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#############################################################################
##
## This file is part of GAP, a system for computational discrete algebra.
## This file's authors include Frank Celler.
##
## 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 methods for polycyclic generating systems dealing
## with or defined by a pc series.
##
#############################################################################
##
#M PcgsByPcSequenceNC( <fam>, <pcs> )
##
#############################################################################
InstallMethod( PcgsByPcSequenceNC, "pc series", true,
[ IsFamily, IsHomogeneousList ], 0,
function( efam, pcs )
local pcgs;
# quick check
if not IsIdenticalObj( efam, ElementsFamily(FamilyObj(pcs)) ) then
Error( "elements family of <pcs> does not match <efam>" );
fi;
# construct a pcgs
pcgs := PcgsByPcSequenceCons(
IsPcgsDefaultRep,
IsPcgs,
efam,
pcs,[] );
# that it
return pcgs;
end );
#############################################################################
InstallMethod( PcgsByPcSequenceNC, "pc series, empty sequence", true,
[ IsFamily, IsList and IsEmpty ], 0,
function( efam, pcs )
local pcgs;
# construct a pcgs
pcgs := PcgsByPcSequenceCons(
IsPcgsDefaultRep, IsPcgs, efam, pcs,[] );
# that it
return pcgs;
end );
#############################################################################
##
#M PcgsByPcSequence( <fam>, <pcs> )
##
#############################################################################
InstallMethod( PcgsByPcSequence,
true,
[ IsFamily,
IsHomogeneousList ],
0,
function( efam, pcs )
#T 96/09/26 fceller do some checks
return PcgsByPcSequenceNC( efam, pcs );
end );
#############################################################################
InstallMethod( PcgsByPcSequence,
true,
[ IsFamily,
IsList and IsEmpty ],
0,
function( efam, pcs )
#T 96/09/26 fceller do some checks
return PcgsByPcSequenceNC( efam, pcs );
end );
#############################################################################
##
#M Pcgs( <grp> ) . . . . . . . . . . . . . . . . . . . . . . pcgs for groups
##
InstallMethod( Pcgs,
"generic method using CompositionSeries",
true,
#T Why was 'IsFinite' required here? This gave this method a higher value it
#T deserved
[ IsGroup],0,
function( grp )
local series, pcgs, orders, i, elm, o;
if HasIsFinite(grp) and not IsFinite(grp) then
Error("requires group to be finite!");
fi;
series := CompositionSeries(grp);
pcgs := [];
orders := [];
for i in [ 1 .. Length(series)-1 ] do
o := Index(series[i],series[i+1]);
if not IsPrime(o) then
Error( "finite group <grp> is not polycyclic" );
fi;
Add( orders, o );
repeat
elm := Random(series[i]);
until not elm in series[i+1];
Add( pcgs, elm );
od;
pcgs := PcgsByPcSequenceNC( FamilyObj(One(grp)), pcgs );
SetPcSeries( pcgs, series );
SetOneOfPcgs( pcgs, One(grp) );
SetRelativeOrders( pcgs, orders );
SetGroupOfPcgs (pcgs, grp);
return pcgs;
end );
#############################################################################
##
#M ExponentsOfPcElement( <pcgs>, <elm> )
##
InstallMethod( ExponentsOfPcElement, "pc series", IsCollsElms,
[ IsPcgs, IsObject ], 0,
function( pcgs, elm )
local series, exps, id, depth, exp,ml;
series := PcSeries(pcgs);
exps := ListWithIdenticalEntries(Length(pcgs),0);
id := OneOfPcgs(pcgs);
depth := 1;
ml:=Length(pcgs)+1;
while elm <> id do
while elm in series[depth] do
depth := depth + 1;
od;
exp := 0;
repeat
exp := exp+1;
if depth<2 or depth>ml then
return fail;
fi;
elm := LeftQuotient( pcgs[depth-1], elm );
until elm in series[depth];
exps[depth-1] := exp;
od;
return exps;
end );
#############################################################################
##
#M RelativeOrders( <pcgs> )
##
InstallMethod( RelativeOrders, "pc series", true, [ IsPcgs ], 0,
function( pcgs )
local ord, pcs, i;
ord := [];
pcs := PcSeries(pcgs);
for i in [ 1 .. Length(pcs)-1 ] do
Add( ord, Size(pcs[i]) / Size(pcs[i+1]) );
od;
return ord;
end );
#############################################################################
##
#M PcSeries( <pcgs> )
##
InstallMethod( PcSeries,"construct subgroups", true, [ IsPcgs ], 0,
function( pcgs )
local grp, series, i,hasro;
# construct the group generated by <pcgs>
#T 1996/10/01 fceller something seems to break for Difference or Set
#T grp := GroupByGenerators( pcgs, One(pcgs) );
#T seems to work now, 1998/12/09 sam
grp := GroupOfPcgs(pcgs);
hasro:=HasRelativeOrders(pcgs);
# construct the series
series := [ grp ];
for i in [ 2 .. Length(pcgs)+1 ] do
if hasro then
# pcgs is all in place -- use induced pcgs for generators to build
# series after pcgs is at work
Add( series, SubgroupByPcgs( grp,
InducedPcgsByPcSequenceNC(pcgs,pcgs{[ i .. Length(pcgs) ]} ) ));
else
# pcgs is being built. Don't induce, but just use subgroup.
Add( series, SubgroupNC( grp, pcgs{[ i .. Length(pcgs) ]} ) );
fi;
od;
return series;
end );
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