Quelle  addgphom.gi   Sprache: Shell

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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.
##


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##
#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 );