#############################################################################
##
## This file is part of recog, a package for the GAP computer algebra system
## which provides a collection of methods for the constructive recognition
## of groups.
##
## This files's authors include Max Neunhöffer, Ákos Seress, Max Horn.
##
## Copyright of recog belongs to its developers whose names are too numerous
## to list here. Please refer to the COPYRIGHT file for details.
##
## SPDX-License-Identifier: GPL-3.0-or-later
##
#############################################################################
#! @BeginCode SLPforElementFuncsGeneric.TrivialGroup
SLPforElementFuncsGeneric.TrivialGroup := function(ri,g)
if not ri!.isone(g) then
return fail;
fi;
return StraightLineProgramNC( [ [1,0] ], 1 );
end;
#! @EndCode
#! @BeginChunk TrivialGroup
#! This method is successful if and only if all generators of a group
#! <A>G</A> are equal to the identity. Otherwise, it returns
#! <K>NeverApplicable</K> indicating that it will never succeed. This method
#! is only installed to handle the trivial case such that we do not have to
#! take this case into account in the other methods.
#! @EndChunk
#! @BeginCode FindHomMethodsGeneric.TrivialGroup
BindRecogMethod(FindHomMethodsGeneric, "TrivialGroup",
"go through generators and compare to the identity",
function(ri, G)
local gens;
# get the generators of the group
gens := GeneratorsOfGroup(G);
# check whether all generators are trivial
# ri!.isone is explained below
if not ForAll(gens, ri!.isone) then
# NeverApplicable because it makes
# no sense to call this method again
return NeverApplicable;
fi;
# The group is trivial! Provide required information:
# size of the group
SetSize(ri, 1);
# explained below
Setslpforelement(ri, SLPforElementFuncsGeneric.TrivialGroup);
# SLP from given generators to nice generators
Setslptonice(ri, StraightLineProgramNC([[[1,0]]],
Length(gens)));
# We have reached a leaf node.
SetFilterObj(ri, IsLeaf);
return Success;
end);
#! @EndCode
