  
  [1X3 [33X[0;0YMajorana representations[133X[101X
  
  
  [1X3.1 [33X[0;0YThe main function[133X[101X
  
  [1X3.1-1 MajoranaRepresentation[101X
  
  [33X[1;0Y[29X[2XMajoranaRepresentation[102X( [3Xinput[103X, [3Xindex[103X[, [3Xoptions[103X] ) [32X function[133X
  [6XReturns:[106X  [33X[0;10Ya record giving a Majorana representation[133X
  
  [33X[0;0YThis  takes two or three arguments, the first of which must be the output of
  the  function [2XShapesOfMajoranaRepresentation[102X ([14X2.1-1[114X) and the second of which
  is the index of the desired shape in list [3Xinput.shapes[103X.[133X
  
  [33X[0;0YIf  the  optional  argument  [3Xoptions[103X  is given then it must be a record. The
  following components of [3Xoptions[103X are recognised:[133X
  
  [8X[10Xaxioms[110X[8X[108X
        [33X[0;6YThis  component must be bound to the string [3X"AllAxioms"[103X or [3X"NoAxioms"[103X.
        If  bound  to  [3X"AllAxioms"[103X  then the algorithm assumes the axioms 2Aa,
        2Ab,  3A,  4A  and 5A as in Seress (2012). If bound to [3X"NoAxioms"[103X then
        the  algorithm  only  assumes the Majorana axioms M1 - M7. The default
        value is [3X"AllAxioms"[103X.[133X
  
  [8X[10Xform[110X[8X[108X
        [33X[0;6YIf this is bound to [3Xtrue[103X then the algorithm assume the existence of an
        inner product (as in the definition of a Majorana algebra). Otherwise,
        if bound to [3Xfalse[103X then no inner product is assumed (and we are in fact
        constructing an axial algebra that satisfies the Majorana fusion law).
        The default value is [3Xtrue[103X.[133X
  
  [8X[10Xembedding[110X[8X[108X
        [33X[0;6YIf  this  is  bound  to  [3Xtrue[103X  then  the  algorithm  first attempts to
        construct   large  subalgebras  of  the  final  representation  before
        starting the main construction. The default value is [3Xfalse[103X.[133X
  
  
  [1X3.2 [33X[0;0YThe n-closed function[133X[101X
  
  [33X[0;0YA  Majorana  algebra [23XV[123X generated by a set of axes [23XA[123X is called [23Xn[123X-closed if it
  is  spanned as a vector space by products of elements of [23XA[123X of length at most
  [23Xn[123X.   As   most   known   Majorana   algebras   are  [23X2[123X-closed,  the  function
  [2XMajoranaRepresentation[102X ([14X3.1-1[114X) only attempts to construct the [23X2[123X-closed part.[133X
  
  [33X[0;0YIf   it   is   not   successful  then  the  output  is  a  partial  Majorana
  representation,  i.e.  a  Majorana  representation with some missing algebra
  products.  In  this  case,  the function [2XMAJORANA_IsComplete[102X ([14X4.2-1[114X) returns
  false.[133X
  
  [33X[0;0YIf   the   user   wishes,  they  may  then  pass  this  incomplete  Majorana
  representation  to  the  function  [2XNClosedMajoranaRepresentation[102X  ([14X3.2-1[114X) in
  order to attempt construction of the [23X3[123X-closed part. This process may then be
  repeated as many times as the user wishes.[133X
  
  [1X3.2-1 NClosedMajoranaRepresentation[101X
  
  [33X[1;0Y[29X[2XNClosedMajoranaRepresentation[102X( [3Xrep[103X ) [32X function[133X
  
  [33X[0;0YTakes  as  its input an incomplete Majorana representation rep that has been
  generated  using the function [2XMajoranaRepresentation[102X ([14X3.1-1[114X). Again runs the
  main  algorithm in order to attempt construction of the [23X3[123X-closed part of the
  algebra.  If the function [2XNClosedMajoranaRepresentation[102X is called [23Xn[123X times on
  the  same Majorana representation rep then this representation will be the [23Xn
  + 2[123X-closed part of the algebra.[133X
  
