C preface.tex 1. Preface S 1.1. The GAP System S 1.2. Authorship and Maintenance S 1.3. Acknowledgements S 1.4. Changes from Earlier Versions S 1.5. Further Information about GAP I 1.5. web sites!for GAP I 1.5. email addresses I 1.5. support!email address C introduc.tex 2. A First Session with GAP S 2.1. Starting and Leaving GAP I 2.1. starting GAP I 2.1. leaving GAP I 2.1. quit I 2.1. whitespace I 2.1. comments S 2.2. Loading Source Code from a File I 2.2. loading source code from a file I 2.2. reading source code from a file I 2.2. Read S 2.3. The Read Evaluate Print Loop I 2.3. read evaluate print loop I 2.3. line editing I 2.3. line editing I 2.3. break loops S 2.4. Constants and Operators I 2.4. constants I 2.4. operators S 2.5. Variables versus Objects I 2.5. variables I 2.5. assignment I 2.5. identifier I 2.5. objects I 2.5. objects!vs. variables I 2.5. last I 2.5. last2 I 2.5. last3 S 2.6. Objects vs. Elements I 2.6. objects!vs. elements I 2.6. elements I 2.6. IsIdenticalObj S 2.7. About Functions I 2.7. maps-to operator S 2.8. Help S 2.9. Further Information introducing the System C lists.tex 3. Lists and Records S 3.1. Plain Lists I 3.1. lists!plain I 3.1. strings I 3.1. lists!dense S 3.2. Identical Lists I 3.2. lists!identical S 3.3. Immutability S 3.4. Sets I 3.4. lists!strictly sorted I 3.4. family S 3.5. Ranges S 3.6. For and While Loops I 3.6. loops!for I 3.6. loops!while S 3.7. List Operations S 3.8. Vectors and Matrices I 3.8. vectors!row I 3.8. matrices S 3.9. Plain Records S 3.10. Further Information about Lists C function.tex 4. Functions S 4.1. Writing Functions S 4.2. If Statements S 4.3. Local Variables S 4.4. Recursion S 4.5. Further Information about Functions C group.tex 5. Groups and Homomorphisms S 5.1. Permutation groups I 5.1. homomorphism!natural S 5.2. Actions of Groups I 5.2. homomorphism!operation I 5.2. homomorphism!action I 5.2. external set I 5.2. right transversal I 5.2. enumerator I 5.2. Position vs. PositionCanonical S 5.3. Subgroups!as Stabilizers S 5.4. Group Homomorphisms!by Images I 5.4. group general mapping I 5.4. cokernel I 5.4. kernel I 5.4. GroupHomomorphismByImages vs. GroupGeneralMappingByImages I 5.4. group general mapping!single-valued I 5.4. group general mapping!total S 5.5. Nice Monomorphisms S 5.6. Further Information about Groups and Homomorphisms C algvspc.tex 6. Vector Spaces and Algebras S 6.1. Vector Spaces S 6.2. Algebras S 6.3. Further Information about Vector Spaces and Algebras C domain.tex 7. Domains S 7.1. Domains as Sets S 7.2. Algebraic Structure S 7.3. Notions of Generation I 7.3. GeneratorsOfSomething S 7.4. Domain Constructors I 7.4. Something S 7.5. Forming Closures of Domains I 7.5. ClosureSomething S 7.6. Changing the Structure I 7.6. AsSomething S 7.7. Subdomains I 7.7. Subsomething I 7.7. SubsomethingNC S 7.8. Further Information about Domains C opers.tex 8. Operations and Methods S 8.1. Attributes I 8.1. getter!of an attribute I 8.1. setter!of an attribute I 8.1. tester!of an attribute I 8.1. methods S 8.2. Properties and Filters I 8.2. filters I 8.2. methods!selection I 8.2. TryNextMethod S 8.3. Immediate and True Methods I 8.3. methods!immediate I 8.3. methods!true S 8.4. Operations and Method Selection I 8.4. operations I 8.4. KnownPropertiesOfObject I 8.4. KnownTruePropertiesOfObject I 8.4. KnownAttributesOfObject I 8.4. ApplicableMethod I 8.4. TraceMethods C migrat.tex 9. Migrating to GAP 4 S 9.1. Changed Command Line Options S 9.2. Fail F 9.2. fail instead of false S 9.3. Changed Functionality F 9.3. Orbit F 9.3. Order F 9.3. Position F 9.3. PermGroupOps.ElementProperty F 9.3. Print F 9.3. PrintTo S 9.4. Changed Variable Names I 9.4. AgGroup I 9.4. ApplyFunc I 9.4. Backtrace I 9.4. CharTable I 9.4. Denominator I 9.4. DepthVector I 9.4. Elements I 9.4. IsBijection I 9.4. IsFunc I 9.4. IsMat I 9.4. IsRec I 9.4. IsSet I 9.4. LengthWord I 9.4. NOfCyc I 9.4. Numerator I 9.4. RandomInvertableMat I 9.4. RecFields I 9.4. X S 9.5. Naming Conventions S 9.6. Immutable Objects S 9.7. Copy I 9.7. StructuralCopy I 9.7. ShallowCopy S 9.8. Attributes vs. Record Components S 9.9. Different Notions of Generation S 9.10. Operations Records S 9.11. Operations vs. Dispatcher Functions S 9.12. Parents and Subgroups S 9.13. Homomorphisms vs. General Mappings S 9.14. Homomorphisms vs. Factor Structures S 9.15. Isomorphisms vs. Isomorphic Structures S 9.16. Elements of Finitely Presented Groups S 9.17. Polynomials S 9.18. The Info Mechanism S 9.19. Debugging I 9.19. Backtrace I 9.19. DownEnv I 9.19. Where S 9.20. Compatibility Mode C authors.tex 10. Authors