127 lines
5.5 KiB
GDScript3
127 lines
5.5 KiB
GDScript3
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#############################################################################
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##
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#W core_methods.gd Most common structural methods [loops]
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##
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#H @(#)$Id: core_methods.gd, v 3.3.0 2016/09/21 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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## GENERATORS
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## -------------------------------------------------------------------------
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DeclareSynonymAttr( "GeneratorsOfQuasigroup", GeneratorsOfMagma );
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DeclareSynonymAttr( "GeneratorsOfLoop", GeneratorsOfQuasigroup );
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# attribute GeneratorsSmallest already declared for groups
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# attribite SmallGeneratingSet already declared for groups
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#############################################################################
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## SECTIONS
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## -------------------------------------------------------------------------
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DeclareAttribute( "LeftSection", IsQuasigroup );
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DeclareAttribute( "RightSection", IsQuasigroup );
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DeclareOperation( "LeftTranslation",
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[ IsQuasigroup, IsQuasigroupElement ] );
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DeclareOperation( "RightTranslation",
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[ IsQuasigroup, IsQuasigroupElement ] );
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#############################################################################
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## MULTIPLICATION GROUPS
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## -------------------------------------------------------------------------
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DeclareAttribute( "LeftMultiplicationGroup", IsQuasigroup );
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DeclareAttribute( "RightMultiplicationGroup", IsQuasigroup );
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DeclareAttribute( "MultiplicationGroup", IsQuasigroup );
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DeclareOperation( "RelativeRightMultiplicationGroup",
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[ IsQuasigroup, IsQuasigroup ] );
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DeclareOperation( "RelativeLeftMultiplicationGroup",
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[ IsQuasigroup, IsQuasigroup ] );
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DeclareOperation( "RelativeMultiplicationGroup",
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[ IsQuasigroup, IsQuasigroup ] );
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#############################################################################
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## INNER MAPPING GROUPS
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## -------------------------------------------------------------------------
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DeclareOperation( "LeftInnerMapping", [ IsLoop, IsLoopElement, IsLoopElement ] );
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DeclareOperation( "RightInnerMapping", [ IsLoop, IsLoopElement, IsLoopElement ] );
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DeclareOperation( "MiddleInnerMapping", [ IsLoop, IsLoopElement ] );
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DeclareAttribute( "InnerMappingGroup", IsLoop );
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DeclareAttribute( "LeftInnerMappingGroup", IsLoop );
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DeclareAttribute( "MiddleInnerMappingGroup", IsLoop );
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DeclareAttribute( "RightInnerMappingGroup", IsLoop );
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#############################################################################
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## SUBQUASIGROUPS AND SUBLOOPS
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## -------------------------------------------------------------------------
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DeclareOperation( "PosInParent", [ IsCollection ] );
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# Position already declared in GAP
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DeclareOperation( "SubquasigroupNC", [ IsQuasigroup, IsSet ] );
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DeclareOperation( "Subquasigroup", [ IsQuasigroup, IsList ] );
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DeclareOperation( "Subloop", [ IsLoop, IsList ] );
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DeclareOperation( "IsSubquasigroup", [ IsQuasigroup, IsQuasigroup ] );
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DeclareOperation( "IsSubloop", [ IsLoop, IsLoop ] );
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DeclareOperation( "AllSubquasigroups", [ IsQuasigroup ] );
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DeclareOperation( "AllSubloops", [ IsLoop ] );
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# RightCosets already declared in GAP
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DeclareOperation( "RightTransversal", [ IsLoop, IsLoop ] );
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#############################################################################
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## NUCLEUS, COMMUTANT, CENTER
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## -------------------------------------------------------------------------
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DeclareAttribute( "LeftNucleus", IsQuasigroup );
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DeclareAttribute( "RightNucleus", IsQuasigroup );
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DeclareAttribute( "MiddleNucleus", IsQuasigroup );
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DeclareAttribute( "Nuc", IsQuasigroup );
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DeclareSynonymAttr( "NucleusOfLoop", Nuc );
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DeclareSynonymAttr( "NucleusOfQuasigroup", Nuc );
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DeclareAttribute( "Commutant", IsQuasigroup );
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DeclareAttribute( "Center", IsQuasigroup );
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DeclareAttribute( "AssociatorSubloop", IsLoop );
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#############################################################################
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## EXPONENT
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## -------------------------------------------------------------------------
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DeclareAttribute( "Exponent", IsLoop );
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#############################################################################
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## NORMALITY
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## -------------------------------------------------------------------------
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InParentFOA( "IsNormal", IsLoop, IsLoop, DeclareProperty );
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InParentFOA( "NormalClosure", IsLoop, IsLoop, DeclareAttribute );
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# IsSimple is already declared for groups
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#############################################################################
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## FACTOR LOOP
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## -------------------------------------------------------------------------
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DeclareOperation( "FactorLoop", [ IsLoop, IsLoop ] );
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DeclareOperation( "NaturalHomomorphismByNormalSubloop", [ IsLoop, IsLoop ] );
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#############################################################################
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## NILPOTENCY
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## -------------------------------------------------------------------------
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DeclareAttribute( "NilpotencyClassOfLoop", IsLoop );
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# IsNilpotent is already declared for groups
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DeclareAttribute( "IsStronglyNilpotent", IsLoop );
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# UpperCentralSeries already declared for groups.
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# LowerCentralSeries already declared for groups.
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#############################################################################
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## SOLVABILITY
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## -------------------------------------------------------------------------
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# IsSolvable is already declared for groups
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DeclareAttribute( "DerivedSubloop", IsLoop );
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# DerivedLength already declared for groups
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DeclareAttribute( "FrattiniSubloop", IsLoop );
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# FrattinifactorSize already declared for groups
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