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MajoranaAlgebras

A package for constructing Majorana algebras and representations

1.5.1

9 December 2022

Markus Pfeiffer
Email: markus.pfeiffer@st-andrews.ac.uk
Homepage: https://markusp.morphism.de/

Madeleine Whybrow
Email: mlw10@ic.ac.uk
Homepage: https://madeleinewhybrow.wordpress.com
Address:
Department of Mathematics, Imperial College, South Kensington, SW7 2AZ

Copyright

© 2018 by Markus Pfeiffer and Madeleine Whybrow

MajoranaAlgebras package is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version.

Contents

1.1 A quick guide

1.2 Understanding the output

1.3 Info levels

1.3-1 InfoMajorana

2 Shapes of a Majorana representation

2.1 The shapes functions

  2.1-1 ShapesOfMajoranaRepresentation
  2.1-2 ShapesOfMajoranaRepresentationAxiomM8
  2.1-3 MAJORANA_IsSixTranspositionGroup
  2.1-4 MAJORANA_RemoveDuplicateShapes

3 Majorana representations

3.1 The main function

3.1-1 MajoranaRepresentation

3.2 The n-closed function

3.2-1 NClosedMajoranaRepresentation

4 Functions for calculating with Majorana representations

4.1 Calculating products

4.1-1 MAJORANA_AlgebraProduct
4.1-2 MAJORANA_InnerProduct

4.2 Basic functions

  4.2-1 MAJORANA_IsComplete
  4.2-2 MAJORANA_Dimension
  4.2-3 MAJORANA_Eigenvectors
  4.2-4 MAJORANA_Basis
  4.2-5 MAJORANA_AdjointAction

4.3 The subalgebra structure

4.3-1 MAJORANA_Subalgebra
4.3-2 MAJORANA_IsJordanAlgebra

5 Functions for testing Majorana representations

5.1 The main function

5.1-1 MajoranaAlgebraTest

5.2 Other functions

  5.2-1 MAJORANA_TestFrobeniusForm
  5.2-2 MAJORANA_TestInnerProduct
  5.2-3 MAJORANA_TestAxiomM2
  5.2-4 MAJORANA_TestPrimitivity

6 Orbital Structures

  6.1-1 IsOrbitalStructure
  6.1-2 OrbitalStructure
  6.1-3 OS_OrbitRepresentative
  6.1-4 OS_CanonisingElement
  6.1-5 OS_CanonisingElementAndRepresentative
  6.1-6 OS_StabilizerOf
  6.1-7 OrbitalRepresentative
  6.1-8 AllOrbitalRepresentatives
  6.1-9 OrbitalCanonizingElement
  6.1-10 OrbitalCanonizingElementInverse
  6.1-11 OrbitalTransversalIterator
  6.1-12 UnorderedOrbitalRepresentative
  6.1-13 AllUnorderedOrbitalRepresentatives
  6.1-14 UnorderedOrbitalTransversalIterator
  6.1-15 UnorderedOrbitalCanonizingElement
  6.1-16 UnorderedOrbitalCanonizingElementInverse

7 Signed Permutations

7.1 Different Representations

7.2 Low-Level Descriptions

  7.2-1 IsSignedPerm
  7.2-2 ListSignedPerm
  7.2-3 ListSignedPerm
  7.2-4 SignedPerm
  7.2-5 NewSignedPerm
  7.2-6 NewSignedPerm
  7.2-7 IsSignedPermRep
  7.2-8 IsSignedPermListRep
  7.2-9 OnPosPoints
  7.2-10 LargestMovedPoint
  7.2-11 RandomSignedPermList
  7.2-12 RandomSignedPerm

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