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############################################################################
##
#W extqs.gi LPRES René Hartung
##
############################################################################
##
#M ExtendQuotientSystem ( <quo> )
##
## Extends the quotient system for G/gamma_i(G) to a consistent quotient
## system for G/gamma_{i+1}(G).
##
InstallMethod( ExtendQuotientSystem,
"using a single-core machine", true,
[ IsObject ], 0,
function(Q)
local c, # nilpotency class
weights, # weight of the generators
Defs, # definitions of each (pseudo) generator and tail
Imgs, # images of the generators of the LpGroup
ftl, # collector of the covering group
b, # number of "old" generators + 1
HNF, # Hermite normal form of the consistency rels/relators
A, # record: endos as matrices and (it.) rels as exp.vecs
i, # loop variable
stack, # stack for the spinning algorithm
ev,evn, # exponent vectors for the spinning algorithm
QS, # (confluent) quotient system for G/\gamma_i+1(G)
time;
# nilpotency class
c:=Maximum(Q.Weights);
# weights of the (old) generators
weights:=ShallowCopy(Q.Weights);
# old definitions and images
Defs:=ShallowCopy(Q.Definitions);
Imgs:=ShallowCopy(Q.Imgs);
# build a (possibly inconsistent) nilpotent presentation for the
# covering group of Q
ftl:=LPRES_QSystemOfCoveringGroupByQSystem(Q.Pccol,weights,Defs,Imgs);
# complete the nilpotent presentation using the tails routine
UpdateNilpotentCollector(ftl,weights,Defs);
# position of the first new (pseudo) generator/tail
b:=Position(weights,Maximum(weights));
# consistency relations (words in T)
HNF := LPRES_CheckConsistencyRelations(ftl,weights);
for i in [1..Length(HNF.mat)] do
if not IsZero(HNF.mat[i]{[1..b-1]}) then
Error("in ExtendQuotientSystem: wrong HNF from consistency check");
fi;
# forget the first b-1 (zero) entries
HNF.mat[i]:=HNF.mat[i]{[b..Length(weights)]};
HNF.Heads[i]:=HNF.Heads[i]-b+1;
od;
# build the endomorphisms
A:=LPRES_EndomorphismsOfCover( Q.Lpres, ftl, Imgs, Defs, weights );
# if the endomorphisms do not induces endomorphisms of the multiplier
if A = fail then
return(fail);
fi;
time:=Runtime();
# spinning algorithm
stack:=A.IteratedRelations;
for i in [1..Length(stack)] do
LPRES_AddRow(HNF,stack[i]);
od;
while not Length(stack)=0 do
Info(InfoLPRES,3,"Spinning stack has size ",Length(stack));
ev:=stack[1];
Remove( stack, 1 );
if not IsZero(ev) then
for i in [1..Length(A.Endomorphisms)] do
evn:=ev*A.Endomorphisms[i];
if LPRES_AddRow(HNF,evn) then
Add(stack,evn);
fi;
od;
fi;
od;
# add the non-iterated relations
for i in [1..Length(A.Relations)] do
LPRES_AddRow(HNF,A.Relations[i]);
od;
Info(InfoLPRES,2,"Time spent for spinning algorithm: ",
StringTime(Runtime()-time));
if Length(HNF.mat)=0 then
# the presentation ftl satisfy the relations and is consistent
QS:=rec();
QS.Lpres:=Q.Lpres;
QS.Weights:=weights;
QS.Definitions:=Defs;
QS.Pccol:=ftl;
QS.Imgs:=ShallowCopy(Imgs);
Imgs:=[];
for i in [1..Length(QS.Imgs)] do
if IsInt(QS.Imgs[i]) then
Add(Imgs,PcpElementByGenExpList(QS.Pccol,[QS.Imgs[i],1]));
else
Add(Imgs,PcpElementByGenExpList(QS.Pccol,QS.Imgs[i]));
fi;
od;
QS.Epimorphism:=GroupHomomorphismByImagesNC(Q.Lpres,
PcpGroupByCollectorNC(QS.Pccol),
GeneratorsOfGroup(Q.Lpres),Imgs);
return(QS);
else
# use the Hermite normal form to compute a consistent presentation
# that satisfy the relations
return(LPRES_BuildNewCollector(Q,ftl,HNF,weights,Defs,Imgs));
fi;
end);
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