############################################################################# ## ## 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> ) ## ## `GroupToAdditiveGroupHomomorphismByFunction' returns a ## group-to-additive-group homomorphism <hom> with ## source <S> and range <R>, such that each element <s> of <S> is mapped to ## the element `<fun>( <s> )', where <fun> is a {\GAP} function. ## ## If the argument <invfun> is bound then <hom> is a bijection between <S> ## and <R>, and the preimage of each element <r> of <R> is given by ## `<invfun>( <r> )', where <invfun> is a {\GAP} function. ## ## No test is performed on whether the functions actually give an ## homomorphism between both groups because this would require testing the ## full multiplication table. ## ## `GroupToAdditiveGroupHomomorphismByFunction' creates a mapping which ## `IsSPGeneralMapping'. ##
DeclareGlobalFunction("GroupToAdditiveGroupHomomorphismByFunction");
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