symbols and their inverses where there are no occurrences of a symbol and its inverse next to each other.
permutation	A permutation is a bijection of a set. Together with function composition this forms a group.
special	Home for special groups.
tree	In order to cut down on exponential growth of words when forming products we are creating the structure of a calculation. When actual calculations need to be done, we can use a morphism to determine the result.

BaseStrongGeneratorLevel	A level in the Schreier-Sims Base Strong generator algorithm.
Group	The actual group.
Morphism	Morphism maps one Group to the other with respect of the group operation.

GroupAction	A group can act on a set. (See Group Action).
GroupElement	The contract for a group element.