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#############################################################################
##
#W iso.gd Isomorphisms and isotopisms [loops]
##
##
#Y Copyright (C) 2004, G. P. Nagy (University of Szeged, Hungary),
#Y P. Vojtechovsky (University of Denver, USA)
##
#############################################################################
## DISCRIMINATOR
## -------------------------------------------------------------------------
DeclareOperation( "Discriminator", [ IsQuasigroup ] );
DeclareOperation( "AreEqualDiscriminators", [ IsList, IsList ] );
#############################################################################
## ISOMORPHISMS OF QUASIGROUPS AND LOOPS
## -------------------------------------------------------------------------
DeclareOperation( "IsomorphismQuasigroups", [ IsQuasigroup, IsQuasigroup ] );
DeclareOperation( "IsomorphismLoops", [ IsLoop, IsLoop ] );
DeclareOperation( "QuasigroupsUpToIsomorphism", [ IsList ] );
DeclareOperation( "LoopsUpToIsomorphism", [ IsList ] );
DeclareOperation( "QuasigroupIsomorph", [ IsQuasigroup, IsPerm ] );
DeclareOperation( "LoopIsomorph", [ IsLoop, IsPerm ] );
DeclareOperation( "IsomorphicCopyByPerm", [ IsQuasigroup, IsPerm ] );
DeclareOperation( "IsomorphicCopyByNormalSubloop", [ IsLoop, IsLoop ] );
#############################################################################
## AUTOMORPHISMS AND AUTOMORPHISM GROUPS
## -------------------------------------------------------------------------
# AutomorphismGroup already declared for groups
#############################################################################
## ISOTOPISM OF LOOPS
## ------------------------------------------------------------------------
DeclareOperation( "IsotopismLoops", [ IsLoop, IsLoop ] );
DeclareOperation( "LoopsUpToIsotopism", [ IsList ] );
#############################################################################
## AUXILIARY
## -------------------------------------------------------------------------
DeclareGlobalFunction( "IsomorphismQuasigroupsNC" );
DeclareGlobalFunction( "LOOPS_EfficientGenerators" );
DeclareGlobalFunction( "LOOPS_ExtendHomomorphismByClosingSource" );
DeclareGlobalFunction( "LOOPS_ExtendIsomorphism" );
DeclareGlobalFunction( "LOOPS_SublistPosition" );
DeclareGlobalFunction( "LOOPS_AutomorphismsFixingSet" );
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