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#############################################################################
##
## This file is part of GAP, a system for computational discrete algebra.
## This file's authors include Bettina Eick.
##
## 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
##
DeclareInfoClass( "InfoRandIso" );
DeclareAttribute( "OmegaAndLowerPCentralSeries", IsGroup );
#############################################################################
##
#F CodePcgs( <pcgs> )
##
## <#GAPDoc Label="CodePcgs">
## <ManSection>
## <Func Name="CodePcgs" Arg='pcgs'/>
##
## <Description>
## returns the code corresponding to <A>pcgs</A>.
## <Example><![CDATA[
## gap> G := CyclicGroup(512);;
## gap> p := Pcgs( G );;
## gap> CodePcgs( p );
## 162895587718739690298008513020159
## ]]></Example>
## </Description>
## </ManSection>
## <#/GAPDoc>
##
DeclareGlobalFunction( "CodePcgs" );
#############################################################################
##
#F CodePcGroup( <G> )
##
## <#GAPDoc Label="CodePcGroup">
## <ManSection>
## <Func Name="CodePcGroup" Arg='G'/>
##
## <Description>
## returns the code for a pcgs of <A>G</A>.
## <Example><![CDATA[
## gap> G := DihedralGroup(512);;
## gap> CodePcGroup( G );
## 2940208627577393070560341803949986912431725641726
## ]]></Example>
## </Description>
## </ManSection>
## <#/GAPDoc>
##
DeclareGlobalFunction( "CodePcGroup" );
#############################################################################
##
#F PcGroupCode( <code>, <size> )
##
## <#GAPDoc Label="PcGroupCode">
## <ManSection>
## <Func Name="PcGroupCode" Arg='code, size'/>
##
## <Description>
## returns a pc group of size <A>size</A> corresponding to <A>code</A>.
## The argument <A>code</A> must be a valid code for a pcgs,
## otherwise anything may happen.
## Valid codes are usually obtained by one of the functions
## <Ref Func="CodePcgs"/> or <Ref Func="CodePcGroup"/>.
## <Example><![CDATA[
## gap> G := SmallGroup( 24, 12 );;
## gap> p := Pcgs( G );;
## gap> code := CodePcgs( p );
## 5790338948
## gap> H := PcGroupCode( code, 24 );
## <pc group of size 24 with 4 generators>
## gap> map := GroupHomomorphismByImages( G, H, p, FamilyPcgs(H) );
## Pcgs([ f1, f2, f3, f4 ]) -> Pcgs([ f1, f2, f3, f4 ])
## gap> IsBijective(map);
## true
## ]]></Example>
## </Description>
## </ManSection>
## <#/GAPDoc>
##
DeclareGlobalFunction( "PcGroupCode" );
#############################################################################
##
#F PcGroupCodeRec( <rec> )
##
## <ManSection>
## <Func Name="PcGroupCodeRec" Arg='record'/>
##
## <Description>
## Here <A>record</A> needs to have entries .code and .order.
## Then <Ref Func="PcGroupCode"/> returns a pc group of size .order
## corresponding to .code.
## <Example><![CDATA[
## gap> G := SmallGroup( 24, 12 );;
## gap> p := Pcgs( G );;
## gap> coderec:=rec( code:=CodePcgs(p), order:=Size(G) );
## rec( code := 5790338948, order := 24 )
## gap> H := PcGroupCodeRec( coderec );
## <pc group of size 24 with 4 generators>
## gap> map := GroupHomomorphismByImages( G, H, p, FamilyPcgs(H) );
## Pcgs([ f1, f2, f3, f4 ]) -> Pcgs([ f1, f2, f3, f4 ])
## gap> IsBijective(map);
## true
## ]]></Example>
## </Description>
## </ManSection>
##
DeclareGlobalFunction( "PcGroupCodeRec" );
#############################################################################
##
#F RandomSpecialPcgsCoded( <G> )
##
## <ManSection>
## <Func Name="RandomSpecialPcgsCoded" Arg='G'/>
##
## <Description>
## returns a code for a random special pcgs of <A>G</A>.
## </Description>
## </ManSection>
##
DeclareGlobalFunction( "RandomSpecialPcgsCoded" );
#############################################################################
##
#F RandomIsomorphismTest( <list>, <n> )
##
## <#GAPDoc Label="RandomIsomorphismTest">
## <ManSection>
## <Func Name="RandomIsomorphismTest" Arg='coderecs, n'/>
##
## <Description>
## The first argument is a list <A>coderecs</A> containing records describing
## groups, and the second argument is a non-negative integer <A>n</A>.
## <P/>
## The test returns a sublist of <A>coderecs</A> where isomorphic copies
## detected by the probabilistic test have been removed.
## <P/>
## The list <A>coderecs</A> should contain records with two components,
## <C>code</C> and <C>order</C>, describing a group via
## <C>PcGroupCode( code, order )</C> (see <Ref Func="PcGroupCode"/>).
## <P/>
## The integer <A>n</A> gives a certain amount of control over the
## probability to detect all isomorphisms. If it is <M>0</M>, then nothing
## will be done at all. The larger <A>n</A> is, the larger is the probability
## of finding all isomorphisms. However, due to the underlying method we
## cannot guarantee that the algorithm finds all isomorphisms, no matter how
## large <A>n</A> is.
## </Description>
## </ManSection>
## <#/GAPDoc>
##
DeclareGlobalFunction( "RandomIsomorphismTest" );
#############################################################################
##
#F ReducedByIsomorphism( <list>, <n> )
##
## <ManSection>
## <Func Name="ReducedByIsomorphism" Arg='list, n'/>
##
## <Description>
## returns a list of disjoint sublist of <A>list</A> such that no two isomorphic
## groups can be in the same sublist.
## </Description>
## </ManSection>
##
DeclareGlobalFunction( "ReducedByIsomorphisms" );
|
