Representing certain kinds of finite groups in terms of generators and rewrite rules. Work in progress. This is probably not the best way to represent groups, but whatever. Contributions are welcome.
The group D_16 can be represented like so
a^2 = e
b^8 = e
ba = ab^7
from groups import AbstractGroup
group = AbstractGroup({"a": 2, "b": 8}, {(("b", 1), ("a", 1)): (("a", 1), ("b", 7))}) # default groupwhere each element is represented as a list of tuples containing the generator, followed by the power of the generator.
To enumerate all the elements in the group you can then do
group.enumerate()To multiply particular elements together you can do
group.multiply(term_1, term_2)To normalize/simplify an element to its simplest form you can do
group.normalize(term_1)To get the inverse of an element, you can do
group.inverse(term_1)Voilà -- some basic group stuff!
More basic group operations (subgroups, conjugacy classes, normal subgroups, etc.) are used in examples/d16.py.
Tests are in groups/test_groups.py.