107 lines
4.8 KiB
GDScript3
107 lines
4.8 KiB
GDScript3
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#############################################################################
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##
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#W classes.gd Testing varieties [loops]
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##
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#H @(#)$Id: classes.gd, v 3.3.0 2016/10/26 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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## ASSOCIATIVITY, COMMUTATIVITY AND GENERALIZATIONS
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## -------------------------------------------------------------------------
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DeclareProperty( "IsAssociative", IsLoop );
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DeclareProperty( "IsCommutative", IsQuasigroup );
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DeclareProperty( "IsPowerAssociative", IsQuasigroup );
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DeclareProperty( "IsDiassociative", IsQuasigroup );
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#############################################################################
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## INVERSE PROPERTIES
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## -------------------------------------------------------------------------
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DeclareProperty( "HasLeftInverseProperty", IsLoop );
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DeclareProperty( "HasRightInverseProperty", IsLoop );
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DeclareProperty( "HasInverseProperty", IsLoop );
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DeclareProperty( "HasWeakInverseProperty", IsLoop );
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DeclareProperty( "HasTwosidedInverses", IsLoop );
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DeclareProperty( "HasAutomorphicInverseProperty", IsLoop );
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DeclareProperty( "HasAntiautomorphicInverseProperty", IsLoop );
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#############################################################################
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## PROPERTIES OF QUASIGROUPS
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## -------------------------------------------------------------------------
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DeclareProperty( "IsSemisymmetric", IsQuasigroup );
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DeclareProperty( "IsTotallySymmetric", IsQuasigroup );
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DeclareProperty( "IsIdempotent", IsQuasigroup );
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DeclareProperty( "IsSteinerQuasigroup", IsQuasigroup );
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DeclareProperty( "IsUnipotent", IsQuasigroup );
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DeclareProperty( "IsLDistributive", IsQuasigroup );
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DeclareProperty( "IsRDistributive", IsQuasigroup );
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DeclareSynonymAttr( "IsLeftDistributive", IsLDistributive );
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DeclareSynonymAttr( "IsRightDistributive", IsRDistributive );
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#IsDistributive already declared in GAP
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DeclareProperty( "IsEntropic", IsQuasigroup );
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DeclareSynonymAttr( "IsMedial", IsEntropic );
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#############################################################################
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## LOOPS OF BOL-MOUFANG TYPE
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## -------------------------------------------------------------------------
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DeclareProperty( "IsExtraLoop", IsLoop );
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DeclareProperty( "IsMoufangLoop", IsLoop );
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DeclareProperty( "IsCLoop", IsLoop );
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DeclareProperty( "IsLeftBolLoop", IsLoop );
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DeclareProperty( "IsRightBolLoop", IsLoop );
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DeclareProperty( "IsLCLoop", IsLoop );
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DeclareProperty( "IsRCLoop", IsLoop );
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DeclareProperty( "IsLeftNuclearSquareLoop", IsLoop );
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DeclareProperty( "IsMiddleNuclearSquareLoop", IsLoop );
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DeclareProperty( "IsRightNuclearSquareLoop", IsLoop );
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DeclareProperty( "IsNuclearSquareLoop", IsLoop );
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DeclareProperty( "IsFlexible", IsQuasigroup );
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DeclareProperty( "IsLeftAlternative", IsQuasigroup );
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DeclareProperty( "IsRightAlternative", IsQuasigroup );
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DeclareProperty( "IsAlternative", IsQuasigroup );
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#############################################################################
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## POWER ALTERNATIVE LOOPS
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## -------------------------------------------------------------------------
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DeclareProperty( "IsLeftPowerAlternative", IsLoop );
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DeclareProperty( "IsRightPowerAlternative", IsLoop );
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DeclareProperty( "IsPowerAlternative", IsLoop );
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#############################################################################
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## CC-LOOPS AND RELATED PROPERTIES
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## -------------------------------------------------------------------------
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DeclareProperty( "IsLCCLoop", IsLoop );
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DeclareSynonymAttr( "IsLeftConjugacyClosedLoop", IsLCCLoop );
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DeclareProperty( "IsRCCLoop", IsLoop );
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DeclareSynonymAttr( "IsRightConjugacyClosedLoop", IsRCCLoop );
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DeclareProperty( "IsCCLoop", IsLoop );
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DeclareSynonymAttr( "IsConjugacyClosedLoop", IsCCLoop );
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DeclareProperty( "IsOsbornLoop", IsLoop );
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############################################################################
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## ADDITIONAL VARIETIES OF LOOPS
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## -------------------------------------------------------------------------
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DeclareProperty( "IsCodeLoop", IsLoop );
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DeclareProperty( "IsSteinerLoop", IsLoop );
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DeclareProperty( "IsLeftBruckLoop", IsLoop );
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DeclareSynonymAttr( "IsLeftKLoop", IsLeftBruckLoop );
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DeclareProperty( "IsRightBruckLoop", IsLoop );
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DeclareSynonymAttr( "IsRightKLoop", IsRightBruckLoop );
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DeclareProperty( "IsALoop", IsLoop );
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DeclareSynonymAttr( "IsAutomorphicLoop", IsALoop );
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DeclareProperty( "IsLeftALoop", IsLoop );
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DeclareSynonymAttr( "IsLeftAutomorphicLoop", IsLeftALoop );
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DeclareProperty( "IsMiddleALoop", IsLoop );
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DeclareSynonymAttr( "IsMiddleAutomorphicLoop", IsMiddleALoop );
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DeclareProperty( "IsRightALoop", IsLoop );
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DeclareSynonymAttr( "IsRightAutomorphicLoop", IsRightALoop );
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