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#############################################################################
##
## This file is part of GAP, a system for computational discrete algebra.
## This file's authors include Scott Murray, Alexander Hulpke.
##
## Copyright of GAP belongs to its developers, whose names are too numerous
## to list here. Please refer to the COPYRIGHT file for details.
##
## SPDX-License-Identifier: GPL-2.0-or-later
##
## This file contains declarations for mappings between groups and additive
## groups.
##
#############################################################################
##
#F GroupToAdditiveGroupHomomorphismByFunction( <S>, <R>, <fun> )
#F GroupToAdditiveGroupHomomorphismByFunction( <S>, <R>, <fun>, <invfun> )
##
InstallGlobalFunction(GroupToAdditiveGroupHomomorphismByFunction,function(arg)
local map;
# no inverse function given
if Length(arg) = 3 then
# make the general mapping
map:= Objectify(
NewType(GeneralMappingsFamily(ElementsFamily(FamilyObj(arg[1])),
ElementsFamily(FamilyObj(arg[2]))),
IsSPMappingByFunctionRep
and IsSingleValued
and IsTotal
and IsGroupToAdditiveGroupHomomorphism ),
rec( fun:= arg[3] ) );
# inverse function given
elif Length(arg) = 4 then
# make the mapping
map:= Objectify(
NewType(GeneralMappingsFamily(ElementsFamily(FamilyObj(arg[1])),
ElementsFamily(FamilyObj(arg[2]))),
IsSPMappingByFunctionWithInverseRep
and IsBijective
and IsGroupToAdditiveGroupHomomorphism ),
rec( fun := arg[3],
invFun := arg[4] ) );
# otherwise signal an error
else
Error(
"usage: GroupToAdditiveGroupHomomorphismByFunction(<D>,<E>,<fun>[, <inv>])");
fi;
SetSource(map,arg[1]);
SetRange(map,arg[2]);
# return the mapping
return map;
end );
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