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#############################################################################
##
#W resolutionAccess_SmallGroupRep.gi HAPcryst package Marc Roeder
##
##
##
##
#Y Copyright (C) 2006 Marc Roeder
#Y
#Y This program is free software; you can redistribute it and/or
#Y modify it under the terms of the GNU General Public License
#Y as published by the Free Software Foundation; either version 2
#Y of the License, or (at your option) any later version.
#Y
#Y This program is distributed in the hope that it will be useful,
#Y but WITHOUT ANY WARRANTY; without even the implied warranty of
#Y MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
#Y GNU General Public License for more details.
#Y
#Y You should have received a copy of the GNU General Public License
#Y along with this program; if not, write to the Free Software
#Y Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301, USA
##
#############################################################################
##
## This file implements a representation for HapResolutions of small groups.
##
## The additional feature of this representation is the multiplication
## via a multiplication table.
## Also, the list of group elements R!.elts is a set. So we can do binary
## search occasionally.
##
## Elements of the modules in these resolutions are still pairs of integers.
##
##
#############################################################################
##
#O PositionInGroupOfResolutionNC(<resolution>,<g>)
#O PositionInGroupOfResolution(<resolution>,<g>)
##
## find the position in <resolution>'s partial list of group elements
## <resolution!.elts>. If <g> is not contained in <resolution!.elts>, it is
## added and the length of <resolution!.elts> is returned.
##
## The SmallGroupRep is consistent. So we just catch.
##
InstallMethod(PositionInGroupOfResolutionNC, "For HapResolutions of small groups",
[IsHapSmallGroupResolutionRep,IsObject],
function(resolution,g)
local pos;
return PositionSet(resolution!.elts,g);
end);
InstallMethod(PositionInGroupOfResolution, "For HapResolutions of small groups",
[IsHapSmallGroupResolutionRep,IsObject],
function(resolution,g)
local pos;
if not g in GroupOfResolution(resolution)
then
Error("<g> is not in <resolution>'s group");
fi;
return PositionInGroupOfResolutionNC(resolution,g);
end);
#############################################################################
##
#O MultiplyGroupEltsNC(<resolution>,<x>,<y>)
##
## catch the call and delegate to special method. No conversion needed.
##
InstallMethod(MultiplyGroupEltsNC,"for HapResolutions of small groups",
[IsHapSmallGroupResolutionRep,IsPosInt,IsPosInt],
function(resolution,x,y)
return resolution!.multtable[x][y];
end);
#############################################################################
#############################################################################
##
## NO "!"s allowed beyond this point
##
#############################################################################
#############################################################################
#############################################################################
##
#O MultiplyFreeZGLetterWithGroupEltNC(<resolution>,<letter>,<g>)
##
## given a pair <letter> of positive integers which represent a generator-
## group element pair, this returns the letter multiplied with the group
## element <g>.
##
##
InstallMethod(MultiplyFreeZGLetterWithGroupEltNC,"For HapResolutions of small groups",
[IsHapSmallGroupResolutionRep,IsDenseList,IsPosInt],
function(resolution,letter,g)
local newgroupel;
newgroupel:=MultiplyGroupEltsNC(resolution,letter[2],g);
return [letter[1],PositionInGroupOfResolution(resolution,newgroupel)];
end);
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