|
#############################################################################
##
## 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 groups defined by a polycyclic
## collector.
##
#############################################################################
##
#C IsElementFinitePolycyclicGroup
#C IsElementFinitePolycyclicGroupCollection
##
## <ManSection>
## <Filt Name="IsElementFinitePolycyclicGroup" Arg='obj' Type='Category'/>
## <Filt Name="IsElementFinitePolycyclicGroupCollection" Arg='obj' Type='Category'/>
##
## <Description>
## This category is set if the group defining a family of polycyclic
## elements is finite. It is used to impliy finiteness for groups generated
## by elements in this family.
## </Description>
## </ManSection>
##
DeclareCategory( "IsElementFinitePolycyclicGroup",
IsMultiplicativeElementWithInverse and IsAssociativeElement );
DeclareCategoryCollections( "IsElementFinitePolycyclicGroup");
InstallTrueMethod(IsSubsetLocallyFiniteGroup,
IsElementFinitePolycyclicGroupCollection);
#############################################################################
##
#C IsMultiplicativeElementWithInverseByPolycyclicCollector
##
## <ManSection>
## <Filt Name="IsMultiplicativeElementWithInverseByPolycyclicCollector" Arg='obj' Type='Category'/>
##
## <Description>
## </Description>
## </ManSection>
##
DeclareCategory(
"IsMultiplicativeElementWithInverseByPolycyclicCollector",
IsMultiplicativeElementWithInverseByRws and IsAssociativeElement );
DeclareCategoryCollections(
"IsMultiplicativeElementWithInverseByPolycyclicCollector" );
#############################################################################
##
#C IsPcGroup( <G> )
##
## <#GAPDoc Label="IsPcGroup">
## <ManSection>
## <Filt Name="IsPcGroup" Arg='G' Type='Category'/>
##
## <Description>
## tests whether <A>G</A> is a pc group.
## <Example><![CDATA[
## gap> G := SmallGroup( 24, 12 );
## <pc group of size 24 with 4 generators>
## gap> IsPcGroup( G );
## true
## gap> IsFpGroup( G );
## false
## ]]></Example>
## </Description>
## </ManSection>
## <#/GAPDoc>
##
DeclareSynonym( "IsPcGroup",
IsMultiplicativeElementWithInverseByPolycyclicCollectorCollection
and IsGroup );
#############################################################################
##
#A DefiningPcgs( <obj> )
##
## <ManSection>
## <Attr Name="DefiningPcgs" Arg='obj'/>
##
## <Description>
## </Description>
## </ManSection>
##
DeclareAttribute(
"DefiningPcgs",
IsObject );
#############################################################################
##
#F IsKernelPcWord(obj)
##
## <ManSection>
## <Func Name="IsKernelPcWord" Arg='obj'/>
##
## <Description>
## This filter is implied by the kernel pc words. It is used solely to
## increase the rank of the pc words representation (NewRepresenattion does
## not admit a rank other than 1).
## </Description>
## </ManSection>
##
DeclareFilter("IsKernelPcWord",100);
#############################################################################
##
#C IsElementsFamilyBy8BitsSingleCollector
##
## <ManSection>
## <Filt Name="IsElementsFamilyBy8BitsSingleCollector" Arg='obj' Type='Category'/>
##
## <Description>
## </Description>
## </ManSection>
##
DeclareCategory(
"IsElementsFamilyBy8BitsSingleCollector",
IsElementsFamilyByRws );
#############################################################################
##
#C IsElementsFamilyBy16BitsSingleCollector
##
## <ManSection>
## <Filt Name="IsElementsFamilyBy16BitsSingleCollector" Arg='obj' Type='Category'/>
##
## <Description>
## </Description>
## </ManSection>
##
DeclareCategory(
"IsElementsFamilyBy16BitsSingleCollector",
IsElementsFamilyByRws );
#############################################################################
##
#C IsElementsFamilyBy32BitsSingleCollector
##
## <ManSection>
## <Filt Name="IsElementsFamilyBy32BitsSingleCollector" Arg='obj' Type='Category'/>
##
## <Description>
## </Description>
## </ManSection>
##
DeclareCategory(
"IsElementsFamilyBy32BitsSingleCollector",
IsElementsFamilyByRws );
#############################################################################
##
#O PolycyclicFactorGroup( <fgrp>, <rels> )
#O PolycyclicFactorGroupNC( <fgrp>, <rels> )
##
## <ManSection>
## <Oper Name="PolycyclicFactorGroup" Arg='fgrp, rels'/>
## <Oper Name="PolycyclicFactorGroupNC" Arg='fgrp, rels'/>
##
## <Description>
## </Description>
## </ManSection>
##
DeclareOperation(
"PolycyclicFactorGroup",
[ IsObject, IsList ] );
DeclareOperation(
"PolycyclicFactorGroupNC",
[ IsObject, IsList ] );
#############################################################################
##
#O PolycyclicFactorGroupByRelators( <fam>, <gens>, <rels> )
##
## <ManSection>
## <Oper Name="PolycyclicFactorGroupByRelators" Arg='fam, gens, rels'/>
##
## <Description>
## </Description>
## </ManSection>
##
DeclareGlobalFunction( "SingleCollectorByRelators" );
DeclareOperation(
"PolycyclicFactorGroupByRelatorsNC",
[ IsFamily, IsList, IsList ] );
DeclareOperation(
"PolycyclicFactorGroupByRelators",
[ IsFamily, IsList, IsList ] );
[ Dauer der Verarbeitung: 0.5 Sekunden
(vorverarbeitet)
]
|
