Expand description
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.
Structs§
- Base
Strong Generator Level - 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.
Traits§
- Group
Action - A group can act on a set. (See Group Action).
- Group
Element - The contract for a group element.