loops/gap/elements.gd

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2017-10-16 19:43:09 +00:00
#############################################################################
##
#W elements.gd Elements and basic arithmetic operations [loops]
##
#H @(#)$Id: quasigroups.gd, v 2.0.0 2008/01/21 gap Exp $
##
#Y Copyright (C) 2004, G. P. Nagy (University of Szeged, Hungary),
#Y P. Vojtechovsky (University of Denver, USA)
##
#############################################################################
## DIVISION
## -------------------------------------------------------------------------
DeclareOperation( "LeftDivision",
[ IsQuasigroupElement, IsQuasigroupElement ] );
DeclareOperation( "RightDivision",
[ IsQuasigroupElement, IsQuasigroupElement ] );
DeclareOperation( "LeftDivisionCayleyTable", [ IsQuasigroup ] );
DeclareOperation( "RightDivisionCayleyTable", [ IsQuasigroup ] );
#############################################################################
## POWERS AND INVERSES
## -------------------------------------------------------------------------
DeclareAttribute( "One", IsLoopElement );
DeclareAttribute( "RightInverse", IsLoopElement );
DeclareAttribute( "LeftInverse", IsLoopElement );
#############################################################################
## ASSOCIATORS AND COMMUTATORS
## -------------------------------------------------------------------------
DeclareOperation( "Associator",
[ IsQuasigroupElement, IsQuasigroupElement, IsQuasigroupElement ] );
DeclareOperation( "Commutator",
[ IsQuasigroupElement, IsQuasigroupElement ] );