GroupTheory`
GroupTheory`

GTRightCosets

GTRightCosets[group,subgroup]

gives the right coset of a group according to a subgroup.

Details and Options

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

Examples

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Basic Examples  (1)

First, load the package:

Calculate the right cosets of with respect to

Options  (2)

GOFast  (2)

The evaluation time can be decreased, using GOFastTrue.

If GOFastFalse is used,the input is validated.

Neat Examples  (1)

The module is independent of the input order.

Group and subgroup can be interchanged.