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#############################################################################
##
#W resolutionBieberbach.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
##
#############################################################################
##
#O ResolutionBieberbachGroup(<group>)
##
InstallMethod(ResolutionBieberbachGroup,
[IsGroup],
function(group)
return ResolutionBieberbachGroup(group,0*[1..Size(Representative(group))-1]);
end);
#############################################################################
##
#O ResolutionBieberbachGroup(<group>,<center>)
##
InstallMethod(ResolutionBieberbachGroup,"for affine cryst groups on right",
[IsGroup,IsVector],
function(group,center)
local gram, poly, fl;
gram:=GramianOfAverageScalarProductFromFiniteMatrixGroup(PointGroup(group));
if not Order(gram)=1
then
Info(InfoHAPcryst,2,"non standard");
fi;
poly:=FundamentalDomainBieberbachGroup(center,group,gram);
fl:=FaceLatticeAndBoundaryBieberbachGroup(poly,group);
RemoveFile(FullFilenameOfPolymakeObject(poly));
return ResolutionFromFLandBoundary(fl, group);
end);
#############################################################################
##
#O ResolutionFromFLandBoundary(<fl>,<group>)
##
InstallMethod(ResolutionFromFLandBoundary,"for affine cryst groups on right",
[IsRecord,IsGroup],
function(fl,group)
local dimension, dimension2, boundary, elts, appendToElts,
boundary2, groupring, resolution, homotopy, hasse,
properties;
dimension:=function(k)
if k<0 or k>Size(fl.hasse)-1
then
return 0;
else
return Size(fl.hasse[k+1]);
fi;
end;
dimension2:=function(resolution,k)
if k<0 or k>Size(resolution!.hasse)-1
then
return 0;
else
return Size(resolution!.hasse[k+1]);
fi;
end;
boundary:=function(k,j)
local word, jsign, stdword, pos, coeffsAndGroupElts, g,
sign, mult, entry, i;
if k<=0 or k>=Size(fl.hasse)
then
return [];
else
word:=fl.hasse[k+1][AbsInt(j)][2];
jsign:=SignInt(j);
stdword:=[];
for pos in [1..Size(word)]
do
coeffsAndGroupElts:=CoefficientsAndMagmaElementsAsLists(word[pos][2]);
for g in [1..Size(coeffsAndGroupElts[1])]
do
sign:=jsign*SignInt(coeffsAndGroupElts[1][g]);
mult:=AbsInt(coeffsAndGroupElts[1][g]);
entry:=[sign*word[pos][1],Position(fl.elts,coeffsAndGroupElts[2][g])];
for i in [1..mult]
do
Add(stdword,entry);
od;
od;
od;
fi;
return stdword;
end;
## this is the usual HAP trick.
## After the termination of ResolutionFromFLandBoundary, <elts> will not
## be collected by GASMAN because appendToElts still uses it.
## It will just float around as a secret global (to appendToElts)
## variable...
##
## same with <group>.
##
elts:=StructuralCopy(fl.elts);
appendToElts:=function(g)
if not g in group
then
Error("not an element of the right group");
fi;
Add(elts,g);
end;
##################################################
##################################################
boundary2:=function(resolution,k,j)
local zero, family, vector, term;
if k<=0 or k>=Size(resolution!.hasse)
then
return [];
else
zero:=Zero(resolution!.groupring);
family:=FamilyObj(zero);
vector:=List([1..Dimension(resolution)(k-1)],i->zero);
for term in resolution!.hasse[k+1][j][2]
do
vector[term[1]]:=vector[term[1]]+
term[2];
od;
fi;
return vector;
end;
if not (IsAffineCrystGroupOnRight(group) and IsStandardSpaceGroup(group))
then
Error("group is not a StandardSpaceGroup acting on right");
fi;
if not ForAll(fl.elts,i->i in group)
then
Error("group does not match face lattice");
fi;
groupring:=fl.groupring;
resolution:=Objectify(HapLargeGroupResolution,
rec(
groupring:=groupring,
dimension:=dimension,
dimension2:=dimension2,
boundary:=boundary,
boundary2:=boundary2,
homotopy:=fail,
elts:=elts,
appendToElts:=appendToElts,
group:=group,
hasse:=fl.hasse,
properties:=
[["length",Size(fl.hasse)],
["type","resolution"],
["characteristic",0]
]
));
return resolution;
end);
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