GroupTheory`
GroupTheory`

GTLeftCosets

GTLeftCosets[group,subgroup]

gives the left cosets of a group according to a subgroup.

Details and Options

  • Suppose a group and a subgroup are given. The set {} is called the left coset of . GTRightCosets gives a list of all distinct right cosets.
  • The following option can be given:
  • GOFast FalseSkips the input validation
  • See: W. Hergert, M. Geilhufe, Group Theory in Solid State Physics and Photonics. Problem Solving with Mathematica, chapter 3.2

Examples

open allclose all

Basic Examples  (1)

First, load the package:

Calculate the left cosets of with respect to

Options  (2)

GOFast  (2)

The evaluation time can be decreased, using GOFast -> True.

If GOFast->False is used, a check of the input will be performed.

Neat Examples  (1)

The module is independent of the input order.