  
  
                               [1X MajoranaAlgebras [101X
  
  
       [1X A package for constructing Majorana algebras and representations [101X
  
  
                                     1.5.1
  
  
                                9 December 2022
  
  
                                Markus Pfeiffer
  
                               Madeleine Whybrow
  
  
  
  Markus Pfeiffer
      Email:    [7Xmailto:markus.pfeiffer@st-andrews.ac.uk[107X
      Homepage: [7Xhttps://markusp.morphism.de/[107X
  Madeleine Whybrow
      Email:    [7Xmailto:mlw10@ic.ac.uk[107X
      Homepage: [7Xhttps://madeleinewhybrow.wordpress.com[107X
      Address:  [33X[0;14YDepartment of Mathematics, Imperial College, South Kensington,
                SW7 2AZ[133X
  
  
  
  -------------------------------------------------------
  [1XCopyright[101X
  [33X[0;0Y© 2018 by Markus Pfeiffer and Madeleine Whybrow[133X
  
  [33X[0;0Y[5XMajoranaAlgebras[105X  package  is  free software; you can redistribute it and/or
  modify   it   under   the   terms   of   the   GNU  General  Public  License
  ([7Xhttps://www.fsf.org/licenses/gpl.html[107X)  as  published  by the Free Software
  Foundation;  either  version 2 of the License, or (at your option) any later
  version.[133X
  
  
  -------------------------------------------------------
  
  
  [1XContents (MajoranaAlgebras)[101X
  
  1 [33X[0;0YIntroduction[133X
    1.1 [33X[0;0YA quick guide[133X
    1.2 [33X[0;0YUnderstanding the output[133X
    1.3 [33X[0;0YInfo levels[133X
      1.3-1 InfoMajorana
  2 [33X[0;0YShapes of a Majorana representation[133X
    2.1 [33X[0;0YThe shapes functions[133X
      2.1-1 ShapesOfMajoranaRepresentation
      2.1-2 ShapesOfMajoranaRepresentationAxiomM8
      2.1-3 MAJORANA_IsSixTranspositionGroup
      2.1-4 MAJORANA_RemoveDuplicateShapes
  3 [33X[0;0YMajorana representations[133X
    3.1 [33X[0;0YThe main function[133X
      3.1-1 MajoranaRepresentation
    3.2 [33X[0;0YThe n-closed function[133X
      3.2-1 NClosedMajoranaRepresentation
  4 [33X[0;0YFunctions for calculating with Majorana representations[133X
    4.1 [33X[0;0YCalculating products[133X
      4.1-1 MAJORANA_AlgebraProduct
      4.1-2 MAJORANA_InnerProduct
    4.2 [33X[0;0YBasic functions[133X
      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 [33X[0;0YThe subalgebra structure[133X
      4.3-1 MAJORANA_Subalgebra
      4.3-2 MAJORANA_IsJordanAlgebra
  5 [33X[0;0YFunctions for testing Majorana representations[133X
    5.1 [33X[0;0YThe main function[133X
      5.1-1 MajoranaAlgebraTest
    5.2 [33X[0;0YOther functions[133X
      5.2-1 MAJORANA_TestFrobeniusForm
      5.2-2 MAJORANA_TestInnerProduct
      5.2-3 MAJORANA_TestAxiomM2
      5.2-4 MAJORANA_TestPrimitivity
  6 [33X[0;0YOrbital Structures[133X
    6.1 [33X[0;0YExamples[133X
      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 [33X[0;0YSigned Permutations[133X
    7.1 [33X[0;0YDifferent Representations[133X
    7.2 [33X[0;0YLow-Level Descriptions[133X
      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
  
  
  [32X
