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#############################################################################
##
## This file is part of GAP, a system for computational discrete algebra.
## This file's authors include 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 the parts of the Dixon-Schneider specific to pc groups
##
#############################################################################
##
#F PcGroupClassMatrixColumn(<D>,<mat>,<r>,<t>) . calculate the t-th column
#F of the r-th class matrix and store it in the appropriate column of M
##
BindGlobal( "PcGroupClassMatrixColumn", function(D,M,r,t)
local c,s,z,i,T,p,orb,chunk;
if t=1 then
M[D.inversemap[r]][t]:=D.classiz[r];
else
orb:=DxGaloisOrbits(D,r);
z:=D.classreps[t];
c:=orb.orbits[t][1];
if c<>t then
p:=RepresentativeAction(orb.group,c,t);
# was the first column of the galois class active?
if ForAny([1..NrRows(M)],i->M[i,c]>0) then
for i in D.classrange do
M[i^p][t]:=M[i][c];
od;
Info(InfoCharacterTable,2,"Computing column ",t,
" : by GaloisImage");
return;
fi;
fi;
T:=DoubleCentralizerOrbit(D,r,t);
Info(InfoCharacterTable,2,"Computing column ",t," :",
Length(T[1])," instead of ",D.classiz[r]);
for i in [1..Length(T[1])] do
T[1][i]:=T[1][i]*z;
od;
#T[3]:=List(T[1],x->Position(D.ids,D.identification(D,x)));
T[3]:=[];
# identify in blocks of at most 5000
chunk:=5000;
for i in [0..QuoInt(Length(T[1]),chunk)] do
orb:=[chunk*i+1..Minimum(chunk*(i+1),Length(T[1]))];
#z:=ClassesSolvableGroup(D.group,0, rec(candidates:=T[1]{orb}));
z:=MultiClassIdsPc(D.classiddat,T[1]{orb});
z:=List(z,x->Position(D.ids,x));
T[3]{orb}:=z;
od;
for i in [1..Length(T[1])] do
s:=T[3][i];
# if s=fail then
# Error("failure");
# s:=Position(D.ids,D.identification(D,T[1][i]));
# fi;
M[s][t]:=M[s][t]+T[2][i];
od;
fi;
end );
#############################################################################
##
#F IdentificationSolvableGroup(<D>,<el>) . . class invariants for el in G
##
BindGlobal( "IdentificationSolvableGroup", function(D,el)
return MultiClassIdsPc(D.classiddat,[el])[1];
#return ClassesSolvableGroup(D.group,0,rec(candidates:=[el]))[1].representative;
end );
#############################################################################
##
#M DxPreparation(<G>)
##
InstallMethod(DxPreparation,"pc group",true,[IsPcGroup,IsRecord],0,
function(G,D)
local i,dat;
if not IsDxLargeGroup(G) then
TryNextMethod();
fi;
D.ClassElement:=ClassElementLargeGroup;
D.identification:=IdentificationSolvableGroup;
D.rationalidentification:=IdentificationGenericGroup;
D.ClassMatrixColumn:=PcGroupClassMatrixColumn;
dat:=rec(group:=G);
D.classiddat:=dat;
D.ids:=MultiClassIdsPc(dat,D.classreps);
D.rids:=[];
for i in D.classrange do
D.rids[i]:=D.rationalidentification(D,D.classreps[i]);
od;
return D;
end);
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