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WPE

Provides efficient methods for working with wreath product elements.

0.8

21 October 2024

Friedrich Rober
Email: friedrich.rober@rwth-aachen.de

Contents

1 Introduction
 1.1 Overview
 1.2 Intuitive Research

  1.2-1 The Power of Component-wise Representation
 1.3 Efficient Computing
2 Notation
 2.1 Wreath Products
 2.2 Wreath Cycles
 2.3 Sparse Wreath Cycles
3 Tutorial
 3.1 Creating Wreath Product Elements
 3.2 Displaying Wreath Product Elements
 3.3 Computing in Wreath Products
 3.4 Conjugacy Problem
 3.5 Conjugacy Classes
 3.6 Centralizer
 3.7 Cycle Index Polynomial
4 Functions
 4.1 Generic Wreath Product Representation

  4.1-1 IsomorphismWreathProduct
 4.2 Accessing Components

  4.2-1 ComponentsOfWreathProduct
  4.2-2 TopGroupOfWreathProduct
  4.2-3 BaseGroupOfWreathProduct
  4.2-4 TopComponentOfWreathProductElement
  4.2-5 BaseComponentOfWreathProductElement
 4.3 Properties of Wreath Product Elements

  4.3-1 Territory
  4.3-2 IsWreathCycle
  4.3-3 IsSparseWreathCycle
  4.3-4 WreathCycleDecomposition
  4.3-5 Yade
 4.4 Printing, Viewing and Displaying

  4.4-1 ViewObj
  4.4-2 DisplayOptionsForWreathProductElements
  4.4-3 SetDisplayOptionsForWreathProductElements
  4.4-4 ResetDisplayOptionsForWreathProductElements
 4.5 Cycle Index of Wreath Products

  4.5-1 CycleIndexWreathProductImprimitiveAction
  4.5-2 CycleIndexWreathProductProductAction
5 Operations
 5.1 Operations List

  5.1-1 Wreath Product Representations
  5.1-2 Operations for all Representations
  5.1-3 Operations for Permutation Representations
  5.1-4 Operations for Generic Representation
References
Index

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