105 lines
4.7 KiB
GDScript3
105 lines
4.7 KiB
GDScript3
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#############################################################################
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##
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#W quasigroups.gd Representing, creating and displaying quasigroups [loops]
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##
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#H @(#)$Id: quasigroups.gd, v 3.2.0 2016/05/02 gap Exp $
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##
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#Y Copyright (C) 2004, G. P. Nagy (University of Szeged, Hungary),
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#Y P. Vojtechovsky (University of Denver, USA)
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##
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#############################################################################
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## GAP CATEGORIES AND REPRESENTATIONS
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## -------------------------------------------------------------------------
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## element of a quasigroup
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DeclareCategory( "IsQuasigroupElement", IsMultiplicativeElement );
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DeclareRepresentation( "IsQuasigroupElmRep",
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IsPositionalObjectRep and IsMultiplicativeElement, [1] );
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## element of a loop
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DeclareCategory( "IsLoopElement",
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IsQuasigroupElement and IsMultiplicativeElementWithInverse );
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DeclareRepresentation( "IsLoopElmRep",
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IsPositionalObjectRep and IsMultiplicativeElementWithInverse, [1] );
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## latin (auxiliary category for GAP to tell apart IsMagma and IsQuasigroup)
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DeclareCategory( "IsLatin", IsObject );
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## quasigroup
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DeclareCategory( "IsQuasigroup", IsMagma and IsLatin );
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## loop
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DeclareCategory( "IsLoop", IsQuasigroup and IsMultiplicativeElementWithInverseCollection);
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#############################################################################
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## TESTING MULTIPLICATION TABLES
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## -------------------------------------------------------------------------
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DeclareOperation( "IsQuasigroupTable", [ IsMatrix ] );
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DeclareSynonym( "IsQuasigroupCayleyTable", IsQuasigroupTable );
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DeclareOperation( "IsLoopTable", [ IsMatrix ] );
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DeclareSynonym( "IsLoopCayleyTable", IsLoopTable );
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DeclareOperation( "CanonicalCayleyTable", [ IsMatrix ] );
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DeclareOperation( "NormalizedQuasigroupTable", [ IsMatrix ] );
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#############################################################################
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## CREATING QUASIGROUPS AND LOOPS MANUALLY
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## -------------------------------------------------------------------------
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DeclareAttribute( "CayleyTable", IsQuasigroup );
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DeclareOperation( "QuasigroupByCayleyTable", [ IsMatrix ] );
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DeclareOperation( "LoopByCayleyTable", [ IsMatrix ] );
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DeclareOperation( "SetQuasigroupElmName", [ IsQuasigroup, IsString ] );
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DeclareSynonym( "SetLoopElmName", SetQuasigroupElmName );
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DeclareOperation( "CanonicalCopy", [ IsQuasigroup ] );
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#############################################################################
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## CREATING QUASIGROUPS AND LOOPS FROM A FILE
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## -------------------------------------------------------------------------
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DeclareOperation( "QuasigroupFromFile", [ IsString, IsString ] );
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DeclareOperation( "LoopFromFile", [ IsString, IsString ] );
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#############################################################################
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## CREATING QUASIGROUPS AND LOOPS BY SECTIONS
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## -------------------------------------------------------------------------
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DeclareOperation( "CayleyTableByPerms", [ IsPermCollection ] );
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DeclareOperation( "QuasigroupByLeftSection", [ IsPermCollection ] );
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DeclareOperation( "LoopByLeftSection", [ IsPermCollection ] );
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DeclareOperation( "QuasigroupByRightSection", [ IsPermCollection ] );
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DeclareOperation( "LoopByRightSection", [ IsPermCollection ] );
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DeclareOperation( "QuasigroupByRightFolder", [ IsGroup, IsGroup, IsMultiplicativeElementCollection ] );
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DeclareOperation( "LoopByRightFolder", [ IsGroup, IsGroup, IsMultiplicativeElementCollection ] );
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#############################################################################
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## CONVERSIONS
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## -------------------------------------------------------------------------
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DeclareOperation( "IntoQuasigroup", [ IsMagma ] );
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DeclareOperation( "PrincipalLoopIsotope",
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[ IsQuasigroup, IsQuasigroupElement, IsQuasigroupElement ] );
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DeclareOperation( "IntoLoop", [ IsMagma ] );
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DeclareOperation( "IntoGroup", [ IsMagma ] );
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#############################################################################
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## PRODUCTS OF QUASIGROUPS AND LOOPS
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## --------------------------------------------------------------------------
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#DirectProduct already declared for groups.
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#############################################################################
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## OPPOSITE QUASIGROUPS AND LOOPS
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## --------------------------------------------------------------------------
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DeclareOperation( "OppositeQuasigroup", [ IsQuasigroup ] );
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DeclareOperation( "OppositeLoop", [ IsLoop ] );
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DeclareAttribute( "Opposite", IsQuasigroup );
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#############################################################################
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## AUXILIARY
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## --------------------------------------------------------------------------
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DeclareGlobalFunction( "LOOPS_ReadCayleyTableFromFile" );
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DeclareGlobalFunction( "LOOPS_CayleyTableByRightFolder" );
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