Group Theory

This is a module (and example on how to use) about group thoery, and group generators that i wrote to make my math homework easier.

What can it do?

Currently, it can produce (using the famous Todd-Coxeter Algorithm) all possible elements of a group given its generators. It currently only supports non-inverse elements (so using standard notation, only capital lettered independant elements; Helpful Information) so identity combinations must be converted using the elements order. For Example if inverse(B) == A, AB is equal to the Identity element and so AB is added as a representation of the identity element.

Use

define groups as strings:

'<{comma seperated identity elements}|{comma seperated representations of the identity element}>'

and pass to the Group object:

from FroupTools import Group
inpt = '<A,B|AAAA,AB,BBBB>'
mygroup = Group(inpt)
mygroup.solve()
print(str(mygroup))

Wanted Features

• element multiplication table
• support for inverse elements
• element equivalence calculation

Changelog

1.0:

• first working prototype