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GAP 4.8.9 installation with standard packages -- copy to your CoCalc project to get it

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                                     ANUPQ 

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                                 ANU p-Quotient 

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                                      3.2

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                                29 November 2017

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                                  Greg Gamble

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                                 Werner Nickel

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                                 Eamonn O'Brien

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                                    Max Horn

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  Greg Gamble

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      Email:    mailto:[email protected]

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      Homepage: http://school.maths.uwa.edu.au/~gregg

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      Address:  Greg Gamble

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                Department of Mathematics and Statistics

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                Curtin University

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                GPO Box U 1987

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                Perth WA 6845

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                Australia

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  Werner Nickel

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      Homepage: http://www.mathematik.tu-darmstadt.de/~nickel/

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  Eamonn O'Brien

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      Email:    mailto:[email protected]

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      Homepage: http://www.math.auckland.ac.nz/~obrien

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      Address:  Department of Mathematics

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                University of Auckland

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                Private Bag 92019

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                Auckland

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                New Zealand

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  Max Horn

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      Email:    mailto:[email protected]

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      Homepage: http://www.quendi.de/math

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      Address:  AG Algebra

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                Mathematisches Institut

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                Justus-Liebig-Universität Gießen

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                Arndtstraße 2

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                35392 Gießen

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                Germany

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  -------------------------------------------------------

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  Contents (ANUPQ)

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  1 Introduction

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    1.1 Overview

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    1.2 How to read this manual

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    1.3 Authors and Acknowledgements

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  2 Mathematical Background and Terminology

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    2.1 Basic notions

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      2.1-1 pc Presentations and Consistency

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      2.1-2 Exponent-p Central Series and Weighted pc Presentations

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      2.1-3 p-Cover, p-Multiplicator

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      2.1-4 Descendants, Capable, Terminal, Nucleus

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      2.1-5 Laws

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    2.2 The p-quotient Algorithm

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      2.2-1 Finding the p-cover

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      2.2-2 Imposing the Relations of the fp Group

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      2.2-3 Imposing Laws

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    2.3 The p-group generation Algorithm, Standard Presentation, Isomorphism

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    Testing

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  3 Infrastructure

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    3.1 Loading the ANUPQ Package

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    3.2 The ANUPQData Record

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      3.2-1 ANUPQData

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      3.2-2 ANUPQDirectoryTemporary

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    3.3 Setting the Verbosity of ANUPQ via Info and InfoANUPQ

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      3.3-1 InfoANUPQ

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    3.4 Utility Functions

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      3.4-1 PqLeftNormComm

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      3.4-2 PqGAPRelators

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      3.4-3 PqParseWord

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      3.4-4 PqExample

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      3.4-5 AllPqExamples

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      3.4-6 GrepPqExamples

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      3.4-7 ToPQLog

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    3.5 Attributes and a Property for fp and pc p-groups

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      3.5-1 NuclearRank

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    3.6 Hints and Warnings regarding the use of Options

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      3.6-1 ANUPQWarnOfOtherOptions

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  4 Non-interactive ANUPQ functions

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    4.1 Computing p-Quotients

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      4.1-1 Pq

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      4.1-2 PqEpimorphism

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      4.1-3 PqPCover

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    4.2 Computing Standard Presentations

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      4.2-1 PqStandardPresentation

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      4.2-2 EpimorphismPqStandardPresentation

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    4.3 Testing p-Groups for Isomorphism

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      4.3-1 IsPqIsomorphicPGroup

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    4.4 Computing Descendants of a p-Group

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      4.4-1 PqDescendants

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      4.4-2 PqSupplementInnerAutomorphisms

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      4.4-3 PqList

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      4.4-4 SavePqList

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  5 Interactive ANUPQ functions

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    5.1 Starting and Stopping Interactive ANUPQ Processes

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      5.1-1 PqStart

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      5.1-2 PqQuit

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      5.1-3 PqQuitAll

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    5.2 Interactive ANUPQ Process Utility Functions

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      5.2-1 PqProcessIndex

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      5.2-2 PqProcessIndices

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      5.2-3 IsPqProcessAlive

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    5.3 Interactive Versions of Non-interactive ANUPQ Functions

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      5.3-1 Pq

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      5.3-2 PqEpimorphism

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      5.3-3 PqPCover

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      5.3-4 PqStandardPresentation

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      5.3-5 EpimorphismPqStandardPresentation

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      5.3-6 PqDescendants

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      5.3-7 PqSetPQuotientToGroup

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    5.4 Low-level Interactive ANUPQ functions based on menu items of the pq

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    program

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    5.5 General commands

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      5.5-1 PqNrPcGenerators

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      5.5-2 PqFactoredOrder

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      5.5-3 PqOrder

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      5.5-4 PqPClass

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      5.5-5 PqWeight

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      5.5-6 PqCurrentGroup

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      5.5-7 PqDisplayPcPresentation

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      5.5-8 PqSetOutputLevel

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      5.5-9 PqEvaluateIdentities

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    5.6 Commands from the Main p-Quotient menu

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      5.6-1 PqPcPresentation

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      5.6-2 PqSavePcPresentation

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      5.6-3 PqRestorePcPresentation

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      5.6-4 PqNextClass

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      5.6-5 PqComputePCover

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    5.7 Commands from the Advanced p-Quotient menu

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      5.7-1 PqCollect

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      5.7-2 PqSolveEquation

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      5.7-3 PqCommutator

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      5.7-4 PqSetupTablesForNextClass

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      5.7-5 PqTails

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      5.7-6 PqComputeTails

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      5.7-7 PqAddTails

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      5.7-8 PqDoConsistencyChecks

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      5.7-9 PqCollectDefiningRelations

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      5.7-10 PqCollectWordInDefiningGenerators

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      5.7-11 PqCommutatorDefiningGenerators

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      5.7-12 PqDoExponentChecks

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      5.7-13 PqEliminateRedundantGenerators

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      5.7-14 PqRevertToPreviousClass

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      5.7-15 PqSetMaximalOccurrences

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      5.7-16 PqSetMetabelian

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      5.7-17 PqDoConsistencyCheck

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      5.7-18 PqCompact

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      5.7-19 PqEchelonise

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      5.7-20 PqSupplyAutomorphisms

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      5.7-21 PqExtendAutomorphisms

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      5.7-22 PqApplyAutomorphisms

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      5.7-23 PqDisplayStructure

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      5.7-24 PqDisplayAutomorphisms

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      5.7-25 PqWritePcPresentation

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    5.8 Commands from the Standard Presentation menu

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      5.8-1 PqSPComputePcpAndPCover

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      5.8-2 PqSPStandardPresentation

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      5.8-3 PqSPSavePresentation

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      5.8-4 PqSPCompareTwoFilePresentations

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      5.8-5 PqSPIsomorphism

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    5.9 Commands from the Main p-Group Generation menu

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      5.9-1 PqPGSupplyAutomorphisms

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      5.9-2 PqPGExtendAutomorphisms

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      5.9-3 PqPGConstructDescendants

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      5.9-4 PqPGSetDescendantToPcp

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    5.10 Commands from the Advanced p-Group Generation menu

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      5.10-1 PqAPGDegree

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      5.10-2 PqAPGPermutations

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      5.10-3 PqAPGOrbits

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      5.10-4 PqAPGOrbitRepresentatives

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      5.10-5 PqAPGSingleStage

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    5.11 Primitive Interactive ANUPQ Process Read/Write Functions

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      5.11-1 PqRead

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      5.11-2 PqReadAll

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      5.11-3 PqReadUntil

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      5.11-4 PqWrite

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  6 ANUPQ Options

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    6.1 Overview

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      6.1-1 AllANUPQoptions

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      6.1-2 ANUPQoptions

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    6.2 Detailed descriptions of ANUPQ Options

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  7 Installing the ANUPQ Package

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    7.1 Testing your ANUPQ installation

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    7.2 Running the pq program as a standalone

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  A Examples

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    A.1 The Relators Option

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    A.2 The Identities Option and PqEvaluateIdentities Function

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    A.3 A Large Example

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    A.4 Developing descendants trees

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      A.4-1 PqDescendantsTreeCoclassOne

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