#
# MajoranaAlgebras: A package for constructing Majorana algebras and representations.
#
# Declarations
#
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##
## The main Majorana representation function.
##
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#! @Arguments input, index, [options]
#! @Returns a record giving a Majorana representation
#! @Description This takes two or three arguments, the first of which must be
#! the output of the function <Ref Func="ShapesOfMajoranaRepresentation"/> and
#! the second of which is the index of the desired shape in list <A>input.shapes</A>.
#!
#! If the optional argument <A>options</A> is given then it must be a record.
#! The following components of <A>options</A> are recognised:
#! <List>
#! <Mark><C>axioms</C></Mark>
#! <Item> This component must be bound to the string <A>"AllAxioms"</A> or
#! <A>"NoAxioms"</A>. If bound to <A>"AllAxioms"</A> then the algorithm assumes the axioms
#! 2Aa, 2Ab, 3A, 4A and 5A as in Seress (2012). If bound to <A>"NoAxioms"</A> then
#! the algorithm only assumes the Majorana axioms M1 - M7. The default value is
#! <A>"AllAxioms"</A>. </Item>
#! <Mark><C>form</C></Mark>
#! <Item> If this is bound to <A>true</A> then the algorithm assume the existence
#! of an inner product (as in the definition of a Majorana algebra). Otherwise, if
#! bound to <A>false</A> 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 <A>true</A>.</Item>
#! <Mark><C>embedding</C></Mark>
#! <Item> If this is bound to <A>true</A> then the algorithm first attempts to construct
#! large subalgebras of the final representation before starting the main construction.
#! The default value is <A>false</A>.</Item>
#! </List>
#! @ChapterInfo Majorana representations, The main function
DeclareGlobalFunction( "MajoranaRepresentation" );
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## The main loop functions
##
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DeclareGlobalFunction( "MAJORANA_MainLoop" );
DeclareGlobalFunction( "MAJORANA_FindInnerProducts" );
DeclareGlobalFunction( "MAJORANA_Fusion" );
DeclareGlobalFunction( "MAJORANA_FindAlgebraProducts" );
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## Functions used in fusion
##
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DeclareGlobalFunction( "MAJORANA_AddEvec" );
DeclareGlobalFunction( "MAJORANA_FuseEigenvectors" );
DeclareGlobalFunction( "MAJORANA_FuseEigenvectorsNoForm" );
DeclareGlobalFunction( "MAJORANA_CheckBasis" );
DeclareGlobalFunction( "MAJORANA_IntersectEigenspaces" );
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## Functions used in MAJORANA_FindAlgebraProducts
##
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DeclareGlobalFunction( "MAJORANA_EigenvectorsAlgebraUnknowns" );
DeclareGlobalFunction( "MAJORANA_NullspaceUnknowns" );
DeclareGlobalFunction( "MAJORANA_Resurrection" );
DeclareGlobalFunction( "MAJORANA_AllConjugates" );
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## The product functions
##
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#! @Arguments u, v, algebraproducts, setup
#! @Returns the algebra product of vectors <A>u</A> and <A>v</A>
#! @Description The arguments <A>u</A> and <A>v</A> must be row vectors in sparse
#! matrix format. The arguments <A>algebraproducts</A> and <A>setup</A> must be
#! the components with these names of a representation as outputted by
#! <Ref Func="MajoranaRepresentation"/>. The output is the algebra product of
#! <A>u</A> and <A>v</A>, also in sparse matrix format.
#! @ChapterInfo Functions for calculating with Majorana representations, Calculating prod
ucts
DeclareGlobalFunction( "MAJORANA_AlgebraProduct" );
#! @Arguments u, v, innerproducts, setup
#! @Returns the inner product of vectors <A>u</A> and <A>v</A>
#! @Description The arguments <A>u</A> and <A>v</A> must be row vectors in sparse
#! matrix format. The arguments <A>innerproducts</A> and <A>setup</A> must be
#! the components with these names of a representation as outputted by
#! <Ref Func="MajoranaRepresentation"/>. The output is the inner product of
#! <A>u</A> and <A>v</A>.
#! @ChapterInfo Functions for calculating with Majorana representations, Calculating products
DeclareGlobalFunction( "MAJORANA_InnerProduct" );
#! @Chapter Functions for calculating with Majorana representations
#! @Section Calculating products
#! @BeginExampleSession
#! gap> G := AlternatingGroup(5);;
#! gap> T := AsList(ConjugacyClass(G, (1,2)(3,4)));;
#! gap> input := ShapesOfMajoranaRepresentation(G,T);;
#! gap> rep := MajoranaRepresentation(input, 1);;
#! gap> Size(rep.setup.coords);
#! 21
#! gap> u := SparseMatrix( 1, 21, [ [ 1 ] ], [ [ 1 ] ], Rationals);;
#! gap> v := SparseMatrix( 1, 21, [ [ 17 ] ], [ [ 1 ] ], Rationals);;
#! gap> MAJORANA_AlgebraProduct(u, v, rep.algebraproducts, rep.setup);
#! <a 1 x 21 sparse matrix over Rationals>
#! gap> MAJORANA_InnerProduct(u, v, rep.innerproducts, rep.setup);
#! -1/8192
#! @EndExampleSession
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## Functions for finding indices that give unknown algebra products
##
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DeclareGlobalFunction( "MAJORANA_FindBadIndices" );
DeclareGlobalFunction( "MAJORANA_ListOfBadIndicesForResurrection" );
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## The conjugating functions
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DeclareGlobalFunction( "MAJORANA_ConjugateVec" );
DeclareGlobalFunction( "MAJORANA_ConjugateRow" );
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## Ancilliary functions for finding unknown algebra products
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DeclareGlobalFunction( "MAJORANA_SeparateAlgebraProduct" );
DeclareGlobalFunction( "MAJORANA_SolutionAlgProducts" );
DeclareGlobalFunction( "MAJORANA_SolveSingleSolution" );
DeclareGlobalFunction( "MAJORANA_RecordSolution" );
DeclareGlobalFunction( "MAJORANA_RemoveKnownAlgProducts" );
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## Ancilliary functions for finding unknown inner products
##
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DeclareGlobalFunction( "MAJORANA_SeparateInnerProduct" );
DeclareGlobalFunction( "MAJORANA_RemoveKnownInnProducts" );
DeclareGlobalFunction( "MAJORANA_SingleInnerSolution" );
DeclareGlobalFunction( "MAJORANA_SolutionInnerProducts" );
DeclareGlobalFunction( "MAJORANA_FillGramMatrix" );
