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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 operations for polycyclic generating systems modulo
## another such system.
##
#############################################################################
##
#O ModuloPcgsByPcSequenceNC( <home>, <pcs>, <modulo> )
##
## <ManSection>
## <Oper Name="ModuloPcgsByPcSequenceNC" Arg='home, pcs, modulo'/>
##
## <Description>
## </Description>
## </ManSection>
##
DeclareOperation(
"ModuloPcgsByPcSequenceNC",
[ IsPcgs, IsList, IsPcgs ] );
#############################################################################
##
#O ModuloPcgsByPcSequence( <home>, <pcs>, <modulo> )
##
## <ManSection>
## <Oper Name="ModuloPcgsByPcSequence" Arg='home, pcs, modulo'/>
##
## <Description>
## </Description>
## </ManSection>
##
DeclareOperation(
"ModuloPcgsByPcSequence",
[ IsPcgs, IsList, IsPcgs ] );
#############################################################################
##
#O ModuloTailPcgsByList( <home>, <list>, <taildepths> )
##
## <ManSection>
## <Oper Name="ModuloTailPcgsByList" Arg='home, list, taildepths'/>
##
## <Description>
## constructs a modulo pcgs whose elements are <A>list</A> and whose denominator
## is the subset of <A>home</A> given by the indices in <A>taildepths</A>. <A>list</A>
## must be a list of elements of different depths so that the exponents for
## this modulo pcgs are just the exponents in home at the indices given by
## the entries in <A>list</A>. (So in particular, <A>list</A> must be a subset of
## <A>home</A> modulo the tail.) No check is performed whether the input is
## valid.
## </Description>
## </ManSection>
##
DeclareGlobalFunction( "ModuloTailPcgsByList" );
#############################################################################
##
#O ModuloPcgs( <G>, <N> )
##
## <#GAPDoc Label="ModuloPcgs">
## <ManSection>
## <Oper Name="ModuloPcgs" Arg='G, N'/>
##
## <Description>
## returns a modulo pcgs for the factor <M><A>G</A>/<A>N</A></M> which must
## be solvable, while <A>N</A> may be non-solvable.
## <Ref Oper="ModuloPcgs"/> will return <E>a</E> pcgs for the factor,
## there is no guarantee that it will be <Q>compatible</Q> with any other
## pcgs.
## If this is required, the <K>mod</K> operator must be used on
## induced pcgs, see <Ref Meth="\mod" Label="for two pcgs"/>.
## </Description>
## </ManSection>
## <#/GAPDoc>
##
DeclareOperation( "ModuloPcgs", [ IsGroup, IsGroup ] );
#############################################################################
##
#A DenominatorOfModuloPcgs( <pcgs> )
##
## <#GAPDoc Label="DenominatorOfModuloPcgs">
## <ManSection>
## <Attr Name="DenominatorOfModuloPcgs" Arg='pcgs'/>
##
## <Description>
## returns a generating set for the denominator of the modulo pcgs
## <A>pcgs</A>.
##
## <Example><![CDATA[
## gap> G := Group( (1,2,3,4,5),(1,2) );
## Group([ (1,2,3,4,5), (1,2) ])
## gap> P := ModuloPcgs(G, DerivedSubgroup(G) );
## Pcgs([ (4,5) ])
## gap> NumeratorOfModuloPcgs(P);
## [ (1,2,3,4,5), (1,2) ]
## gap> DenominatorOfModuloPcgs(P);
## [ (1,3,2), (1,4,3), (2,5,4) ]
## gap> RelativeOrders(P);
## [ 2 ]
## gap> ExponentsOfPcElement( P, (1,2,3,4,5) );
## [ 0 ]
## gap> ExponentsOfPcElement( P, (4,5) );
## [ 1 ]
## ]]></Example>
## </Description>
## </ManSection>
## <#/GAPDoc>
##
DeclareAttribute( "DenominatorOfModuloPcgs", IsModuloPcgs );
#############################################################################
##
#A NumeratorOfModuloPcgs( <pcgs> )
##
## <#GAPDoc Label="NumeratorOfModuloPcgs">
## <ManSection>
## <Attr Name="NumeratorOfModuloPcgs" Arg='pcgs'/>
##
## <Description>
## returns a generating set for the numerator of the modulo pcgs
## <A>pcgs</A>.
## </Description>
## </ManSection>
## <#/GAPDoc>
##
DeclareAttribute( "NumeratorOfModuloPcgs", IsModuloPcgs );
#############################################################################
##
#P IsNumeratorParentPcgsFamilyPcgs( <mpcgs> )
##
## <ManSection>
## <Prop Name="IsNumeratorParentPcgsFamilyPcgs" Arg='mpcgs'/>
##
## <Description>
## This property indicates that the numerator of the modulo pcgs
## <A>mpcgs</A> is induced with respect to a family pcgs.
## </Description>
## </ManSection>
##
DeclareProperty( "IsNumeratorParentPcgsFamilyPcgs", IsModuloPcgs );
#############################################################################
##
#O ExponentsConjugateLayer( <mpcgs>, <elm>, <e> )
##
## <#GAPDoc Label="ExponentsConjugateLayer">
## <ManSection>
## <Oper Name="ExponentsConjugateLayer" Arg='mpcgs, elm, e'/>
##
## <Description>
## Computes the exponents of <A>elm</A><C>^</C><A>e</A> with respect to
## <A>mpcgs</A>; <A>elm</A> must be in the span of <A>mpcgs</A>,
## <A>e</A> a pc element in the span of the
## parent pcgs of <A>mpcgs</A> and <A>mpcgs</A> must be the modulo pcgs for
## an abelian layer. (This is the usual case when acting on a chief
## factor). In this case if <A>mpcgs</A> is induced by the family pcgs (see
## section <Ref Sect="Subgroups of Polycyclic Groups - Induced Pcgs"/>),
## the exponents can be computed directly by looking up exponents without
## having to compute in the group and having to collect a potential tail.
## </Description>
## </ManSection>
## <#/GAPDoc>
##
DeclareOperation( "ExponentsConjugateLayer",
[IsModuloPcgs,IsMultiplicativeElementWithInverse,
IsMultiplicativeElementWithInverse] );
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