# Magma Handbook

> Documentation for Magma V2.28, a computer algebra system for computations
> in algebra, number theory, algebraic geometry and combinatorics.

Magma provides implementations of many algorithms across computational
mathematics. This handbook documents all functions, data types and algorithms
available in the system.

- [General Index](genindex.html): Alphabetical index of all Magma functions and types.
- [References](references.html): Full bibliography cited throughout the handbook.
- [Object Index](object-index.md): Every documented Magma object (name, signature, link), grouped by kind, for exact-name lookup.

## Language and Foundations

### [The Magma Language](MagmaLanguage/index-magma-language.html)

- [Statements and Expressions](MagmaLanguage/StatementsAndExpressions/index-statements-and-expressions.html): Identifiers, assignment, booleans and coercion.
- [Functions, Procedures and Packages](MagmaLanguage/FunctionsProceduresAndPackages/index-functions-procedures-and-packages.html): Defining functions and procedures, packages, attributes and verbose flags.
- [Input and Output](MagmaLanguage/InputOutput/index-input-output.html): Strings, printing and reading input.
- [Environment and Options](MagmaLanguage/EnvironmentAndOptions/index-environment-and-options.html): Command-line options, environment variables and verbose/info settings.
- [Parallelism](MagmaLanguage/Parallelism/index-parallelism.html): Kernel-distributed parallelism, GPUs and parallel linear algebra.
- [Magma Semantics](MagmaLanguage/MagmaSemantics/index-magma-semantics.html): Definitions, assignment, evaluation and scope.
- [The Magma Profiler](MagmaLanguage/TheMagmaProfiler/index-the-magma-profiler.html): Profiling basics, call graphs and recursive profiling.
- [Debugging Magma Code](MagmaLanguage/DebuggingMagmaCode/index-debugging-magma-code.html): Using the interactive debugger.

### [Sets, Sequences and Mappings](SetsSequencesMappings/index-sets-sequences-mappings.html)

- [Introduction to Aggregates](SetsSequencesMappings/IntroductionToAggregates/index-introduction-to-aggregates.html): Overview of aggregate types, nesting, multi-indexing and common operations.
- [Sets](SetsSequencesMappings/Sets/index-sets.html): Enumerated sets, set-builder notation, membership, operations and power sets.
- [Sequences](SetsSequencesMappings/Sequences/index-sequences.html): Ordered sequences: indexing, slicing, sorting, modification and iteration.
- [Tuples and Cartesian Products](SetsSequencesMappings/TuplesCartesianProducts/index-tuples-cartesian-products.html): Fixed-length tuples, Cartesian product parents and component access.
- [Lists](SetsSequencesMappings/Lists/index-lists.html): Mutable dynamic lists and list operations.
- [Associative Arrays](SetsSequencesMappings/AssociativeArrays/index-associative-arrays.html): Key-value maps with arbitrary index types.
- [Coproducts](SetsSequencesMappings/Coproducts/index-coproducts.html): Disjoint union types and access to their elements.
- [Records](SetsSequencesMappings/Records/index-records.html): Named-field record structures and record formats.
- [Mappings](SetsSequencesMappings/Mappings/index-mappings.html): Maps between sets: injections, surjections, bijections and coercion maps.

### [Basic Rings](BasicRings/index-basic-rings.html)

- [Introduction to Rings](BasicRings/IntroductionToRings/index-introduction-to-rings.html): The ring/field world, coercion and generic ring functionality.
- [Ring of Integers](BasicRings/Integers/index-integers.html): Integer arithmetic, divisibility, primes and number-theoretic functions.
- [Integer Residue Class Rings](BasicRings/ResidueClassRings/index-residue-class-rings.html): Rings Z/nZ, Chinese remainder theorem and Hensel lifting.
- [Rational Field](BasicRings/Rationals/index-rationals.html): Rational number arithmetic and conversion.
- [Finite Fields](BasicRings/FiniteFields/index-finite-fields.html): Construction, arithmetic and extensions of finite fields.
- [Nearfields](BasicRings/Nearfields/index-nearfields.html): Nearfield construction, properties and element operations.
- [Univariate Polynomial Rings](BasicRings/UnivariatePolynomialRings/index-univariate-polynomial-rings.html): Univariate polynomial ring creation, operations and elements.
- [Multivariate Polynomial Rings](BasicRings/MultivariatePolynomialRings/index-multivariate-polynomial-rings.html): Multivariate polynomial ring creation, operations and elements.
- [Real and Complex Fields](BasicRings/RealAndComplexFields/index-real-and-complex-fields.html): Real and complex field creation, structure and element operations.

### [Matrices and Linear Algebra](MatricesLinearAlgebra/index-matrices-linear-algebra.html)

- [Matrices](MatricesLinearAlgebra/Matrices/index-matrices.html): Creating matrices over rings and fields.
- [Sparse Matrices](MatricesLinearAlgebra/SparseMatrices/index-sparse-matrices.html): Sparse matrix creation, access and entries.
- [Vector Spaces](MatricesLinearAlgebra/VectorSpaces/index-vector-spaces.html): Bases, subspaces, quotients and inner products.
- [Polar Spaces](MatricesLinearAlgebra/PolarSpaces/index-polar-spaces.html): Reflexive sesquilinear and quadratic forms, and polar space structure.

## Number Theory

### [Lattices and Quadratic Forms](LatticesQuadraticForms/index-lattices-quadratic-forms.html)

- [Lattices](LatticesQuadraticForms/Lattices/index-lattices.html): Integer lattice construction, bases, reduction and enumeration.
- [Lattices over Number Fields](LatticesQuadraticForms/LatticesOverNumberFields/index-lattices-over-number-fields.html): Lattices over number fields, including Lorentzian lattices.
- [Lattices with Group Action](LatticesQuadraticForms/LatticesWithGroupAction/index-lattices-with-group-action.html): Lattices with a group action: automorphisms and isometries.
- [Quadratic Forms](LatticesQuadraticForms/QuadraticForms/index-quadratic-forms.html): Quadratic forms: construction, local invariants and equivalence testing.
- [Binary Quadratic Forms](LatticesQuadraticForms/BinaryQuadraticForms/index-binary-quadratic-forms.html): Binary quadratic forms: reduction, invariants and class groups.

### [Global Fields](GlobalFields/index-global-fields.html)

- [Number Fields](GlobalFields/NumberFields/index-number-fields.html): Defining number fields, elements and embeddings.
- [Quadratic Fields](GlobalFields/QuadraticFields/index-quadratic-fields.html): Quadratic field creation, structure and element operations.
- [Cyclotomic Fields](GlobalFields/CyclotomicFields/index-cyclotomic-fields.html): Cyclotomic field creation, structure and element operations.
- [Number Fields and Orders](GlobalFields/NumberFieldsAndOrders/index-number-fields-and-orders.html): Orders in number fields: creation, arithmetic and printing.
- [Galois Groups and Automorphisms](GlobalFields/GaloisGroupsAndAutomorphisms/index-galois-groups-and-automorphisms.html): Automorphism groups, Galois groups, subfields and cohomology.
- [Class Field Theory](GlobalFields/ClassFieldTheory/index-class-field-theory.html): Abelian extensions, ray class fields and Galois module structure.
- [Étale Algebras](GlobalFields/EtaleAlgebras/index-etale-algebras.html): Étale algebra construction, attributes and homomorphisms.
- [Dirichlet and Hecke Characters](GlobalFields/DirichletAndHeckeCharacters/index-dirichlet-and-hecke-characters.html): Dirichlet and Hecke character construction and properties.
- [Algebraically Closed Fields](GlobalFields/AlgebraicallyClosedFields/index-algebraically-closed-fields.html): Algebraically closed field representation, structure and creation.
- [Rational Function Fields](GlobalFields/RationalFunctionFields/index-rational-function-fields.html): Rational function field creation, operations and elements.
- [Algebraic Function Fields](GlobalFields/AlgebraicFunctionFields/index-algebraic-function-fields.html): Algebraic function field creation and structural invariants.
- [Class Field Theory for Global Function Fields](GlobalFields/ClassFieldTheoryForGlobalFunctionFields/index-class-field-theory-for-global-function-fields.html): Class groups, abelian extensions and Witt rings for function fields.
- [Artin Representations](GlobalFields/ArtinRepresentations/index-artin-representations.html): Artin representation functions, invariants and arithmetic.

### [Local Fields](LocalFields/index-local-fields.html)

- [p-adic Rings and Their Extensions](LocalFields/PAdicRingsAndTheirExtensions/index-padic-rings-and-their-extensions.html): p-adic ring background, creation and extensions.
- [General p-adic Extensions](LocalFields/GeneralPAdicExtensions/index-general-padic-extensions.html): General p-adic extension construction, operations and maximal orders.
- [Power, Laurent and Puiseux Series](LocalFields/PowerLaurentAndPuiseuxSeries/index-power-laurent-and-puiseux-series.html): Power, Laurent and Puiseux series ring creation and operations.
- [Lazy Power Series Rings](LocalFields/LazyPowerSeriesRings/index-lazy-power-series-rings.html): Lazy power series ring creation, operations and elements.
- [Algebraic Power Series Rings](LocalFields/AlgebraicPowerSeriesRings/index-algebraic-power-series-rings.html): Algebraic power series ring construction and accessors.
- [Valuation Rings](LocalFields/ValuationRings/index-valuation-rings.html): Valuation ring creation, structure and element operations.
- [Galois Rings](LocalFields/GaloisRings/index-galois-rings.html): Galois ring creation, operations and elements.
- [Newton Polygons](LocalFields/NewtonPolygons/index-newton-polygons.html): Newton polygon computation and applications to factorisation.
- [Series Rings over p-adic Rings](LocalFields/SeriesRingsOverPAdicRings/index-series-rings-over-padic-rings.html): Series rings over p-adic rings, matrices and modules.
- [Local Galois Representations](LocalFields/LocalGaloisRepresentations/index-local-galois-representations.html): Local Galois representation functions, invariants and arithmetic.

## Groups

### [Finite Groups](FiniteGroups/index-finite-groups.html)

- [Groups](FiniteGroups/Groups/index-groups.html): General group creation and standard group extension constructors.
- [Permutation Groups](FiniteGroups/PermutationGroups/index-permutation-groups.html): Permutation group constructors, operations and homomorphisms.
- [Matrix Groups over General Rings](FiniteGroups/MatrixGroupsOverGeneralRings/index-matrix-groups-over-general-rings.html): General linear group creation, homomorphisms and element operations.
- [Matrix Groups over Finite Fields](FiniteGroups/MatrixGroupsOverFiniteFields/index-matrix-groups-over-finite-fields.html): Element order, Monte Carlo methods and Aschbacher reduction.
- [Matrix Groups over Infinite Fields](FiniteGroups/MatrixGroupsOverInfiniteFields/index-matrix-groups-over-infinite-fields.html): Congruence, finiteness and virtual membership tests.
- [Matrix Groups over Q and Z](FiniteGroups/MatrixGroupsOverQAndZ/index-matrix-groups-over-qand-z.html): Invariant forms, endomorphisms and related constructions.
- [Finite Soluble Groups](FiniteGroups/FiniteSolubleGroups/index-finite-soluble-groups.html): PC-group definition, properties and homomorphisms.
- [Black-box Groups](FiniteGroups/BlackBoxGroups/index-black-box-groups.html): Black-box group creation, operations and element operations.
- [Almost Simple Groups](FiniteGroups/AlmostSimpleGroups/index-almost-simple-groups.html): Double covers, standard constructions and group recognition.
- [Databases of Groups](FiniteGroups/DatabasesOfGroups/index-databases-of-groups.html): Small groups, simple groups and p-group databases.
- [Automorphism Groups](FiniteGroups/AutomorphismGroups/index-automorphism-groups.html): Automorphism group creation, access and order.
- [Cohomology and Extensions](FiniteGroups/CohomologyAndExtensions/index-cohomology-and-extensions.html): Cohomology groups, structural invariants and group extensions.
- [Reductive Groups](FiniteGroups/ReductiveGroups/index-reductive-groups.html): Reductive group creation, properties and operations.

### [Finitely Presented Groups](FinitelyPresentedGroups/index-finitely-presented-groups.html)

- [Abelian Groups](FinitelyPresentedGroups/AbelianGroups/index-abelian-groups.html): Abelian group creation, generic abelian groups and elements.
- [Free Groups](FinitelyPresentedGroups/FreeGroups/index-free-groups.html): Free group creation, subgroups and automorphisms.
- [Introduction to FP-Groups](FinitelyPresentedGroups/IntroductionToFPGroups/index-introduction-to-fpgroups.html): FP-group construction, properties and subgroups.
- [Finitely Presented Groups](FinitelyPresentedGroups/FPGroups/index-fpgroups.html): FP-group construction, simplification and standard constructions.
- [Polycyclic Groups](FinitelyPresentedGroups/PolycyclicGroups/index-polycyclic-groups.html): Polycyclic group construction, subgroups, quotients and conversion.
- [Braid Groups](FinitelyPresentedGroups/BraidGroups/index-braid-groups.html): Braid group construction and element creation.
- [Groups Defined by Rewrite Systems](FinitelyPresentedGroups/GroupsDefinedByRewriteSystems/index-groups-defined-by-rewrite-systems.html): Rewriting system creation, properties and arithmetic for groups.
- [Automatic and Hyperbolic Groups](FinitelyPresentedGroups/AutomaticAndHyperbolicGroups/index-automatic-and-hyperbolic-groups.html): Automatic groups and hyperbolic groups.
- [Groups of Straight-line Programs](FinitelyPresentedGroups/GroupsOfStraightLinePrograms/index-groups-of-straight-line-programs.html): Straight-line program group creation and operations.
- [Finitely Presented Semigroups](FinitelyPresentedGroups/FinitelyPresentedSemigroups/index-finitely-presented-semigroups.html): Semigroup presentation creation, operations and properties.
- [Monoids Given by Rewrite Systems](FinitelyPresentedGroups/MonoidsGivenByRewriteSystems/index-monoids-given-by-rewrite-systems.html): Rewriting system creation, operations and homomorphisms for monoids.

### [Representation Theory](RepresentationTheory/index-representation-theory.html)

- [Modules over an Algebra and Group Representations](RepresentationTheory/ModulesOverAnAlgebraAndGroupRepresentations/index-modules-over-an-algebra-and-group-representations.html): Modules over an algebra, K[G]-modules and the operation of a group on a module.
- [Characters of Finite Groups](RepresentationTheory/CharactersOfFiniteGroups/index-characters-of-finite-groups.html): Character tables, character rings and Brauer characters.
- [Representations of Symmetric Groups](RepresentationTheory/RepresentationsOfSymmetricGroups/index-representations-of-symmetric-groups.html): Specht modules, representations and characters of symmetric and alternating groups.
- [Mod p Galois Representations](RepresentationTheory/ModPGaloisRepresentations/index-mod-pgalois-representations.html): Mod p Galois representations and their associated modules.
- [Group Representations](RepresentationTheory/GroupRepresentations/index-group-representations.html): Creation, properties, operations and morphisms of group representations.

### [Lie Theory](LieTheory/index-lie-theory.html)

- [Introduction to Lie Theory](LieTheory/Introduction/index-introduction.html): Overview of Lie theory in Magma.
- [Coxeter Systems](LieTheory/CoxeterSystems/index-coxeter-systems.html): Coxeter matrices, Coxeter graphs, Cartan matrices and Dynkin diagrams.
- [Root Systems](LieTheory/RootSystems/index-root-systems.html): Root systems, Dynkin diagrams and Cartan matrices.
- [Root Data](LieTheory/RootData/index-root-data.html): Root data, coroots, weights and related constructions.
- [Coxeter Groups](LieTheory/CoxeterGroups/index-coxeter-groups.html): Coxeter group constructors, word arithmetic and Bruhat order.
- [Reflection Groups](LieTheory/ReflectionGroups/index-reflection-groups.html): Real and complex reflection groups and their properties.
- [Lie Algebras](LieTheory/LieAlgebras/index-lie-algebras.html): Structure constants, subalgebras, ideals and derivations.
- [Kac-Moody Lie Algebras](LieTheory/KacMoodyLieAlgebras/index-kac-moody-lie-algebras.html): Construction and structural invariants of Kac-Moody Lie algebras.
- [Quantum Groups](LieTheory/QuantumGroups/index-quantum-groups.html): Quantized enveloping algebras, their representations and Hopf structure.
- [Groups of Lie Type](LieTheory/ChevalleyGroups/index-chevalley-groups.html): Groups of Lie type, Borel subgroups and parabolic subgroups.
- [Representations of Lie Groups and Algebras](LieTheory/RepresentationsOfLieGroupsAndAlgebras/index-representations-of-lie-groups-and-algebras.html): Highest weight representations of Lie algebras and reductive algebraic groups.

## Algebra

### [Modules](Modules/index-modules.html)

- [Introduction to Modules](Modules/IntroductionToModules/index-introduction-to-modules.html): Overview, definitions and presentations of modules.
- [Free Modules](Modules/FreeModules/index-free-modules.html): Free modules, bases and rank.
- [Modules over Dedekind Domains](Modules/ModulesOverDedekindDomains/index-modules-over-dedekind-domains.html): Creation, arithmetic, basis and homomorphisms of modules over Dedekind domains.
- [Chain Complexes](Modules/ChainComplexes/index-chain-complexes.html): Ext, Tor and projective resolutions.
- [Multilinear Algebra](Modules/MultilinearAlgebra/index-multilinear-algebra.html): Tensors, tensor spaces and multilinear invariants.

### [Algebras](Algebras/index-algebras.html)

- [Algebras](Algebras/IntroductionToAlgebras/index-introduction-to-algebras.html): Overview, creation, substructures and general operations on algebras.
- [Structure Constant Algebras](Algebras/StructureConstantAlgebras/index-structure-constant-algebras.html): Algebras defined by structure constants.
- [Associative Algebras](Algebras/AssociativeAlgebras/index-associative-algebras.html): Structure, subalgebras, ideals and the Jacobson radical.
- [Finitely Presented Algebras](Algebras/FinitelyPresentedAlgebras/index-finitely-presented-algebras.html): Algebras given by generators and relations.
- [Matrix Algebras](Algebras/MatrixAlgebras/index-matrix-algebras.html): Matrix algebras: creation, substructures and extensions.
- [Group Algebras](Algebras/GroupAlgebras/index-group-algebras.html): Group algebras: creation, substructures and element operations.
- [Basic Algebras](Algebras/BasicAlgebras/index-basic-algebras.html): Basic algebras, gradings, idempotents and their homomorphisms.
- [Quaternion Algebras](Algebras/QuaternionAlgebras/index-quaternion-algebras.html): Quaternion algebra constructors, maximal orders and splitting.
- [Algebras with Involution](Algebras/AlgebrasWithInvolution/index-algebras-with-involution.html): Star algebras, involutions and their decompositions.
- [Clifford Algebras](Algebras/CliffordAlgebras/index-clifford-algebras.html): Clifford algebras, involutions and spin groups.
- [Non-associative Algebras](Algebras/NonAssociativeAlgebras/index-non-associative-algebras.html): Jordan algebras, alternative algebras and octonions.

### [Commutative Algebra](CommutativeAlgebra/index-commutative-algebra.html)

- [Gröbner Bases](CommutativeAlgebra/GrobnerBases/index-grobner-bases.html): Buchberger’s algorithm and Gröbner basis configuration.
- [Polynomial Ring Ideal Operations](CommutativeAlgebra/PolynomialRingIdealOperations/index-polynomial-ring-ideal-operations.html): Ideal creation, operations, varieties and multiplicities.
- [Local Polynomial Rings](CommutativeAlgebra/LocalPolynomialRings/index-local-polynomial-rings.html): Element orders, creation, Gröbner bases and ideal operations.
- [Affine Algebras](CommutativeAlgebra/AffineAlgebras/index-affine-algebras.html): Affine algebra creation, operations and maps.
- [Modules over Multivariate Rings](CommutativeAlgebra/ModulesOverMultivariateRings/index-modules-over-multivariate-rings.html): Module creation, order, embedded components and homomorphisms.
- [Invariant Theory](CommutativeAlgebra/InvariantTheory/index-invariant-theory.html): Invariant rings, group actions and permutation/matrix invariants.
- [Differential Rings](CommutativeAlgebra/DifferentialRings/index-differential-rings.html): Differential rings and the Galois theory of linear differential equations.

## Geometry

### [Algebraic Geometry](AlgebraicGeometry/index-algebraic-geometry.html)

- [Schemes](AlgebraicGeometry/Schemes/index-schemes.html): Ambient spaces, scheme creation and basic scheme operations.
- [Coherent Sheaves](AlgebraicGeometry/Sheaves/index-sheaves.html): Sheaf creation, accessors and sheaf homomorphisms.
- [Algebraic Curves](AlgebraicGeometry/AlgebraicCurves/index-algebraic-curves.html): Curve ambients, local and global properties, and maps between curves.
- [Resolution Graphs and Splice Diagrams](AlgebraicGeometry/ResolutionGraphsAndSpliceDiagrams/index-resolution-graphs-and-splice-diagrams.html): Resolution graphs, splice diagrams and translation between them.
- [Algebraic Surfaces](AlgebraicGeometry/AlgebraicSurfaces/index-algebraic-surfaces.html): Surface schemes, resolution by blow-up and surfaces in projective space.
- [Riemann Surfaces](AlgebraicGeometry/RiemannSurfaces/index-riemann-surfaces.html): Riemann surface creation, points, divisors and the Abel-Jacobi map.
- [Hilbert Series of Polarised Varieties](AlgebraicGeometry/HilbertSeriesOfPolarisedVarieties/index-hilbert-series-of-polarised-varieties.html): Hilbert series, baskets of singularities and polarised varieties.
- [Toric Varieties](AlgebraicGeometry/ToricVarieties/index-toric-varieties.html): Toric fans, cones, Cox rings and toric divisors.

### [Arithmetic Geometry](ArithmeticGeometry/index-arithmetic-geometry.html)

- [Rational Curves and Conics](ArithmeticGeometry/RationalCurvesAndConics/index-rational-curves-and-conics.html): Rational curves and conics: models and rational points.
- [Elliptic Curves](ArithmeticGeometry/EllipticCurves/index-elliptic-curves.html): Elliptic curve creation, arithmetic and the function field.
- [Elliptic Curves over Finite Fields](ArithmeticGeometry/EllipticCurvesOverFiniteFields/index-elliptic-curves-over-finite-fields.html): Supersingular curves, point counting, group structure and pairings.
- [Elliptic Curves over Q and Number Fields](ArithmeticGeometry/EllipticCurvesOverQAndNumberFields/index-elliptic-curves-over-qand-number-fields.html): Curves over number fields and p-adic fields, and Mordell-Weil groups.
- [Elliptic Curves over Function Fields](ArithmeticGeometry/EllipticCurvesOverFunctionFields/index-elliptic-curves-over-function-fields.html): Curve search, heights and torsion over function fields.
- [Models of Genus One Curves](ArithmeticGeometry/ModelsOfGenusOneCurves/index-models-of-genus-one-curves.html): Genus one curve models, transformations and equivalence.
- [Plane Quartics](ArithmeticGeometry/PlaneQuartics/index-plane-quartics.html): Quartic invariants, reconstruction from invariants, and twists.
- [Hyperelliptic Curves](ArithmeticGeometry/HyperellipticCurves/index-hyperelliptic-curves.html): Hyperelliptic curve models and divisor arithmetic.
- [Hypergeometric Motives](ArithmeticGeometry/HypergeometricMotives/index-hypergeometric-motives.html): Hypergeometric motives and Jacobi motives.
- [L-Functions](ArithmeticGeometry/LFunctions/index-lfunctions.html): Built-in and general L-series, and their invariants.

### [Modular Arithmetic Geometry](ModularArithmeticGeometry/index-modular-arithmetic-geometry.html)

- [Modular Curves](ModularArithmeticGeometry/ModularCurves/index-modular-curves.html): Modular curve creation and attributes.
- [Small Modular Curves](ModularArithmeticGeometry/SmallModularCurves/index-small-modular-curves.html): Explicit models, projections and automorphisms of small modular curves.
- [Congruence Subgroups of PSL2(R)](ModularArithmeticGeometry/CongruenceSubgroupsOfPSL2R/index-congruence-subgroups-of-psl2-r.html): Congruence subgroups, their structure and group elements.
- [Arithmetic Fuchsian Groups and Shimura Curves](ModularArithmeticGeometry/ArithmeticFuchsianGroupsAndShimuraCurves/index-arithmetic-fuchsian-groups-and-shimura-curves.html): Fuchsian groups, fundamental domains and triangle groups.
- [Modular Forms](ModularArithmeticGeometry/ModularForms/index-modular-forms.html): Spaces of modular forms, bases and q-expansions.
- [Modular Symbols](ModularArithmeticGeometry/ModularSymbols/index-modular-symbols.html): Modular symbols spaces, creation and bases.
- [Brandt Modules](ModularArithmeticGeometry/BrandtModules/index-brandt-modules.html): Brandt modules, subspaces and Hecke operators.
- [Supersingular Divisors on Modular Curves](ModularArithmeticGeometry/SupersingularDivisorsOnModularCurves/index-supersingular-divisors-on-modular-curves.html): Supersingular divisors: creation, basis and properties.
- [Modular Abelian Varieties](ModularArithmeticGeometry/ModularAbelianVarieties/index-modular-abelian-varieties.html): Modular abelian varieties, homology and morphisms.
- [Hilbert Modular Forms](ModularArithmeticGeometry/HilbertModularForms/index-hilbert-modular-forms.html): Hilbert modular forms: creation and basic properties.
- [Modular Forms over Imaginary Quadratic Fields](ModularArithmeticGeometry/ModularFormsOverImaginaryQuadraticFields/index-modular-forms-over-imaginary-quadratic-fields.html): Bianchi modular forms, basic properties and Hecke operators.
- [Algebraic Modular Forms](ModularArithmeticGeometry/AlgebraicModularForms/index-algebraic-modular-forms.html): Algebraic modular forms: creation, properties and elements.
- [Representations of Local Fields](ModularArithmeticGeometry/RepresentationsOfLocalFields/index-representations-of-local-fields.html): Admissible representations of GL\ :sub:2\ (Q\ :sub:p\ ) and local Langlands.

### [Topology](Topology/index-topology.html)

- [Simplicial Homology](Topology/SimplicialHomology/index-simplicial-homology.html): Finite simplicial complexes, construction, and homology computation.

### [Geometry](Geometry/index-geometry.html)

- [Finite Planes](Geometry/FinitePlanes/index-finite-planes.html): Point-line sets, incidence and support in finite planes.
- [Incidence Geometry](Geometry/IncidenceGeometry/index-incidence-geometry.html): Incidence structures, residues and their conversion between representations.
- [Convex Polytopes and Polyhedra](Geometry/Polytopes/index-polytopes.html): Convex polytopes, faces, f-vectors and symmetry groups.

## Applications

### [Combinatorics](Combinatorics/index-combinatorics.html)

- [Enumerative Combinatorics](Combinatorics/EnumerativeCombinatorics/index-enumerative-combinatorics.html): Combinatorial counting, partitions and subset enumeration.
- [Partitions, Words and Young Tableaux](Combinatorics/PartitionsWordsTableaux/index-partitions-words-tableaux.html): Words, partitions and Young tableaux.
- [Symmetric Functions](Combinatorics/SymmetricFunctions/index-symmetric-functions.html): The algebra of symmetric functions: creation, operations and matrix representations.
- [Incidence Structures and Designs](Combinatorics/Designs/index-designs.html): Block designs, Latin squares and t-designs.
- [Hadamard Matrices](Combinatorics/HadamardMatrices/index-hadamard-matrices.html): Hadamard matrices, their construction and equivalence testing.
- [Graphs](Combinatorics/Graphs/index-graphs.html): Graph constructors, adjacency, traversal, colouring, cliques and independent sets.
- [Multigraphs](Combinatorics/Multigraphs/index-multigraphs.html): Multigraph construction, decorations, connectivity, spanning trees and shortest paths.
- [Networks](Combinatorics/Networks/index-networks.html): Network construction and flow algorithms.

### [Coding Theory](CodingTheory/index-coding-theory.html)

- [Linear Codes over Finite Fields](CodingTheory/LinearCodes/index-linear-codes.html): Linear code constructors, generator matrices and parameters.
- [Algebraic-Geometric Codes](CodingTheory/AlgebraicGeometricCodes/index-algebraic-geometric-codes.html): Codes constructed from algebraic curves, and their decoding.
- [Low Density Parity Check Codes](CodingTheory/LowDensityParityCheckCodes/index-low-density-parity-check-codes.html): LDPC code construction and properties.
- [Linear Codes over Finite Rings](CodingTheory/LinearCodesOverFiniteRings/index-linear-codes-over-finite-rings.html): Linear codes over finite rings: creation, subcodes and Boolean operations.
- [Linear Codes over the Integer Residue Ring Z4](CodingTheory/LinearCodesOverZ4/index-linear-codes-over-z4.html): Linear codes over :math:\mathbb{Z}_4, invariants, weight enumerators and decoding.
- [Additive Codes](CodingTheory/AdditiveCodes/index-additive-codes.html): Additive code constructors, subcodes and Boolean operations.
- [Quantum Codes](CodingTheory/QuantumCodes/index-quantum-codes.html): Quantum error-correcting codes, inner products and code combination.

### [Cryptography](Cryptography/index-cryptography.html)

- [Pseudo-random Bit Sequences](Cryptography/PseudoRandomBitSequences/index-pseudo-random-bit-sequences.html): Generation and testing of pseudo-random bit sequences.

### [Optimization](Optimization/index-optimization.html)

- [Linear Programming](Optimization/LinearProgramming/index-linear-programming.html): Linear programming problem construction and solution.

## Additional Pages

- [Page Not Found](404.html)
- [Ambient Spaces](AlgebraicGeometry/AlgebraicCurves/ambients.html)
- [Minimal Degree Functions and Plane Models](AlgebraicGeometry/AlgebraicCurves/arith-2.html)
- [Curves over Global Fields](AlgebraicGeometry/AlgebraicCurves/arith.html)
- [Automorphism Groups of Curves](AlgebraicGeometry/AlgebraicCurves/crv_isos.html)
- [Algebraic Curves](AlgebraicGeometry/AlgebraicCurves/curves.html)
- [Divisors](AlgebraicGeometry/AlgebraicCurves/divisors.html)
- [First Examples](AlgebraicGeometry/AlgebraicCurves/examples1.html)
- [Advanced Examples](AlgebraicGeometry/AlgebraicCurves/examples2.html)
- [Function Fields](AlgebraicGeometry/AlgebraicCurves/function_field.html)
- [Global Geometry](AlgebraicGeometry/AlgebraicCurves/global-curvepl.html)
- [Linear Equivalence of Divisors](AlgebraicGeometry/AlgebraicCurves/linear-equivalence.html)
- [Local Geometry](AlgebraicGeometry/AlgebraicCurves/local-curve.html)
- [Maps and Curves](AlgebraicGeometry/AlgebraicCurves/maps-crvpl.html)
- [Degree \(2\) K3 Surfaces](AlgebraicGeometry/AlgebraicSurfaces/deg-2-K3-srfcs.html)
- [Desingularisation by Blow Up](AlgebraicGeometry/AlgebraicSurfaces/desing-by-blow-up.html)
- [Del Pezzo Surfaces](AlgebraicGeometry/AlgebraicSurfaces/dp-srfcs.html)
- [General Surfaces](AlgebraicGeometry/AlgebraicSurfaces/gen-sfcs.html)
- [Introduction](AlgebraicGeometry/AlgebraicSurfaces/intro-main.html)
- [Generalities](AlgebraicGeometry/AlgebraicSurfaces/srfc-sch-recap.html)
- [Surfaces in \({\mathbb{P}}^3\)](AlgebraicGeometry/AlgebraicSurfaces/srfcs-P3.html)
- [Baskets of Singularities](AlgebraicGeometry/HilbertSeriesOfPolarisedVarieties/baskets.html)
- [Calabi–Yau 3-folds](AlgebraicGeometry/HilbertSeriesOfPolarisedVarieties/cy.html)
- [Point Counting on Degree Two K3 Surfaces](AlgebraicGeometry/HilbertSeriesOfPolarisedVarieties/deg_2_K3_surf.html)
- [Fano 3-folds](AlgebraicGeometry/HilbertSeriesOfPolarisedVarieties/fano.html)
- [Building Databases](AlgebraicGeometry/HilbertSeriesOfPolarisedVarieties/gr-makedb.html)
- [Introduction](AlgebraicGeometry/HilbertSeriesOfPolarisedVarieties/introduction.html)
- [K3 Surfaces](AlgebraicGeometry/HilbertSeriesOfPolarisedVarieties/k3.html)
- [The K3 Database](AlgebraicGeometry/HilbertSeriesOfPolarisedVarieties/k3db.html)
- [Generic Polarised Varieties](AlgebraicGeometry/HilbertSeriesOfPolarisedVarieties/pol-var.html)
- [Hilbert Series and Graded Rings](AlgebraicGeometry/HilbertSeriesOfPolarisedVarieties/series.html)
- [Subcanonical Curves](AlgebraicGeometry/HilbertSeriesOfPolarisedVarieties/subcan.html)
- [Weil Polynomials](AlgebraicGeometry/HilbertSeriesOfPolarisedVarieties/weilpoly.html)
- [Introduction](AlgebraicGeometry/ResolutionGraphsAndSpliceDiagrams/introduction.html)
- [Resolution Graphs](AlgebraicGeometry/ResolutionGraphsAndSpliceDiagrams/resolution-graphs.html)
- [Splice Diagrams](AlgebraicGeometry/ResolutionGraphsAndSpliceDiagrams/splice-diagrams.html)
- [Translation Between Graphs](AlgebraicGeometry/ResolutionGraphsAndSpliceDiagrams/translation.html)
- [Introduction to Riemann Surfaces](AlgebraicGeometry/RiemannSurfaces/Introduction.html)
- [Points on Riemann Surfaces](AlgebraicGeometry/RiemannSurfaces/Points.html)
- [Abel–Jacobi Map](AlgebraicGeometry/RiemannSurfaces/abel-jacobi.html)
- [Period Matrix Functions](AlgebraicGeometry/RiemannSurfaces/anal-jac.html)
- [Properties of Riemann Surfaces](AlgebraicGeometry/RiemannSurfaces/attribute-functions.html)
- [Divisors on Riemann Surfaces](AlgebraicGeometry/RiemannSurfaces/divisors.html)
- [Creation Functions](AlgebraicGeometry/RiemannSurfaces/rie-srf-creation.html)
- [Arithmetic Properties of Schemes and Points](AlgebraicGeometry/Schemes/anfs.html)
- [Introduction and First Examples](AlgebraicGeometry/Schemes/introduction.html)
- [Linear Systems](AlgebraicGeometry/Schemes/linsys.html)
- [Maps between Schemes](AlgebraicGeometry/Schemes/maps.html)
- [Advanced Examples](AlgebraicGeometry/Schemes/scheme-advanced.html)
- [Divisors](AlgebraicGeometry/Schemes/scheme-divisors.html)
- [Isolated Points on Schemes](AlgebraicGeometry/Schemes/scheme-isolated-points.html)
- [Ambients](AlgebraicGeometry/Schemes/schemes-ambient.html)
- [Base Change for Schemes](AlgebraicGeometry/Schemes/schemes-base-change.html)
- [Basic Attributes of Schemes](AlgebraicGeometry/Schemes/schemes-basic.html)
- [Affine Patches and Projective Closure](AlgebraicGeometry/Schemes/schemes-closure.html)
- [Zero-dimensional Schemes](AlgebraicGeometry/Schemes/schemes-clusters.html)
- [Constructing Schemes](AlgebraicGeometry/Schemes/schemes-creation.html)
- [Function Fields and their Elements](AlgebraicGeometry/Schemes/schemes-function-elements.html)
- [Global Geometry of Schemes](AlgebraicGeometry/Schemes/schemes-global.html)
- [Local Geometry of Schemes](AlgebraicGeometry/Schemes/schemes-local.html)
- [Rational Points and Point Sets](AlgebraicGeometry/Schemes/schemes-points.html)
- [Different Types of Scheme](AlgebraicGeometry/Schemes/schemes-types.html)
- [Classification and Normal Forms of Singularities](AlgebraicGeometry/Schemes/sing-norm-form.html)
- [Tangent and Secant Varieties and Isomorphic Projections](AlgebraicGeometry/Schemes/tan-sec-proj.html)
- [Accessor Functions](AlgebraicGeometry/Sheaves/accessors.html)
- [Creation Functions](AlgebraicGeometry/Sheaves/creation.html)
- [Divisor Maps and Riemann-Roch Spaces](AlgebraicGeometry/Sheaves/div_maps.html)
- [Introduction](AlgebraicGeometry/Sheaves/introduction.html)
- [Basic Constructions](AlgebraicGeometry/Sheaves/more-cons.html)
- [Sheaf Homomorphisms](AlgebraicGeometry/Sheaves/sheaf-homs.html)
- [Examples](AlgebraicGeometry/Sheaves/shf:exs.html)
- [Miscellaneous](AlgebraicGeometry/Sheaves/shf:misc.html)
- [Predicates](AlgebraicGeometry/Sheaves/shf:preds.html)
- [Cox Rings](AlgebraicGeometry/ToricVarieties/cox-rings.html)
- [Introduction and First Examples](AlgebraicGeometry/ToricVarieties/introduction.html)
- [Geometrical Properties of Cones and Polyhedra](AlgebraicGeometry/ToricVarieties/toric-cones-and-polyhedra.html)
- [Invariant Divisors and Riemann-Roch Spaces](AlgebraicGeometry/ToricVarieties/toric-divisors.html)
- [Fans in Toric Lattices](AlgebraicGeometry/ToricVarieties/toric-fans.html)
- [The Geometry of Toric Varieties](AlgebraicGeometry/ToricVarieties/toric-geometry.html)
- [Maps of Toric Varieties](AlgebraicGeometry/ToricVarieties/toric-maps.html)
- [Schemes in Toric Varieties](AlgebraicGeometry/ToricVarieties/toric-subschemes.html)
- [Toric Varieties](AlgebraicGeometry/ToricVarieties/toric-varieties.html)
- [Decompositions of \(\ast\)-Algebras](Algebras/AlgebrasWithInvolution/decompositions.html)
- [Introduction](Algebras/AlgebrasWithInvolution/introduction.html)
- [Intersections of Classical Groups](Algebras/AlgebrasWithInvolution/isometry.html)
- [Recognition of \(\ast\)-Algebras](Algebras/AlgebrasWithInvolution/recognition.html)
- [Algebras with Involution](Algebras/AlgebrasWithInvolution/star-algebras.html)
- [Orders](Algebras/AssociativeAlgebras/alg_ass_ord.html)
- [Construction of Associative Algebras](Algebras/AssociativeAlgebras/creation.html)
- [Elements of Orders](Algebras/AssociativeAlgebras/elements.html)
- [Ideals of Orders](Algebras/AssociativeAlgebras/ideals.html)
- [Introduction](Algebras/AssociativeAlgebras/introduction.html)
- [Operations on Algebras and their Elements](Algebras/AssociativeAlgebras/ops.html)
- [A-infinity Algebra Structures on Group Cohomology](Algebras/BasicAlgebras/a-infinity.html)
- [Basic Algebras](Algebras/BasicAlgebras/algebras.html)
- [Automorphisms and Isomorphisms](Algebras/BasicAlgebras/automorphism.html)
- [Cohomology](Algebras/BasicAlgebras/cohomology.html)
- [Duals and Injectives](Algebras/BasicAlgebras/duals-injectives.html)
- [Minimal Forms and Gradings](Algebras/BasicAlgebras/forms-gradings-permute-idempotents.html)
- [Homomorphisms](Algebras/BasicAlgebras/homomorphisms-algebras.html)
- [Homomorphisms of Modules](Algebras/BasicAlgebras/homomorphisms.html)
- [Introduction](Algebras/BasicAlgebras/introduction.html)
- [Modules over Basic Algebras](Algebras/BasicAlgebras/modules.html)
- [Group Algebras of \(p\)-groups](Algebras/BasicAlgebras/p-groups.html)
- [Quiver and Relations](Algebras/BasicAlgebras/quiver.html)
- [Subalgebras and Quotient Algebras](Algebras/BasicAlgebras/sub-quo.html)
- [Clifford Algebras](Algebras/CliffordAlgebras/creation.html)
- [Introduction](Algebras/CliffordAlgebras/introduction.html)
- [The Main Involutions](Algebras/CliffordAlgebras/involutions.html)
- [Clifford Algebra Structure](Algebras/CliffordAlgebras/operations.html)
- [Vector and Spin Representations](Algebras/CliffordAlgebras/spin.html)
- [Creation of Free Algebras and Elements](Algebras/FinitelyPresentedAlgebras/algebras.html)
- [Changing Coefficient Ring](Algebras/FinitelyPresentedAlgebras/change-ring.html)
- [Creation of FP-Algebras](Algebras/FinitelyPresentedAlgebras/creation.html)
- [Exterior Algebras](Algebras/FinitelyPresentedAlgebras/exterior.html)
- [Finite Dimensional FP-Algebras](Algebras/FinitelyPresentedAlgebras/finite-dimension-quotient.html)
- [Finitely Presented Algebras](Algebras/FinitelyPresentedAlgebras/fp-algebra.html)
- [Basic Operations on Ideals](Algebras/FinitelyPresentedAlgebras/ideal-operation.html)
- [Ideals and Gröbner Bases](Algebras/FinitelyPresentedAlgebras/ideals.html)
- [Introduction](Algebras/FinitelyPresentedAlgebras/introduction.html)
- [Element Operations](Algebras/FinitelyPresentedAlgebras/operation-element.html)
- [Structure Operations](Algebras/FinitelyPresentedAlgebras/operation.html)
- [Operations on FP-Algebras](Algebras/FinitelyPresentedAlgebras/operations.html)
- [Representation and Monomial Orders](Algebras/FinitelyPresentedAlgebras/order.html)
- [Vector Enumeration](Algebras/FinitelyPresentedAlgebras/vector-enumeration.html)
- [Construction of Group Algebras and their Elements](Algebras/GroupAlgebras/creation.html)
- [Operations on Elements](Algebras/GroupAlgebras/elt-ops.html)
- [Operations on Group Algebras and their Subalgebras](Algebras/GroupAlgebras/grp-alg-ops.html)
- [Introduction](Algebras/GroupAlgebras/introduction.html)
- [Construction of Subalgebras, Ideals and Quotient Algebras](Algebras/GroupAlgebras/subring-ideal-quotient.html)
- [Construction of General Algebras and their Elements](Algebras/IntroductionToAlgebras/creation.html)
- [Introduction](Algebras/IntroductionToAlgebras/introduction.html)
- [Operations on Elements of an Algebra](Algebras/IntroductionToAlgebras/ops-2.html)
- [Operations on Algebras and Subalgebras](Algebras/IntroductionToAlgebras/ops.html)
- [Construction of Subalgebras, Ideals and Quotient Algebras](Algebras/IntroductionToAlgebras/subs-quos.html)
- [Canonical Forms](Algebras/MatrixAlgebras/canonical-form.html)
- [Changing Rings](Algebras/MatrixAlgebras/change-ring.html)
- [Construction of Matrix Algebras and their Elements](Algebras/MatrixAlgebras/creation.html)
- [Diagonalising Commutative Algebras over a Field](Algebras/MatrixAlgebras/diag.html)
- [Elementary Operations on Elements](Algebras/MatrixAlgebras/element.html)
- [The Construction of Extensions and their Elements](Algebras/MatrixAlgebras/extension.html)
- [Elements of \(M_n\) as Homomorphisms](Algebras/MatrixAlgebras/homomorphism-element.html)
- [Introduction](Algebras/MatrixAlgebras/introduction.html)
- [Accessing and Modifying a Matrix](Algebras/MatrixAlgebras/operation-element.html)
- [Operations on Matrix Algebras](Algebras/MatrixAlgebras/operation.html)
- [Presentations for Matrix Algebras](Algebras/MatrixAlgebras/presentations.html)
- [Solutions of Systems of Linear Equations](Algebras/MatrixAlgebras/solution-equation.html)
- [Elementary Operations on Subalgebras and Ideals](Algebras/MatrixAlgebras/subalgebra-ideal.html)
- [Construction of Subalgebras, Ideals and Quotient Rings](Algebras/MatrixAlgebras/subring-ideal-quotient.html)
- [Composition Algebras](Algebras/NonAssociativeAlgebras/Composition-algebras.html)
- [Generic Operations](Algebras/NonAssociativeAlgebras/Generics-for-nonassociative-algebras.html)
- [Invariants](Algebras/NonAssociativeAlgebras/Invariants-of-nonassociative-algebras.html)
- [Jordan Algebras](Algebras/NonAssociativeAlgebras/Jordan-algebras.html)
- [Attributes of Quaternion Algebras](Algebras/QuaternionAlgebras/algebra-attributes.html)
- [Creation of Quaternion Algebras](Algebras/QuaternionAlgebras/creation.html)
- [Elements of Quaternion Algebras](Algebras/QuaternionAlgebras/elements.html)
- [Hilbert Symbols and Embeddings](Algebras/QuaternionAlgebras/hilbert-symbols.html)
- [Ideal Theory of Orders](Algebras/QuaternionAlgebras/ideal-theory.html)
- [Introduction](Algebras/QuaternionAlgebras/introduction.html)
- [Isomorphisms](Algebras/QuaternionAlgebras/isomorphisms.html)
- [Recognition Functions](Algebras/QuaternionAlgebras/matrix-ring-test.html)
- [Norm Spaces and Basis Reduction](Algebras/QuaternionAlgebras/norm-space.html)
- [Attributes of Orders](Algebras/QuaternionAlgebras/order-attributes.html)
- [Creation of Quaternion Orders](Algebras/QuaternionAlgebras/order-creation.html)
- [Operations with Orders](Algebras/QuaternionAlgebras/order-ops.html)
- [Predicates of Orders](Algebras/QuaternionAlgebras/order-pred.html)
- [Predicates on Algebras](Algebras/QuaternionAlgebras/predicates.html)
- [Units and Unit Groups](Algebras/QuaternionAlgebras/unit-group.html)
- [Operations on Structure Constant Algebras and Elements](Algebras/StructureConstantAlgebras/creation-2.html)
- [Construction of Structure Constant Algebras and Elements](Algebras/StructureConstantAlgebras/creation.html)
- [Introduction](Algebras/StructureConstantAlgebras/introduction.html)
- [Creation Functions](ArithmeticGeometry/EllipticCurves/creation.html)
- [The Formal Group](ArithmeticGeometry/EllipticCurves/formal.html)
- [Polynomials](ArithmeticGeometry/EllipticCurves/function_field.html)
- [Introduction](ArithmeticGeometry/EllipticCurves/introduction.html)
- [Morphisms](ArithmeticGeometry/EllipticCurves/morphism.html)
- [Operations on Curves](ArithmeticGeometry/EllipticCurves/operations_curve.html)
- [Operations on Points](ArithmeticGeometry/EllipticCurves/point.html)
- [Operations on Point Sets](ArithmeticGeometry/EllipticCurves/pointset.html)
- [Subgroup Schemes](ArithmeticGeometry/EllipticCurves/subgroup_schemes.html)
- [Abelian Group Structure](ArithmeticGeometry/EllipticCurvesOverFiniteFields/abelian_group.html)
- [Discrete Logarithms](ArithmeticGeometry/EllipticCurvesOverFiniteFields/discrete_logs.html)
- [Weil Descent in Characteristic Two](ArithmeticGeometry/EllipticCurvesOverFiniteFields/ec_weil_desc.html)
- [The Order of the Group of Points](ArithmeticGeometry/EllipticCurvesOverFiniteFields/ff_curves-group_points.html)
- [Enumeration of Points](ArithmeticGeometry/EllipticCurvesOverFiniteFields/ff_curves-points.html)
- [Supersingular Curves](ArithmeticGeometry/EllipticCurvesOverFiniteFields/ff_curves-supersingular_curves.html)
- [Pairings on Elliptic Curves](ArithmeticGeometry/EllipticCurvesOverFiniteFields/pairings.html)
- [The \(L\)-function and Counting Points](ArithmeticGeometry/EllipticCurvesOverFunctionFields/Lfunction.html)
- [Elliptic Curves of Given Conductor](ArithmeticGeometry/EllipticCurvesOverFunctionFields/ecsearch.html)
- [Extended Examples](ArithmeticGeometry/EllipticCurvesOverFunctionFields/extended-examples.html)
- [Action of Frobenius](ArithmeticGeometry/EllipticCurvesOverFunctionFields/frobenius-action.html)
- [Heights](ArithmeticGeometry/EllipticCurvesOverFunctionFields/heights.html)
- [Local Computations](ArithmeticGeometry/EllipticCurvesOverFunctionFields/local.html)
- [The Mordell–Weil Group](ArithmeticGeometry/EllipticCurvesOverFunctionFields/mordell-weil-group.html)
- [An Overview of Relevant Theory](ArithmeticGeometry/EllipticCurvesOverFunctionFields/theory.html)
- [The Torsion Subgroup](ArithmeticGeometry/EllipticCurvesOverFunctionFields/torsion.html)
- [Two Descent](ArithmeticGeometry/EllipticCurvesOverFunctionFields/two-descent.html)
- [Curves over the Rationals](ArithmeticGeometry/EllipticCurvesOverQAndNumberFields/intro-2.html)
- [Introduction](ArithmeticGeometry/EllipticCurvesOverQAndNumberFields/intro.html)
- [Mordell–Weil Groups and Descent Methods](ArithmeticGeometry/EllipticCurvesOverQAndNumberFields/mordell-weil.html)
- [Curves over Number Fields](ArithmeticGeometry/EllipticCurvesOverQAndNumberFields/over_anf.html)
- [Curves over \(p\)-adic Fields](ArithmeticGeometry/EllipticCurvesOverQAndNumberFields/over_pad.html)
- [Analytic Jacobians of Hyperelliptic Curves](ArithmeticGeometry/HyperellipticCurves/analytic.html)
- [Chabauty’s Method](ArithmeticGeometry/HyperellipticCurves/chabauty-method.html)
- [Creation Functions](ArithmeticGeometry/HyperellipticCurves/creation.html)
- [Cyclic Covers of \({\mathbb{P}}^1\)](ArithmeticGeometry/HyperellipticCurves/cyclic-covers.html)
- [Function Field](ArithmeticGeometry/HyperellipticCurves/function_field.html)
- [Introduction](ArithmeticGeometry/HyperellipticCurves/introduction.html)
- [Invariants](ArithmeticGeometry/HyperellipticCurves/invariants-isomorphisms.html)
- [Jacobians](ArithmeticGeometry/HyperellipticCurves/jacobian.html)
- [Jacobians over Number Fields or \({\mathbb{Q}}\)](ArithmeticGeometry/HyperellipticCurves/jacobians-number-fields.html)
- [Kummer Surfaces](ArithmeticGeometry/HyperellipticCurves/kummer-surfaces.html)
- [Rational Points and Group Structure over Finite Fields](ArithmeticGeometry/HyperellipticCurves/point_structures_jacobian.html)
- [Points on the Jacobian](ArithmeticGeometry/HyperellipticCurves/points-jac.html)
- [Points](ArithmeticGeometry/HyperellipticCurves/points.html)
- [Points on the Kummer Surface](ArithmeticGeometry/HyperellipticCurves/points_kummer.html)
- [Reduced Automorphism Group and Reduced Isomorphism Testing](ArithmeticGeometry/HyperellipticCurves/redisomor-check.html)
- [Richelot Isogenies](ArithmeticGeometry/HyperellipticCurves/richelot.html)
- [Operations on Curves](ArithmeticGeometry/HyperellipticCurves/structure_operations.html)
- [Isomorphisms and Transformations](ArithmeticGeometry/HyperellipticCurves/transforms.html)
- [Two-Selmer Set of a Curve](ArithmeticGeometry/HyperellipticCurves/two-selmer-set.html)
- [Functionality](ArithmeticGeometry/HypergeometricMotives/Functionality.html)
- [Introduction](ArithmeticGeometry/HypergeometricMotives/Introduction.html)
- [Jacobi Motives](ArithmeticGeometry/HypergeometricMotives/Jacobi_motives.html)
- [Examples](ArithmeticGeometry/HypergeometricMotives/hypergeom-examples.html)
- [Jacobi Motive Functionality](ArithmeticGeometry/HypergeometricMotives/jacmot-functionality.html)
- [Jacobi Motive Examples](ArithmeticGeometry/HypergeometricMotives/jacobi-examples.html)
- [Arithmetic with \(L\)-series](ArithmeticGeometry/LFunctions/arithmetic.html)
- [Built-in \(L\)-series](ArithmeticGeometry/LFunctions/builtin.html)
- [Computing \(L\)-values](ArithmeticGeometry/LFunctions/computing.html)
- [Advanced Examples](ArithmeticGeometry/LFunctions/examples.html)
- [General \(L\)-series](ArithmeticGeometry/LFunctions/general.html)
- [Accessing the Invariants](ArithmeticGeometry/LFunctions/invariants.html)
- [Modifying the \(L\)-function](ArithmeticGeometry/LFunctions/modifyL.html)
- [Overview](ArithmeticGeometry/LFunctions/overview.html)
- [Precision](ArithmeticGeometry/LFunctions/precision.html)
- [Verbose Printing](ArithmeticGeometry/LFunctions/verbose.html)
- [Attributes of Genus One Models](ArithmeticGeometry/ModelsOfGenusOneCurves/attributes.html)
- [Covariants and Contravariants for Genus One Models](ArithmeticGeometry/ModelsOfGenusOneCurves/covariants.html)
- [Genus One Models as Coverings](ArithmeticGeometry/ModelsOfGenusOneCurves/coverings.html)
- [Creation of Genus One Models](ArithmeticGeometry/ModelsOfGenusOneCurves/creation.html)
- [Equivalence of Genus One Models](ArithmeticGeometry/ModelsOfGenusOneCurves/equivalence.html)
- [Examples](ArithmeticGeometry/ModelsOfGenusOneCurves/extended-examples.html)
- [Minimisation and Reduction](ArithmeticGeometry/ModelsOfGenusOneCurves/g1minred.html)
- [Introduction](ArithmeticGeometry/ModelsOfGenusOneCurves/introduction.html)
- [Invariants for Genus One Models](ArithmeticGeometry/ModelsOfGenusOneCurves/invariants.html)
- [Local Solubility](ArithmeticGeometry/ModelsOfGenusOneCurves/local-solubility.html)
- [Families of Elliptic Curves with Prescribed \(n\)-Torsion](ArithmeticGeometry/ModelsOfGenusOneCurves/n-torsion-families.html)
- [Transformations between Genus One Models](ArithmeticGeometry/ModelsOfGenusOneCurves/transformations.html)
- [Creation from Invariants](ArithmeticGeometry/PlaneQuartics/quartic_from_invariants.html)
- [Invariants](ArithmeticGeometry/PlaneQuartics/quartic_invariants.html)
- [Isomorphisms](ArithmeticGeometry/PlaneQuartics/quartic_isomorphisms.html)
- [Twists](ArithmeticGeometry/PlaneQuartics/quartic_twists.html)
- [Conics](ArithmeticGeometry/RationalCurvesAndConics/crvcon-sec:models.html)
- [Rational Points on Conics](ArithmeticGeometry/RationalCurvesAndConics/crvcon-sec:ratpoints.html)
- [Automorphisms](ArithmeticGeometry/RationalCurvesAndConics/crvgen0-sec:autom.html)
- [Introduction](ArithmeticGeometry/RationalCurvesAndConics/crvgen0-sec:introduction.html)
- [Isomorphisms](ArithmeticGeometry/RationalCurvesAndConics/crvgen0-sec:isoms.html)
- [Rational Curves and Conics](ArithmeticGeometry/RationalCurvesAndConics/crvgen0-sec:main.html)
- [Local-Global Correspondence](ArithmeticGeometry/RationalCurvesAndConics/local-global.html)
- [Creation Functions](BasicRings/FiniteFields/creation.html)
- [Introduction](BasicRings/FiniteFields/introduction.html)
- [Discrete Logarithms](BasicRings/FiniteFields/log.html)
- [Element Operations](BasicRings/FiniteFields/operation-element.html)
- [Structure Operations](BasicRings/FiniteFields/operation.html)
- [Permutation Polynomials](BasicRings/FiniteFields/permutation-polynomials.html)
- [Polynomials for Finite Fields](BasicRings/FiniteFields/polynomial.html)
- [Arithmetic Functions](BasicRings/Integers/arithmetic-function.html)
- [Combinatorial Functions](BasicRings/Integers/combinatorics.html)
- [Creation Functions](BasicRings/Integers/creation.html)
- [Factorization](BasicRings/Integers/factor.html)
- [Factorization Sequences](BasicRings/Integers/factorization-sequence.html)
- [GCD and LCM](BasicRings/Integers/gcd-lcm.html)
- [Infinities](BasicRings/Integers/infinity.html)
- [Introduction](BasicRings/Integers/introduction.html)
- [Modular Arithmetic](BasicRings/Integers/modular.html)
- [Advanced Factorization Techniques: The Number Field Sieve](BasicRings/Integers/nfs.html)
- [Element Operations](BasicRings/Integers/operation-element.html)
- [Structure Operations](BasicRings/Integers/operation.html)
- [Primes and Primality Testing](BasicRings/Integers/prime.html)
- [Random Numbers](BasicRings/Integers/random.html)
- [Coercion](BasicRings/IntroductionToRings/coercion.html)
- [Other Ring Constructions](BasicRings/IntroductionToRings/creation-other.html)
- [Generic Element Functions](BasicRings/IntroductionToRings/element.html)
- [Generic Ring Functions](BasicRings/IntroductionToRings/generic.html)
- [Ideals and Quotient Rings](BasicRings/IntroductionToRings/ideal-quotient.html)
- [Overview](BasicRings/IntroductionToRings/overview.html)
- [The World of Rings](BasicRings/IntroductionToRings/world.html)
- [Greatest Common Divisors](BasicRings/MultivariatePolynomialRings/common.html)
- [Factorization and Irreducibility](BasicRings/MultivariatePolynomialRings/factorization-irreducibility.html)
- [Polynomials over the Integers](BasicRings/MultivariatePolynomialRings/integer.html)
- [Introduction](BasicRings/MultivariatePolynomialRings/introduction.html)
- [Element Operations](BasicRings/MultivariatePolynomialRings/operation-element.html)
- [Structure Operations](BasicRings/MultivariatePolynomialRings/operation.html)
- [Resultants and Discriminants](BasicRings/MultivariatePolynomialRings/resultant-discriminant.html)
- [Polynomial Rings and Polynomials](BasicRings/MultivariatePolynomialRings/rings.html)
- [Introduction](BasicRings/Nearfields/Introduction.html)
- [Constructing Nearfields](BasicRings/Nearfields/nearfield-code.html)
- [Operations on Elements](BasicRings/Nearfields/nearfield-eltops.html)
- [Automorphisms](BasicRings/Nearfields/nearfield-iso.html)
- [Operations on Nearfields](BasicRings/Nearfields/nearfield-ops.html)
- [Nearfield Planes](BasicRings/Nearfields/nearfield-planes.html)
- [Nearfield Properties](BasicRings/Nearfields/nearfield-properties.html)
- [The Group of Units](BasicRings/Nearfields/nearfield-units.html)
- [Creation Functions](BasicRings/Rationals/creation.html)
- [Element Operations](BasicRings/Rationals/element.html)
- [Introduction](BasicRings/Rationals/introduction.html)
- [Structure Operations](BasicRings/Rationals/operation.html)
- [Creation Functions](BasicRings/RealAndComplexFields/creation.html)
- [Elliptic and Modular Functions](BasicRings/RealAndComplexFields/elliptic-modular.html)
- [Gamma, Bessel and Associated Functions](BasicRings/RealAndComplexFields/gamma-bessel.html)
- [The Hypergeometric Function](BasicRings/RealAndComplexFields/hypergeometric.html)
- [Summation of Infinite Series](BasicRings/RealAndComplexFields/infinite-summation.html)
- [Numerical Integration](BasicRings/RealAndComplexFields/integration1.html)
- [Introduction](BasicRings/RealAndComplexFields/introduction.html)
- [Element Operations](BasicRings/RealAndComplexFields/operation-element.html)
- [Structure Operations](BasicRings/RealAndComplexFields/operation-structure.html)
- [Other Special Functions](BasicRings/RealAndComplexFields/special.html)
- [Theta Functions](BasicRings/RealAndComplexFields/theta.html)
- [Transcendental Functions](BasicRings/RealAndComplexFields/transcendental.html)
- [Dirichlet Characters](BasicRings/ResidueClassRings/dirichlet-characters.html)
- [Elements of Residue Class Rings](BasicRings/ResidueClassRings/elements.html)
- [Ideal Operations](BasicRings/ResidueClassRings/ideal-ops.html)
- [Ideals of \({\mathbb{Z}}\)](BasicRings/ResidueClassRings/integer-ideals.html)
- [Introduction](BasicRings/ResidueClassRings/introduction.html)
- [\({\mathbb{Z}}\) as a Number Field Order](BasicRings/ResidueClassRings/number-field-like.html)
- [Residue Class Rings](BasicRings/ResidueClassRings/residue-class-rings.html)
- [The Unit Group](BasicRings/ResidueClassRings/unit-group.html)
- [Common Divisors and Common Multiples](BasicRings/UnivariatePolynomialRings/common.html)
- [Creation Functions](BasicRings/UnivariatePolynomialRings/creation.html)
- [Factorization](BasicRings/UnivariatePolynomialRings/factorization.html)
- [Special Families of Polynomials](BasicRings/UnivariatePolynomialRings/families-polynomials.html)
- [Polynomials over Finite Fields](BasicRings/UnivariatePolynomialRings/finitefields.html)
- [Ideals and Quotient Rings](BasicRings/UnivariatePolynomialRings/ideal-quotient.html)
- [Polynomials over the Integers](BasicRings/UnivariatePolynomialRings/integer.html)
- [Introduction](BasicRings/UnivariatePolynomialRings/introduction.html)
- [Element Operations](BasicRings/UnivariatePolynomialRings/operation-element.html)
- [Structure Operations](BasicRings/UnivariatePolynomialRings/operation.html)
- [Properties of Codes](CodingTheory/AdditiveCodes/Boolean.html)
- [Invariants of an Additive Code](CodingTheory/AdditiveCodes/access.html)
- [Automorphism Group](CodingTheory/AdditiveCodes/additive-automorphisms.html)
- [Construction of Additive Codes](CodingTheory/AdditiveCodes/creation.html)
- [Operations on Codewords](CodingTheory/AdditiveCodes/element.html)
- [Families of Linear Codes](CodingTheory/AdditiveCodes/families.html)
- [Introduction](CodingTheory/AdditiveCodes/introduction.html)
- [New Codes from Old](CodingTheory/AdditiveCodes/operation.html)
- [The Weight Distribution](CodingTheory/AdditiveCodes/structural.html)
- [Subcodes](CodingTheory/AdditiveCodes/subcode.html)
- [Access Functions](CodingTheory/AlgebraicGeometricCodes/access.html)
- [Creation of an Algebraic Geometric Code](CodingTheory/AlgebraicGeometricCodes/creation.html)
- [Toric Codes](CodingTheory/AlgebraicGeometricCodes/decode-2.html)
- [Decoding AG Codes](CodingTheory/AlgebraicGeometricCodes/decode.html)
- [Introduction](CodingTheory/AlgebraicGeometricCodes/introduction.html)
- [Properties of AG–Codes](CodingTheory/AlgebraicGeometricCodes/properties.html)
- [Properties of Codes](CodingTheory/LinearCodes/Boolean.html)
- [Invariants of a Code](CodingTheory/LinearCodes/access.html)
- [Best Known Linear Codes](CodingTheory/LinearCodes/best-codes.html)
- [Bounds](CodingTheory/LinearCodes/bound.html)
- [Coding Theory and Cryptography](CodingTheory/LinearCodes/codingcrypto.html)
- [Coset Leaders](CodingTheory/LinearCodes/coset-leader.html)
- [Construction of Codes](CodingTheory/LinearCodes/creation.html)
- [Decoding](CodingTheory/LinearCodes/decoding.html)
- [Operations on Codewords](CodingTheory/LinearCodes/element.html)
- [Families of Linear Codes](CodingTheory/LinearCodes/families.html)
- [Automorphism Groups](CodingTheory/LinearCodes/group-action.html)
- [Introduction](CodingTheory/LinearCodes/introduction.html)
- [New Codes from Existing](CodingTheory/LinearCodes/operation.html)
- [The Weight Distribution](CodingTheory/LinearCodes/structural.html)
- [Subcodes](CodingTheory/LinearCodes/subcode.html)
- [Transforms](CodingTheory/LinearCodes/transforms.html)
- [Boolean Predicates](CodingTheory/LinearCodesOverFiniteRings/Boolean.html)
- [Invariants](CodingTheory/LinearCodesOverFiniteRings/access.html)
- [Constructions](CodingTheory/LinearCodesOverFiniteRings/creation.html)
- [Codeword Operations](CodingTheory/LinearCodesOverFiniteRings/element.html)
- [Introduction](CodingTheory/LinearCodesOverFiniteRings/introduction.html)
- [New Codes from Old](CodingTheory/LinearCodesOverFiniteRings/operation.html)
- [Subcodes](CodingTheory/LinearCodesOverFiniteRings/subcode.html)
- [Weight Distributions](CodingTheory/LinearCodesOverFiniteRings/weight-distribution.html)
- [Weight Enumerators](CodingTheory/LinearCodesOverFiniteRings/weight-enumerator.html)
- [Automorphism Groups](CodingTheory/LinearCodesOverZ4/aut_group.html)
- [Constructions for \({\mathbb{Z}}_4\) Codes](CodingTheory/LinearCodesOverZ4/constructions.html)
- [Decoding](CodingTheory/LinearCodesOverZ4/decoding.html)
- [Introduction](CodingTheory/LinearCodesOverZ4/introduction.html)
- [Weight Distributions](CodingTheory/LinearCodesOverZ4/weight-distribution.html)
- [Weight Enumerators](CodingTheory/LinearCodesOverZ4/weight-enumerator.html)
- [Invariants](CodingTheory/LinearCodesOverZ4/z4-invar.html)
- [Introduction](CodingTheory/LowDensityParityCheckCodes/introduction.html)
- [Access Functions](CodingTheory/QuantumCodes/access.html)
- [Automorphism Group](CodingTheory/QuantumCodes/additive-automorphisms.html)
- [Best Known Bounds](CodingTheory/QuantumCodes/best-known-quantum-bounds.html)
- [Best Known Quantum Codes](CodingTheory/QuantumCodes/best-known-quantum-codes.html)
- [New Codes From Old](CodingTheory/QuantumCodes/combining-codes.html)
- [Constructing Quantum Codes](CodingTheory/QuantumCodes/creation.html)
- [Hilbert Spaces](CodingTheory/QuantumCodes/hilbert-space.html)
- [Inner Products and Duals](CodingTheory/QuantumCodes/inner-products.html)
- [Introduction](CodingTheory/QuantumCodes/introduction.html)
- [Weight Distribution and Minimum Weight](CodingTheory/QuantumCodes/weight-distribution.html)
- [The Automorphism Group of an Incidence Structure](Combinatorics/Designs/automorphism-group.html)
- [Elementary Properties of Incidence Structures and Designs](Combinatorics/Designs/boolean.html)
- [Conversion Functions](Combinatorics/Designs/conversion.html)
- [Construction of Incidence Structures and Designs](Combinatorics/Designs/creation.html)
- [Elementary Invariants of a Design](Combinatorics/Designs/design-invariant.html)
- [Identity and Isomorphism](Combinatorics/Designs/equality.html)
- [Incidence Structures, Graphs and Codes](Combinatorics/Designs/graph-code.html)
- [Introduction](Combinatorics/Designs/introduction.html)
- [Elementary Invariants of an Incidence Structure](Combinatorics/Designs/invariant.html)
- [Automorphisms of Matrices](Combinatorics/Designs/matrix-aut.html)
- [Operations on Points and Blocks](Combinatorics/Designs/operation-point-block.html)
- [General Design Constructions](Combinatorics/Designs/operation.html)
- [The Point-Set and Block-Set of an Incidence Structure](Combinatorics/Designs/point-block-set.html)
- [Resolutions, Parallelisms and Parallel Classes](Combinatorics/Designs/resolutions.html)
- [Combinatorial Functions](Combinatorics/EnumerativeCombinatorics/combinatorics.html)
- [Introduction](Combinatorics/EnumerativeCombinatorics/introduction.html)
- [Subsets of a Finite Set](Combinatorics/EnumerativeCombinatorics/subsets.html)
- [Elementary Graph Predicates](Combinatorics/Graphs/Boolean.html)
- [Adjacency and Degree](Combinatorics/Graphs/adjacency-degree.html)
- [Automorphism Group of a Graph or Digraph](Combinatorics/Graphs/automorphism-group-graph.html)
- [Cliques, Independent Sets](Combinatorics/Graphs/clique-independent-set.html)
- [Colourings](Combinatorics/Graphs/colouring.html)
- [Connectedness](Combinatorics/Graphs/connectedness-path-circuit.html)
- [Converting between Graphs and Digraphs](Combinatorics/Graphs/conversion-graph-digraph.html)
- [Directed Trees](Combinatorics/Graphs/directed-tree.html)
- [Maximum Flow, Minimum Cut, and Shortest Paths](Combinatorics/Graphs/flow.html)
- [Graph Databases and Graph Generation](Combinatorics/Graphs/graph-databases.html)
- [Construction of Graphs and Digraphs](Combinatorics/Graphs/graph-digraph.html)
- [Construction from Groups, Codes and Designs](Combinatorics/Graphs/group-code-design.html)
- [Introduction](Combinatorics/Graphs/introduction.html)
- [Elementary Invariants of a Graph](Combinatorics/Graphs/invariant.html)
- [Labelled, Capacitated and Weighted Graphs](Combinatorics/Graphs/labels.html)
- [Matrices and Vector Spaces Associated with a Graph or Digraph](Combinatorics/Graphs/matrix-vector-space.html)
- [Standard Constructions for Graphs](Combinatorics/Graphs/operation.html)
- [Distances, Paths and Circuits in a Graph](Combinatorics/Graphs/path-circuit-graph.html)
- [Planar Graphs](Combinatorics/Graphs/planarity.html)
- [Spanning Trees of a Graph or Digraph](Combinatorics/Graphs/spanning-tree.html)
- [Graphs with a Sparse Representation](Combinatorics/Graphs/sparse-graphs.html)
- [Symmetry and Regularity Properties of Graphs](Combinatorics/Graphs/symmetry-regularity.html)
- [Unions and Products of Graphs](Combinatorics/Graphs/union-product.html)
- [The Vertex–Set and Edge–Set of a Graph](Combinatorics/Graphs/vertex-edge-set.html)
- [Associated \(3\)-Designs](Combinatorics/HadamardMatrices/designs.html)
- [Databases](Combinatorics/HadamardMatrices/hadamard-database.html)
- [Automorphism Group](Combinatorics/HadamardMatrices/hadamard-misc.html)
- [Equivalence Testing](Combinatorics/HadamardMatrices/hadamard.html)
- [Introduction](Combinatorics/HadamardMatrices/introduction.html)
- [Adjacency and Degree](Combinatorics/Multigraphs/multig-adj-deg.html)
- [Connectedness](Combinatorics/Multigraphs/multig-connectedness.html)
- [Construction of Multigraphs](Combinatorics/Multigraphs/multig-constr.html)
- [Conversion Functions](Combinatorics/Multigraphs/multig-conversion.html)
- [Vertex and Edge Decorations](Combinatorics/Multigraphs/multig-decorations.html)
- [Elementary Invariants and Predicates for Multigraphs](Combinatorics/Multigraphs/multig-elem.html)
- [Introduction](Combinatorics/Multigraphs/multig-introduction.html)
- [Standard Construction for Multigraphs](Combinatorics/Multigraphs/multig-stand-constr.html)
- [The Vertex–Set and Edge–Set of Multigraphs](Combinatorics/Multigraphs/multig-vertex-edge-set.html)
- [Planar Graphs](Combinatorics/Multigraphs/planarity.html)
- [Distances, Shortest Paths and Minimum Weight Trees](Combinatorics/Multigraphs/shortest-paths.html)
- [Spanning Trees](Combinatorics/Multigraphs/spanning-tree.html)
- [Maximum Flow and Minimum Cut](Combinatorics/Networks/flow.html)
- [Introduction](Combinatorics/Networks/introduction.html)
- [Construction of Networks](Combinatorics/Networks/network-constr.html)
- [Standard Construction for Networks](Combinatorics/Networks/network-stand-constr.html)
- [Introduction](Combinatorics/PartitionsWordsTableaux/introduction.html)
- [Partitions](Combinatorics/PartitionsWordsTableaux/partitions.html)
- [Tableaux](Combinatorics/PartitionsWordsTableaux/tableaux.html)
- [Words](Combinatorics/PartitionsWordsTableaux/words.html)
- [Creation](Combinatorics/SymmetricFunctions/creation.html)
- [Introduction](Combinatorics/SymmetricFunctions/introduction.html)
- [Transition Matrices](Combinatorics/SymmetricFunctions/matrices.html)
- [Element Operations](Combinatorics/SymmetricFunctions/operation-element.html)
- [Structure Operations](Combinatorics/SymmetricFunctions/operation.html)
- [Maps between Affine Algebras](CommutativeAlgebra/AffineAlgebras/affine-algebra-maps.html)
- [Creation of Affine Algebras](CommutativeAlgebra/AffineAlgebras/creation.html)
- [Affine Algebras which are Fields](CommutativeAlgebra/AffineAlgebras/field.html)
- [Finite Dimensional Affine Algebras](CommutativeAlgebra/AffineAlgebras/finite-dimension-quotient.html)
- [Rings and Fields of Fractions of Affine Algebras](CommutativeAlgebra/AffineAlgebras/fractions.html)
- [Introduction](CommutativeAlgebra/AffineAlgebras/introduction.html)
- [Operations on Affine Algebras](CommutativeAlgebra/AffineAlgebras/operations.html)
- [Changing Related Structures](CommutativeAlgebra/DifferentialRings/changing-attributes-diff-op-rings.html)
- [Changing Related Structures](CommutativeAlgebra/DifferentialRings/changing-attributes-diff-rings.html)
- [Differential Operator Rings](CommutativeAlgebra/DifferentialRings/creation-diff-op-rings.html)
- [Differential Rings and Fields](CommutativeAlgebra/DifferentialRings/creation-diff-rings.html)
- [Element Operations on Differential Operators](CommutativeAlgebra/DifferentialRings/element-operations-diff-op-rings.html)
- [Element Operations on Differential Ring Elements](CommutativeAlgebra/DifferentialRings/element-operations.html)
- [Euclidean Algorithms, GCDs and LCMs](CommutativeAlgebra/DifferentialRings/euclidean-algorithms.html)
- [Ring and Field Extensions](CommutativeAlgebra/DifferentialRings/extensions-ring-diff.html)
- [Ideals and Quotient Rings](CommutativeAlgebra/DifferentialRings/ideal-quotient-ring.html)
- [Introduction](CommutativeAlgebra/DifferentialRings/introduction.html)
- [Newton Polygons](CommutativeAlgebra/DifferentialRings/newton-polygon.html)
- [Factorisation of Operators over Differential Laurent Series Rings](CommutativeAlgebra/DifferentialRings/operators-factorisation-over-laurent-series-ring.html)
- [Differential Operators of Algebraic Functions](CommutativeAlgebra/DifferentialRings/operators-of-functions.html)
- [Rational Solutions](CommutativeAlgebra/DifferentialRings/rational-sols.html)
- [Related Maps](CommutativeAlgebra/DifferentialRings/related-maps-diff-op-rings.html)
- [Related Matrices](CommutativeAlgebra/DifferentialRings/related-matrix.html)
- [Singular Places and Indicial Polynomials](CommutativeAlgebra/DifferentialRings/singularities.html)
- [Structure Operations on Differential Operator Rings](CommutativeAlgebra/DifferentialRings/structure-operations-diff-op-rings.html)
- [Structure Operations on Differential Rings](CommutativeAlgebra/DifferentialRings/structure-operations-diff-rings.html)
- [Symmetric Powers](CommutativeAlgebra/DifferentialRings/symmetric-power.html)
- [Wronskian Matrix](CommutativeAlgebra/DifferentialRings/wronskians.html)
- [Changing Monomial Order](CommutativeAlgebra/GrobnerBases/change-order.html)
- [Changing Coefficient Ring](CommutativeAlgebra/GrobnerBases/change-ring.html)
- [Polynomial Rings and Ideals](CommutativeAlgebra/GrobnerBases/creation.html)
- [Gröbner Bases](CommutativeAlgebra/GrobnerBases/groebner.html)
- [Hilbert-driven Gröbner Basis Construction](CommutativeAlgebra/GrobnerBases/hilbert-groebner.html)
- [Introduction](CommutativeAlgebra/GrobnerBases/introduction.html)
- [Representation and Monomial Orders](CommutativeAlgebra/GrobnerBases/order.html)
- [SAT solver](CommutativeAlgebra/GrobnerBases/sat.html)
- [The Algebra of an Invariant Ring and Algebraic Relations](CommutativeAlgebra/InvariantTheory/algebra-relations.html)
- [Algebraic Group Actions on Polynomials](CommutativeAlgebra/InvariantTheory/algebraic.html)
- [Attributes of Invariant Rings and Fields](CommutativeAlgebra/InvariantTheory/attributes.html)
- [Fundamental Invariants](CommutativeAlgebra/InvariantTheory/fundamental.html)
- [Construction of \(G\)-modules](CommutativeAlgebra/InvariantTheory/gmodule.html)
- [Group Actions on Polynomials](CommutativeAlgebra/InvariantTheory/group-action.html)
- [Introduction](CommutativeAlgebra/InvariantTheory/introduction.html)
- [Invariant Fields](CommutativeAlgebra/InvariantTheory/invariant-field.html)
- [Invariant Rings of Linear Algebraic Groups](CommutativeAlgebra/InvariantTheory/invariant-ring-algebraic.html)
- [Invariant Rings of Finite Groups](CommutativeAlgebra/InvariantTheory/invariant-ring.html)
- [Construction of Invariants of Specified Degree](CommutativeAlgebra/InvariantTheory/invariants.html)
- [Matrix Group Actions on Polynomials](CommutativeAlgebra/InvariantTheory/matrix.html)
- [Minimalization and Homogeneous Module Testing](CommutativeAlgebra/InvariantTheory/minimalize-module.html)
- [The Module of an Invariant Ring](CommutativeAlgebra/InvariantTheory/module.html)
- [Molien Series](CommutativeAlgebra/InvariantTheory/molien.html)
- [Permutation Group Actions on Polynomials](CommutativeAlgebra/InvariantTheory/permutation.html)
- [Primary Invariants](CommutativeAlgebra/InvariantTheory/primary.html)
- [Properties of Invariant Rings](CommutativeAlgebra/InvariantTheory/properties.html)
- [Secondary Invariants](CommutativeAlgebra/InvariantTheory/secondary.html)
- [Steenrod Operations](CommutativeAlgebra/InvariantTheory/steenrod.html)
- [Invariants of the Symmetric Group](CommutativeAlgebra/InvariantTheory/symmetric.html)
- [Verbosity](CommutativeAlgebra/InvariantTheory/verbose.html)
- [Changing Monomial Order](CommutativeAlgebra/LocalPolynomialRings/change-order.html)
- [Changing Coefficient Ring](CommutativeAlgebra/LocalPolynomialRings/change-ring.html)
- [Local Polynomial Rings and Ideals](CommutativeAlgebra/LocalPolynomialRings/creation.html)
- [Dimension of Ideals](CommutativeAlgebra/LocalPolynomialRings/dimension.html)
- [Elements and Local Monomial Orders](CommutativeAlgebra/LocalPolynomialRings/elements-order.html)
- [Standard Bases](CommutativeAlgebra/LocalPolynomialRings/groebner.html)
- [Operations on Ideals](CommutativeAlgebra/LocalPolynomialRings/ideal-operation.html)
- [Introduction](CommutativeAlgebra/LocalPolynomialRings/introduction.html)
- [Tensor Products and Tor](CommutativeAlgebra/ModulesOverMultivariateRings/Tensor.html)
- [Basic Module Constructions](CommutativeAlgebra/ModulesOverMultivariateRings/basic_mod_cons.html)
- [Changing Ring](CommutativeAlgebra/ModulesOverMultivariateRings/change-ring.html)
- [Cohomology Of Coherent Sheaves](CommutativeAlgebra/ModulesOverMultivariateRings/cohomology.html)
- [Basic Creation and Access](CommutativeAlgebra/ModulesOverMultivariateRings/creation-access.html)
- [Module Basics: Embedded and Reduced Modules](CommutativeAlgebra/ModulesOverMultivariateRings/embedded-reduced.html)
- [Free Resolutions](CommutativeAlgebra/ModulesOverMultivariateRings/free-resolution.html)
- [Hilbert Series](CommutativeAlgebra/ModulesOverMultivariateRings/hilbert.html)
- [The Hom Module and Ext](CommutativeAlgebra/ModulesOverMultivariateRings/hom-module-and-ext.html)
- [The Homomorphism Type](CommutativeAlgebra/ModulesOverMultivariateRings/homomorphism-type.html)
- [Introduction](CommutativeAlgebra/ModulesOverMultivariateRings/introduction.html)
- [Module Operations](CommutativeAlgebra/ModulesOverMultivariateRings/operations.html)
- [Monomial Orders](CommutativeAlgebra/ModulesOverMultivariateRings/order.html)
- [Predicates](CommutativeAlgebra/ModulesOverMultivariateRings/predicates.html)
- [Submodules and Quotient Modules](CommutativeAlgebra/ModulesOverMultivariateRings/sub-quo.html)
- [Functions for Polynomial Algebra and Module Generators](CommutativeAlgebra/PolynomialRingIdealOperations/algebra-module.html)
- [Dimension of Ideals](CommutativeAlgebra/PolynomialRingIdealOperations/dimension.html)
- [Creation of Polynomial Rings and their Ideals](CommutativeAlgebra/PolynomialRingIdealOperations/dpoly_ideal_create.html)
- [Elimination](CommutativeAlgebra/PolynomialRingIdealOperations/elimination.html)
- [Extension and Contraction of Ideals](CommutativeAlgebra/PolynomialRingIdealOperations/extension-contraction.html)
- [Hilbert Series and Hilbert Polynomial](CommutativeAlgebra/PolynomialRingIdealOperations/hilbert.html)
- [Homogenization of Ideals](CommutativeAlgebra/PolynomialRingIdealOperations/homogenization.html)
- [First Operations on Ideals](CommutativeAlgebra/PolynomialRingIdealOperations/ideal-operation.html)
- [Introduction](CommutativeAlgebra/PolynomialRingIdealOperations/introduction.html)
- [Maps between Rings](CommutativeAlgebra/PolynomialRingIdealOperations/maps.html)
- [Multiplicities](CommutativeAlgebra/PolynomialRingIdealOperations/multiplicities.html)
- [Normalisation and Noether Normalisation](CommutativeAlgebra/PolynomialRingIdealOperations/normalisations.html)
- [Radical and Decomposition of Ideals](CommutativeAlgebra/PolynomialRingIdealOperations/radical-decomposition.html)
- [Symmetric Polynomials](CommutativeAlgebra/PolynomialRingIdealOperations/symmetric.html)
- [Syzygies](CommutativeAlgebra/PolynomialRingIdealOperations/syzygy-matrix.html)
- [Variable Extension of Ideals](CommutativeAlgebra/PolynomialRingIdealOperations/variable-extension.html)
- [Computation of Varieties](CommutativeAlgebra/PolynomialRingIdealOperations/variety.html)
- [Correlation Functions](Cryptography/PseudoRandomBitSequences/correlation.html)
- [Introduction](Cryptography/PseudoRandomBitSequences/introduction.html)
- [Linear Feedback Shift Registers](Cryptography/PseudoRandomBitSequences/lfsr.html)
- [Decimation](Cryptography/PseudoRandomBitSequences/misc.html)
- [Number Theoretic Bit Generators](Cryptography/PseudoRandomBitSequences/ntbg.html)
- [Automorphism Groups of Finite Simple Groups](FiniteGroups/AlmostSimpleGroups/autgpsimgpss.html)
- [Double Covers of the Alternating and Symmetric Groups](FiniteGroups/AlmostSimpleGroups/double-covers-alt-sym.html)
- [Group Recognition](FiniteGroups/AlmostSimpleGroups/group-recognition.html)
- [Introduction](FiniteGroups/AlmostSimpleGroups/introduction.html)
- [Properties of Finite Groups Of Lie Type](FiniteGroups/AlmostSimpleGroups/properties-lie-groups.html)
- [Atlas Data for the Sporadic Groups](FiniteGroups/AlmostSimpleGroups/related.html)
- [Creating Finite Groups of Lie Type](FiniteGroups/AlmostSimpleGroups/standard.html)
- [Access Functions](FiniteGroups/AutomorphismGroups/access.html)
- [Stored Attributes of an Automorphism Group](FiniteGroups/AutomorphismGroups/attributes.html)
- [Creation of Automorphism Groups](FiniteGroups/AutomorphismGroups/creation.html)
- [Automorphisms](FiniteGroups/AutomorphismGroups/element.html)
- [Holomorphs](FiniteGroups/AutomorphismGroups/holomorphs.html)
- [Introduction](FiniteGroups/AutomorphismGroups/introduction.html)
- [Order Functions](FiniteGroups/AutomorphismGroups/order.html)
- [Representations of an Automorphism Group](FiniteGroups/AutomorphismGroups/representations.html)
- [Construction of an SLP-Group and its Elements](FiniteGroups/BlackBoxGroups/creation.html)
- [Introduction](FiniteGroups/BlackBoxGroups/introduction.html)
- [Operations on Elements](FiniteGroups/BlackBoxGroups/operation-element.html)
- [Arithmetic with Elements](FiniteGroups/BlackBoxGroups/operation.html)
- [Set-Theoretic Operations](FiniteGroups/BlackBoxGroups/set.html)
- [Cocycles](FiniteGroups/CohomologyAndExtensions/cocycles.html)
- [Calculating Cohomology](FiniteGroups/CohomologyAndExtensions/cohomology-groups.html)
- [Creation of a Cohomology Module](FiniteGroups/CohomologyAndExtensions/creation.html)
- [Constructing Distinct Extensions](FiniteGroups/CohomologyAndExtensions/extensions-2.html)
- [Constructing Extensions](FiniteGroups/CohomologyAndExtensions/extensions.html)
- [Finite Group Cohomology](FiniteGroups/CohomologyAndExtensions/group-cohomology.html)
- [Introduction](FiniteGroups/CohomologyAndExtensions/intro.html)
- [Other Operations on Cohomology Modules](FiniteGroups/CohomologyAndExtensions/other-operations.html)
- [The Restriction to a Subgroup](FiniteGroups/CohomologyAndExtensions/restriction.html)
- [Accessing Properties of the Cohomology Module](FiniteGroups/CohomologyAndExtensions/structure-invar.html)
- [Fundamental Groups of 3-Manifolds](FiniteGroups/DatabasesOfGroups/3-manifolds-database.html)
- [Database of ATLAS Groups](FiniteGroups/DatabasesOfGroups/ATLAS-database.html)
- [Automatic Groups of 3-Manifolds](FiniteGroups/DatabasesOfGroups/automatic-group-database.html)
- [Database of Integral Maximal Finite Matrix Groups](FiniteGroups/DatabasesOfGroups/intgps.html)
- [Introduction](FiniteGroups/DatabasesOfGroups/introduction.html)
- [Database of Irreducible Matrix Groups](FiniteGroups/DatabasesOfGroups/irrgp-data.html)
- [Database of Soluble Irreducible Groups](FiniteGroups/DatabasesOfGroups/isolgps-database.html)
- [The \(p\)-groups of Order Dividing \(p^7\)](FiniteGroups/DatabasesOfGroups/p-groups.html)
- [Database of Perfect Groups](FiniteGroups/DatabasesOfGroups/pfgps.html)
- [Database of Primitive Groups](FiniteGroups/DatabasesOfGroups/primgp-data.html)
- [Database of Quasisimple Matrix Groups](FiniteGroups/DatabasesOfGroups/quasisimplematgp-data.html)
- [Database of Finite Quaternionic Matrix Groups](FiniteGroups/DatabasesOfGroups/quatgps.html)
- [Database of Rational Maximal Finite Matrix Groups](FiniteGroups/DatabasesOfGroups/ratgps.html)
- [Metacyclic \(p\)-groups](FiniteGroups/DatabasesOfGroups/search.html)
- [Database of Almost-Simple Groups](FiniteGroups/DatabasesOfGroups/sgdb.html)
- [Database of Simple Groups](FiniteGroups/DatabasesOfGroups/simgps-database.html)
- [Database of Small Groups](FiniteGroups/DatabasesOfGroups/smlgps-database.html)
- [Database of Finite Symplectic Matrix Groups](FiniteGroups/DatabasesOfGroups/symplgps.html)
- [Database of Transitive Groups](FiniteGroups/DatabasesOfGroups/transgp-data.html)
- [Automorphism Group](FiniteGroups/FiniteSolubleGroups/automorphism-group.html)
- [Central Extensions](FiniteGroups/FiniteSolubleGroups/central-extensions.html)
- [Representation Theory](FiniteGroups/FiniteSolubleGroups/character-representation.html)
- [Cosets](FiniteGroups/FiniteSolubleGroups/cosets.html)
- [Creation of a Group](FiniteGroups/FiniteSolubleGroups/definition.html)
- [Elements](FiniteGroups/FiniteSolubleGroups/elements.html)
- [Conjugacy](FiniteGroups/FiniteSolubleGroups/elt-conjugacy.html)
- [New Groups from Existing](FiniteGroups/FiniteSolubleGroups/extension.html)
- [Basic Group Properties](FiniteGroups/FiniteSolubleGroups/group-properties.html)
- [Homomorphisms](FiniteGroups/FiniteSolubleGroups/homomorphisms.html)
- [Introduction](FiniteGroups/FiniteSolubleGroups/introduction.html)
- [More About Presentations](FiniteGroups/FiniteSolubleGroups/more-presentations.html)
- [Normal Subgroups and Subgroup Series](FiniteGroups/FiniteSolubleGroups/normal-series.html)
- [Optimizing Magma Code](FiniteGroups/FiniteSolubleGroups/optimization.html)
- [Generating \(p\)-groups](FiniteGroups/FiniteSolubleGroups/p-groups.html)
- [Quotient Groups](FiniteGroups/FiniteSolubleGroups/quotient.html)
- [Subgroups](FiniteGroups/FiniteSolubleGroups/subgroups.html)
- [\(p\)-Groups of Tame Genus](FiniteGroups/FiniteSolubleGroups/tame.html)
- [Transfer Between Group Categories](FiniteGroups/FiniteSolubleGroups/transfer-functions.html)
- [All Subgroups and Intermediate Subgroups](FiniteGroups/Groups/all-subgroups.html)
- [Transfer Functions Between Group Categories](FiniteGroups/Groups/category-transfer.html)
- [Characters and Representations](FiniteGroups/Groups/character-representation.html)
- [Characteristic Subgroups and Normal Structure](FiniteGroups/Groups/characteristic-subgroup-normal-structure.html)
- [Cohomology](FiniteGroups/Groups/cohomology.html)
- [Conjugacy Classes of Elements](FiniteGroups/Groups/conjugate.html)
- [Construction of a General Group](FiniteGroups/Groups/creation-general.html)
- [Construction of Elements](FiniteGroups/Groups/creation-symmetric.html)
- [Databases of Groups](FiniteGroups/Groups/databases.html)
- [Operations on the Set of Elements](FiniteGroups/Groups/element.html)
- [Standard Groups and Extensions](FiniteGroups/Groups/extension-standard-group.html)
- [Introduction](FiniteGroups/Groups/introduction.html)
- [Standard Subgroup Constructions](FiniteGroups/Groups/operation-subgroup.html)
- [Basic Operations](FiniteGroups/Groups/operation.html)
- [Conjugacy Classes of Subgroups](FiniteGroups/Groups/subgroup.html)
- [The LMG functions](FiniteGroups/MatrixGroupsOverFiniteFields/LMG.html)
- [Unipotent Matrix Groups](FiniteGroups/MatrixGroupsOverFiniteFields/UnipPC.html)
- [Aschbacher Reduction](FiniteGroups/MatrixGroupsOverFiniteFields/aschbacher-reduction.html)
- [Composition Trees for Matrix Groups](FiniteGroups/MatrixGroupsOverFiniteFields/composition-tree.html)
- [Finding Elements with Prescribed Properties](FiniteGroups/MatrixGroupsOverFiniteFields/element-order.html)
- [Finding a Base](FiniteGroups/MatrixGroupsOverFiniteFields/findbase.html)
- [Introduction](FiniteGroups/MatrixGroupsOverFiniteFields/introduction.html)
- [Monte Carlo Algorithms for Subgroups](FiniteGroups/MatrixGroupsOverFiniteFields/monte-carlo.html)
- [Constructive Recognition for Simple Groups](FiniteGroups/MatrixGroupsOverFiniteFields/natural-copy-classical.html)
- [Base and Strong Generating Set](FiniteGroups/MatrixGroupsOverGeneralRings/BSGS-base-strong-generator.html)
- [Abstract Group Predicates](FiniteGroups/MatrixGroupsOverGeneralRings/abstract-group.html)
- [Matrix Group Actions](FiniteGroups/MatrixGroupsOverGeneralRings/actions.html)
- [Automorphism Groups](FiniteGroups/MatrixGroupsOverGeneralRings/automorphisms.html)
- [Representation Theory](FiniteGroups/MatrixGroupsOverGeneralRings/character-representation.html)
- [Normal and Subnormal Subgroups](FiniteGroups/MatrixGroupsOverGeneralRings/characteristic-subgroup-normal-structure.html)
- [Conjugacy](FiniteGroups/MatrixGroupsOverGeneralRings/conjugate.html)
- [Coset Tables and Transversals](FiniteGroups/MatrixGroupsOverGeneralRings/coset-table-transversal.html)
- [Creation of a Matrix Group](FiniteGroups/MatrixGroupsOverGeneralRings/creation-general-linear-group.html)
- [Presentations](FiniteGroups/MatrixGroupsOverGeneralRings/finitely_presented_group.html)
- [Global Properties](FiniteGroups/MatrixGroupsOverGeneralRings/global-properties.html)
- [Homomorphisms](FiniteGroups/MatrixGroupsOverGeneralRings/homomorphism.html)
- [Introduction](FiniteGroups/MatrixGroupsOverGeneralRings/introduction.html)
- [Operations on Matrices](FiniteGroups/MatrixGroupsOverGeneralRings/operation-element.html)
- [Quotient Groups](FiniteGroups/MatrixGroupsOverGeneralRings/quotient.html)
- [Soluble Matrix Groups](FiniteGroups/MatrixGroupsOverGeneralRings/soluble-matrix-group.html)
- [Subgroups](FiniteGroups/MatrixGroupsOverGeneralRings/subgroups.html)
- [Overview](FiniteGroups/MatrixGroupsOverInfiniteFields/Overview.html)
- [Construction of Congruence Homomorphisms](FiniteGroups/MatrixGroupsOverInfiniteFields/congruence.html)
- [Examples](FiniteGroups/MatrixGroupsOverInfiniteFields/examples.html)
- [Testing Finiteness](FiniteGroups/MatrixGroupsOverInfiniteFields/finite-test.html)
- [Hirsch Number and Pr{üfer Rank](FiniteGroups/MatrixGroupsOverInfiniteFields/hirsch_rank.html)
- [Other Functions for Nilpotent Matrix Groups](FiniteGroups/MatrixGroupsOverInfiniteFields/nilpotent_groups.html)
- [Other Properties of Linear Groups](FiniteGroups/MatrixGroupsOverInfiniteFields/other-properties.html)
- [Deciding Virtual Properties of Linear Groups](FiniteGroups/MatrixGroupsOverInfiniteFields/virtual_tests.html)
- [Conjugacy](FiniteGroups/MatrixGroupsOverQAndZ/Conjugacy.html)
- [Conjugacy Tests for Matrices](FiniteGroups/MatrixGroupsOverQAndZ/Conjugacy_Matrices.html)
- [Endomorphisms](FiniteGroups/MatrixGroupsOverQAndZ/Endomorphisms.html)
- [Examples](FiniteGroups/MatrixGroupsOverQAndZ/Examples.html)
- [Perfect Forms and Normalizers](FiniteGroups/MatrixGroupsOverQAndZ/Normalizer.html)
- [New Groups From Others](FiniteGroups/MatrixGroupsOverQAndZ/Others.html)
- [Overview](FiniteGroups/MatrixGroupsOverQAndZ/Overview.html)
- [Invariant Forms](FiniteGroups/MatrixGroupsOverQAndZ/forms.html)
- [Base and Strong Generating Set](FiniteGroups/PermutationGroups/BSGS-base-strong-generator.html)
- [Permutation Group Actions](FiniteGroups/PermutationGroups/actions.html)
- [Automorphism Groups](FiniteGroups/PermutationGroups/automorphisms.html)
- [Building Permutation Groups](FiniteGroups/PermutationGroups/building-groups.html)
- [Ordering of Permutation Groups](FiniteGroups/PermutationGroups/canonical-gens.html)
- [Representation Theory](FiniteGroups/PermutationGroups/character-representation.html)
- [Normal and Subnormal Subgroups](FiniteGroups/PermutationGroups/characteristic-subgroup-normal-structure.html)
- [Cohomology](FiniteGroups/PermutationGroups/cohomology.html)
- [Conjugacy](FiniteGroups/PermutationGroups/conjugate.html)
- [Cosets and Transversals](FiniteGroups/PermutationGroups/cosets-transversals.html)
- [Creation of a Permutation Group](FiniteGroups/PermutationGroups/creation-symmetric.html)
- [Permutation Group Databases](FiniteGroups/PermutationGroups/databases.html)
- [Homomorphisms](FiniteGroups/PermutationGroups/homomorphism.html)
- [Identification](FiniteGroups/PermutationGroups/identification.html)
- [Introduction](FiniteGroups/PermutationGroups/introduction.html)
- [Permutation Representations of Linear Groups](FiniteGroups/PermutationGroups/linear-group.html)
- [Elementary Properties of a Group](FiniteGroups/PermutationGroups/operation.html)
- [Ordered Partition Stacks](FiniteGroups/PermutationGroups/ordered-partn-stack.html)
- [Permutations](FiniteGroups/PermutationGroups/permutations.html)
- [Presentations](FiniteGroups/PermutationGroups/presentations.html)
- [Quotient Groups](FiniteGroups/PermutationGroups/quotient.html)
- [Subgroups](FiniteGroups/PermutationGroups/subgroup.html)
- [Creation of Reductive Groups](FiniteGroups/ReductiveGroups/creation.html)
- [Elements of Reductive Groups](FiniteGroups/ReductiveGroups/elements.html)
- [Introduction](FiniteGroups/ReductiveGroups/introduction.html)
- [Operations on Reductive Groups](FiniteGroups/ReductiveGroups/ops.html)
- [Properties of Reductive Groups](FiniteGroups/ReductiveGroups/properties.html)
- [Automorphism Groups](FinitelyPresentedGroups/AbelianGroups/autgp.html)
- [Representation Theory](FinitelyPresentedGroups/AbelianGroups/character-representation.html)
- [Cohomology](FinitelyPresentedGroups/AbelianGroups/cohomology.html)
- [Coset Spaces](FinitelyPresentedGroups/AbelianGroups/coset-space.html)
- [Construction of a Finitely Presented Abelian Group and its Elements](FinitelyPresentedGroups/AbelianGroups/creation.html)
- [Canonical Decomposition](FinitelyPresentedGroups/AbelianGroups/decomposition.html)
- [Elements](FinitelyPresentedGroups/AbelianGroups/elements.html)
- [Construction of a Generic Abelian Group](FinitelyPresentedGroups/AbelianGroups/generic-abelian.html)
- [General Group Properties](FinitelyPresentedGroups/AbelianGroups/group-Boolean.html)
- [The Hom Functor](FinitelyPresentedGroups/AbelianGroups/hom.html)
- [Homomorphisms](FinitelyPresentedGroups/AbelianGroups/homomorphisms.html)
- [Introduction](FinitelyPresentedGroups/AbelianGroups/introduction.html)
- [Invariants of an Abelian Group](FinitelyPresentedGroups/AbelianGroups/invariant.html)
- [Operations on Elements](FinitelyPresentedGroups/AbelianGroups/operation-element.html)
- [Set-Theoretic Operations](FinitelyPresentedGroups/AbelianGroups/set.html)
- [Standard Constructions and Conversions](FinitelyPresentedGroups/AbelianGroups/standard-construction.html)
- [Subgroup Chains](FinitelyPresentedGroups/AbelianGroups/subgroup-chains.html)
- [Subgroup Constructions](FinitelyPresentedGroups/AbelianGroups/subgroup-constructions.html)
- [Construction of Subgroups and Quotient Groups](FinitelyPresentedGroups/AbelianGroups/subgroup-quotient.html)
- [Automatic Groups](FinitelyPresentedGroups/AutomaticAndHyperbolicGroups/automatic-groups.html)
- [Hyperbolic Groups](FinitelyPresentedGroups/AutomaticAndHyperbolicGroups/hyperbolic-groups.html)
- [Introduction](FinitelyPresentedGroups/AutomaticAndHyperbolicGroups/introduction.html)
- [Constructing and Accessing Braid Groups](FinitelyPresentedGroups/BraidGroups/braid-groups-construction.html)
- [Creating Elements of a Braid Group](FinitelyPresentedGroups/BraidGroups/braid-groups-element-creation.html)
- [Working with Elements of a Braid Group](FinitelyPresentedGroups/BraidGroups/braid-groups-elements.html)
- [Introduction](FinitelyPresentedGroups/BraidGroups/braid-groups-introduction.html)
- [Homomorphisms](FinitelyPresentedGroups/BraidGroups/homomorphism.html)
- [Coset Spaces and Tables](FinitelyPresentedGroups/FPGroups/coset-space-table.html)
- [Some Developed Examples](FinitelyPresentedGroups/FPGroups/developed-examples.html)
- [Finite FP-Groups](FinitelyPresentedGroups/FPGroups/finite-fp-groups.html)
- [Construction of an FP-Group](FinitelyPresentedGroups/FPGroups/fp-group-construction.html)
- [Properties of an FP-Group](FinitelyPresentedGroups/FPGroups/fp-group-properties.html)
- [Homomorphisms](FinitelyPresentedGroups/FPGroups/homomorphism.html)
- [Introduction](FinitelyPresentedGroups/FPGroups/introduction.html)
- [\(KG\)-Modules](FinitelyPresentedGroups/FPGroups/kg-modules.html)
- [Quotient Group Methods](FinitelyPresentedGroups/FPGroups/quotient.html)
- [Simplification](FinitelyPresentedGroups/FPGroups/simplification.html)
- [Standard Constructions](FinitelyPresentedGroups/FPGroups/standard.html)
- [Subgroups of Finite Index](FinitelyPresentedGroups/FPGroups/subgroup-fin-index.html)
- [Subgroups](FinitelyPresentedGroups/FPGroups/subgroup-general.html)
- [The Construction of Free Semigroups and their Elements](FinitelyPresentedGroups/FinitelyPresentedSemigroups/creation.html)
- [Extensions](FinitelyPresentedGroups/FinitelyPresentedSemigroups/extension.html)
- [Introduction](FinitelyPresentedGroups/FinitelyPresentedSemigroups/introduction.html)
- [Elementary Tietze Transformations](FinitelyPresentedGroups/FinitelyPresentedSemigroups/modification-Tietze.html)
- [String Operations on Words](FinitelyPresentedGroups/FinitelyPresentedSemigroups/operation-element.html)
- [Elementary Operators for Words](FinitelyPresentedGroups/FinitelyPresentedSemigroups/operation.html)
- [Specification of a Presentation](FinitelyPresentedGroups/FinitelyPresentedSemigroups/presentation.html)
- [Subsemigroups, Ideals and Quotients](FinitelyPresentedGroups/FinitelyPresentedSemigroups/subsemigroup-ideal-quotient.html)
- [The Automorphism Group of a Free Group](FinitelyPresentedGroups/FreeGroups/autfree.html)
- [Free Groups and Words](FinitelyPresentedGroups/FreeGroups/creation.html)
- [Introduction](FinitelyPresentedGroups/FreeGroups/introduction.html)
- [Finitely Generated Subgroups of Free Groups](FinitelyPresentedGroups/FreeGroups/subfree.html)
- [Operations on the Set of Group Elements](FinitelyPresentedGroups/GroupsDefinedByRewriteSystems/Set.html)
- [Arithmetic with Words](FinitelyPresentedGroups/GroupsDefinedByRewriteSystems/arithmetic.html)
- [Conversion to a Finitely Presented Group](FinitelyPresentedGroups/GroupsDefinedByRewriteSystems/conversion.html)
- [Constructing Confluent Presentations](FinitelyPresentedGroups/GroupsDefinedByRewriteSystems/creation.html)
- [Homomorphisms](FinitelyPresentedGroups/GroupsDefinedByRewriteSystems/homomorphism.html)
- [Introduction](FinitelyPresentedGroups/GroupsDefinedByRewriteSystems/introduction.html)
- [Properties of a Rewrite Group](FinitelyPresentedGroups/GroupsDefinedByRewriteSystems/properties.html)
- [Construction of an SLP-Group and its Elements](FinitelyPresentedGroups/GroupsOfStraightLinePrograms/creation.html)
- [Addition of Extra Generators](FinitelyPresentedGroups/GroupsOfStraightLinePrograms/extra-generators.html)
- [Creating Homomorphisms](FinitelyPresentedGroups/GroupsOfStraightLinePrograms/homomorphisms.html)
- [Introduction](FinitelyPresentedGroups/GroupsOfStraightLinePrograms/introduction.html)
- [Operations on Elements](FinitelyPresentedGroups/GroupsOfStraightLinePrograms/operation-element.html)
- [Arithmetic with Elements](FinitelyPresentedGroups/GroupsOfStraightLinePrograms/operation.html)
- [Set-Theoretic Operations](FinitelyPresentedGroups/GroupsOfStraightLinePrograms/set.html)
- [Finite FP-Groups](FinitelyPresentedGroups/IntroductionToFPGroups/Finite.html)
- [Properties of an FP-group](FinitelyPresentedGroups/IntroductionToFPGroups/Properties.html)
- [Construction of FP-Groups](FinitelyPresentedGroups/IntroductionToFPGroups/fp-group-construction.html)
- [Homomorphisms of FP-Groups](FinitelyPresentedGroups/IntroductionToFPGroups/homomorphism.html)
- [Introduction](FinitelyPresentedGroups/IntroductionToFPGroups/introduction.html)
- [Quotient Groups](FinitelyPresentedGroups/IntroductionToFPGroups/quotient.html)
- [Subgroups](FinitelyPresentedGroups/IntroductionToFPGroups/subgroup-general.html)
- [Set Operations](FinitelyPresentedGroups/MonoidsGivenByRewriteSystems/Set.html)
- [Conversion to a Finitely Presented Monoid](FinitelyPresentedGroups/MonoidsGivenByRewriteSystems/conversion.html)
- [Construction of a Rewrite Monoid](FinitelyPresentedGroups/MonoidsGivenByRewriteSystems/creation.html)
- [Homomorphisms](FinitelyPresentedGroups/MonoidsGivenByRewriteSystems/homomorphism.html)
- [Introduction](FinitelyPresentedGroups/MonoidsGivenByRewriteSystems/introduction.html)
- [Basic Operations](FinitelyPresentedGroups/MonoidsGivenByRewriteSystems/operation.html)
- [Access Functions for Groups](FinitelyPresentedGroups/PolycyclicGroups/access.html)
- [Normal Structure and Characteristic Subgroups](FinitelyPresentedGroups/PolycyclicGroups/characteristic-subgroup-normal-structure.html)
- [Conjugacy](FinitelyPresentedGroups/PolycyclicGroups/conjugate.html)
- [Conversion between Categories](FinitelyPresentedGroups/PolycyclicGroups/conversion.html)
- [Coset Spaces](FinitelyPresentedGroups/PolycyclicGroups/coset-space.html)
- [General Group Properties](FinitelyPresentedGroups/PolycyclicGroups/group-boolean.html)
- [Introduction](FinitelyPresentedGroups/PolycyclicGroups/introduction.html)
- [Polycyclic Groups and Polycyclic Presentations](FinitelyPresentedGroups/PolycyclicGroups/polycyclic-groups.html)
- [Power Groups](FinitelyPresentedGroups/PolycyclicGroups/power-group.html)
- [Representation Theory](FinitelyPresentedGroups/PolycyclicGroups/representation-theory.html)
- [Set-Theoretic Operations in a Group](FinitelyPresentedGroups/PolycyclicGroups/set.html)
- [Subgroups, Quotient Groups, Homomorphisms and Extensions](FinitelyPresentedGroups/PolycyclicGroups/subgroup-quotient-homomorphism-extension.html)
- [The Subgroup Structure](FinitelyPresentedGroups/PolycyclicGroups/subgroup-structure.html)
- [Structures Associated with a Plane](Geometry/FinitePlanes/access.html)
- [Arcs](Geometry/FinitePlanes/arc.html)
- [Properties of Planes](Geometry/FinitePlanes/boolean.html)
- [The Collineation Group of a Plane](Geometry/FinitePlanes/collineation-group.html)
- [Construction of a Plane](Geometry/FinitePlanes/creation.html)
- [Planes and Designs](Geometry/FinitePlanes/designs.html)
- [Identity and Isomorphism](Geometry/FinitePlanes/equality.html)
- [Planes, Graphs and Codes](Geometry/FinitePlanes/graph-code.html)
- [Introduction](Geometry/FinitePlanes/introduction.html)
- [Numerical Invariants of a Plane](Geometry/FinitePlanes/invariant.html)
- [Operations on Points and Lines](Geometry/FinitePlanes/operation.html)
- [The Point-Set and Line-Set of a Plane](Geometry/FinitePlanes/point-line-set.html)
- [The Set of Points and Set of Lines](Geometry/FinitePlanes/point-line.html)
- [The Connection between Projective and Affine Planes](Geometry/FinitePlanes/projective-affine.html)
- [Subplanes](Geometry/FinitePlanes/subplane.html)
- [The Defining Points of a Plane](Geometry/FinitePlanes/support.html)
- [Translation Planes](Geometry/FinitePlanes/translation-planes.html)
- [Unitals](Geometry/FinitePlanes/unital.html)
- [Elementary Invariants](Geometry/IncidenceGeometry/access.html)
- [Automorphism Group and Correlation Group](Geometry/IncidenceGeometry/automorphisms.html)
- [C-Groups](Geometry/IncidenceGeometry/cgroups.html)
- [Conversion Functions](Geometry/IncidenceGeometry/conversion-functions.html)
- [\(C^+\)-Groups](Geometry/IncidenceGeometry/cplusgroups.html)
- [Construction of Incidence and Coset Geometries](Geometry/IncidenceGeometry/creation.html)
- [Diagram of an Incidence Geometry](Geometry/IncidenceGeometry/diagram.html)
- [Intersection Properties of Coset Geometries](Geometry/IncidenceGeometry/intersectionproperties.html)
- [Introduction](Geometry/IncidenceGeometry/introduction.html)
- [Primitivity Properties on Coset Geometries](Geometry/IncidenceGeometry/primitivityproperties.html)
- [Properties of Incidence Geometries and Coset Geometries](Geometry/IncidenceGeometry/properties.html)
- [Residues](Geometry/IncidenceGeometry/residues.html)
- [Shadow Spaces](Geometry/IncidenceGeometry/shadow-space.html)
- [Shadows](Geometry/IncidenceGeometry/shadows.html)
- [Truncations](Geometry/IncidenceGeometry/truncations.html)
- [Basic Combinatorics of Polytopes and Polyhedra](Geometry/Polytopes/basic-combinatorics.html)
- [The Combinatorics of Polytopes](Geometry/Polytopes/combinatorics.html)
- [Cones and Polyhedra](Geometry/Polytopes/cones-polyhedra.html)
- [Introduction and First Examples](Geometry/Polytopes/introduction.html)
- [Polytopes, Cones and Polyhedra](Geometry/Polytopes/polytopes-cones-polyhedra.html)
- [Toric Lattices](Geometry/Polytopes/toric-lattices.html)
- [Places](GlobalFields/AlgebraicFunctionFields/Places.html)
- [Automorphism Group](GlobalFields/AlgebraicFunctionFields/automorphism-group.html)
- [Creation of Algebraic Function Fields and their Orders](GlobalFields/AlgebraicFunctionFields/creation.html)
- [Function Field Database](GlobalFields/AlgebraicFunctionFields/database.html)
- [Differentials](GlobalFields/AlgebraicFunctionFields/differentials.html)
- [Divisors in OM representation](GlobalFields/AlgebraicFunctionFields/divisors-in-om-representation.html)
- [Divisors](GlobalFields/AlgebraicFunctionFields/divisors.html)
- [Elements](GlobalFields/AlgebraicFunctionFields/elements.html)
- [Galois Groups](GlobalFields/AlgebraicFunctionFields/galois.html)
- [Global Function Fields](GlobalFields/AlgebraicFunctionFields/global.html)
- [Homomorphisms](GlobalFields/AlgebraicFunctionFields/hom.html)
- [Ideal Operations](GlobalFields/AlgebraicFunctionFields/ideal-op.html)
- [Ideals in OM Representation](GlobalFields/AlgebraicFunctionFields/ideal-rep.html)
- [Ideals](GlobalFields/AlgebraicFunctionFields/ideals.html)
- [Introduction](GlobalFields/AlgebraicFunctionFields/introduction.html)
- [The Montes Algorithm](GlobalFields/AlgebraicFunctionFields/montes.html)
- [General Structure Invariants](GlobalFields/AlgebraicFunctionFields/structure-invar.html)
- [Structure Predicates](GlobalFields/AlgebraicFunctionFields/structure-predicates.html)
- [Related Structures](GlobalFields/AlgebraicFunctionFields/structure-related.html)
- [Subfields](GlobalFields/AlgebraicFunctionFields/subfields.html)
- [Weil Descent](GlobalFields/AlgebraicFunctionFields/weil_descent.html)
- [Absolute Field](GlobalFields/AlgebraicallyClosedFields/absolute.html)
- [Creation of Elements](GlobalFields/AlgebraicallyClosedFields/creation.html)
- [Introduction](GlobalFields/AlgebraicallyClosedFields/introduction.html)
- [Element Operations](GlobalFields/AlgebraicallyClosedFields/operation-element.html)
- [Ring Predicates and Properties](GlobalFields/AlgebraicallyClosedFields/predicate.html)
- [Properties](GlobalFields/AlgebraicallyClosedFields/property.html)
- [Related Structures](GlobalFields/AlgebraicallyClosedFields/related.html)
- [Representation](GlobalFields/AlgebraicallyClosedFields/representation.html)
- [Simplification](GlobalFields/AlgebraicallyClosedFields/simplify.html)
- [Creation of Structures](GlobalFields/AlgebraicallyClosedFields/structure.html)
- [Arithmetic](GlobalFields/ArtinRepresentations/arithmetic.html)
- [Constructing Artin Representations](GlobalFields/ArtinRepresentations/functions.html)
- [Basic Invariants](GlobalFields/ArtinRepresentations/invariants.html)
- [Implementation Notes](GlobalFields/ArtinRepresentations/notes.html)
- [Overview](GlobalFields/ArtinRepresentations/overview.html)
- [Attributes](GlobalFields/ClassFieldTheory/attributes.html)
- [Automorphisms](GlobalFields/ClassFieldTheory/automorphisms.html)
- [Conversion to Number Fields](GlobalFields/ClassFieldTheory/conversion.html)
- [Creation](GlobalFields/ClassFieldTheory/creation.html)
- [Galois Module Structure](GlobalFields/ClassFieldTheory/galois-module-structure.html)
- [Group Theoretic Functions](GlobalFields/ClassFieldTheory/group-theory.html)
- [Introduction](GlobalFields/ClassFieldTheory/introduction.html)
- [Invariants](GlobalFields/ClassFieldTheory/invariants.html)
- [Norm Equations](GlobalFields/ClassFieldTheory/norm-equations.html)
- [Ray Class Groups](GlobalFields/ClassFieldTheoryForGlobalFunctionFields/class-groups.html)
- [Analytic Theory](GlobalFields/ClassFieldTheoryForGlobalFunctionFields/drinfeld.html)
- [Creation of Class Fields](GlobalFields/ClassFieldTheoryForGlobalFunctionFields/fields.html)
- [Enumeration of Places](GlobalFields/ClassFieldTheoryForGlobalFunctionFields/place-enumeration.html)
- [Properties of Class Fields](GlobalFields/ClassFieldTheoryForGlobalFunctionFields/properties.html)
- [Related Functions](GlobalFields/ClassFieldTheoryForGlobalFunctionFields/related.html)
- [The Ring of Twisted Polynomials](GlobalFields/ClassFieldTheoryForGlobalFunctionFields/twisted-polynomials.html)
- [The Ring of Witt Vectors of Finite Length](GlobalFields/ClassFieldTheoryForGlobalFunctionFields/witt-rings.html)
- [Creation Functions](GlobalFields/CyclotomicFields/creation.html)
- [Element Operations](GlobalFields/CyclotomicFields/element.html)
- [Introduction](GlobalFields/CyclotomicFields/introduction.html)
- [Structure Operations](GlobalFields/CyclotomicFields/structure.html)
- [Introduction](GlobalFields/DirichletAndHeckeCharacters/introduction.html)
- [Totally Real and Positive](GlobalFields/EtaleAlgebras/TotRealTotPos.html)
- [Attributes](GlobalFields/EtaleAlgebras/attr.html)
- [Completion](GlobalFields/EtaleAlgebras/completion.html)
- [Complex Multiplication](GlobalFields/EtaleAlgebras/complex-mult.html)
- [Complex Conjugation](GlobalFields/EtaleAlgebras/complex_conj.html)
- [Construction](GlobalFields/EtaleAlgebras/construct.html)
- [Chinese Remainder Theorem](GlobalFields/EtaleAlgebras/crt.html)
- [Elements](GlobalFields/EtaleAlgebras/elements.html)
- [Factorization and Primes](GlobalFields/EtaleAlgebras/factor_primes.html)
- [Over Order Graph](GlobalFields/EtaleAlgebras/graph_over_orders.html)
- [Homomorphisms](GlobalFields/EtaleAlgebras/homs.html)
- [Ideal Class Monoid](GlobalFields/EtaleAlgebras/ideal_class_monoid.html)
- [Ideals](GlobalFields/EtaleAlgebras/ideals.html)
- [Ideals of Index](GlobalFields/EtaleAlgebras/ideals_of_index.html)
- [Intermediate Ideals](GlobalFields/EtaleAlgebras/intermediate_ideals.html)
- [Introduction](GlobalFields/EtaleAlgebras/intro.html)
- [Low Cohen Macauley Type](GlobalFields/EtaleAlgebras/low_cohen_macauley_type.html)
- [Minimal Generators](GlobalFields/EtaleAlgebras/minimal_generators.html)
- [Orders of Algebras](GlobalFields/EtaleAlgebras/orders.html)
- [Over Orders](GlobalFields/EtaleAlgebras/over_orders.html)
- [Picard Group](GlobalFields/EtaleAlgebras/picard_group.html)
- [Printing and Saving](GlobalFields/EtaleAlgebras/print_save.html)
- [Quotients](GlobalFields/EtaleAlgebras/quotients.html)
- [Short Element and Small Representative](GlobalFields/EtaleAlgebras/short_elt_small_rep.html)
- [Trace and Norm](GlobalFields/EtaleAlgebras/trace_norm.html)
- [Weak Classes](GlobalFields/EtaleAlgebras/weak_classes.html)
- [Weak Testing](GlobalFields/EtaleAlgebras/weak_testing.html)
- [Automorphism Groups](GlobalFields/GaloisGroupsAndAutomorphisms/automorphism.html)
- [Galois Cohomology](GlobalFields/GaloisGroupsAndAutomorphisms/cohomology.html)
- [Automorphisms of Fields](GlobalFields/GaloisGroupsAndAutomorphisms/fld_auts.html)
- [Galois Groups](GlobalFields/GaloisGroupsAndAutomorphisms/galois.html)
- [Subfields](GlobalFields/GaloisGroupsAndAutomorphisms/subfields.html)
- [Acknowledgement](GlobalFields/NumberFields/acknowledgement.html)
- [Class Group and Unit Group](GlobalFields/NumberFields/class-unit-group.html)
- [Creation Functions](GlobalFields/NumberFields/creation.html)
- [Number Field Database](GlobalFields/NumberFields/database.html)
- [Places and Divisors](GlobalFields/NumberFields/divisors.html)
- [Fields with a Labelled Embedding](GlobalFields/NumberFields/embedded-number-fields.html)
- [Galois Theory](GlobalFields/NumberFields/galois-theory.html)
- [Introduction](GlobalFields/NumberFields/introduction.html)
- [Solving Norm Equations](GlobalFields/NumberFields/norm-equation.html)
- [Element Operations](GlobalFields/NumberFields/operation-element.html)
- [Structure Operations](GlobalFields/NumberFields/operation.html)
- [Acknowledgement](GlobalFields/NumberFieldsAndOrders/acknowledgement.html)
- [Creation Functions](GlobalFields/NumberFieldsAndOrders/creation.html)
- [Places and Divisors](GlobalFields/NumberFieldsAndOrders/divisors.html)
- [Diophantine Equations](GlobalFields/NumberFieldsAndOrders/equation.html)
- [Ideal Class Groups](GlobalFields/NumberFieldsAndOrders/ideal-class-group.html)
- [Ideal Operations](GlobalFields/NumberFieldsAndOrders/ideal-op.html)
- [Ideals in OM Representation](GlobalFields/NumberFieldsAndOrders/ideal-rep.html)
- [Ideals and Quotients](GlobalFields/NumberFieldsAndOrders/ideal.html)
- [Introduction](GlobalFields/NumberFieldsAndOrders/introduction.html)
- [The Montes Algorithm](GlobalFields/NumberFieldsAndOrders/montes.html)
- [Element Operations](GlobalFields/NumberFieldsAndOrders/operation-element.html)
- [Structure Operations](GlobalFields/NumberFieldsAndOrders/operation.html)
- [Real Precision](GlobalFields/NumberFieldsAndOrders/precision.html)
- [Printing](GlobalFields/NumberFieldsAndOrders/printing.html)
- [Unit Groups](GlobalFields/NumberFieldsAndOrders/unit-group.html)
- [Creation of Structures](GlobalFields/QuadraticFields/creation.html)
- [Special Element Operations](GlobalFields/QuadraticFields/elements.html)
- [Introduction](GlobalFields/QuadraticFields/introduction.html)
- [Special Functions for Ideals](GlobalFields/QuadraticFields/special-ideals.html)
- [Operations on Structures](GlobalFields/QuadraticFields/structure_ops.html)
- [Creation Functions](GlobalFields/RationalFunctionFields/creation.html)
- [Element Operations](GlobalFields/RationalFunctionFields/element.html)
- [Introduction](GlobalFields/RationalFunctionFields/introduction.html)
- [Structure Operations](GlobalFields/RationalFunctionFields/operation.html)
- [Padé-Hermite Approximants](GlobalFields/RationalFunctionFields/padehermite.html)
- [Class Groups](LatticesQuadraticForms/BinaryQuadraticForms/class-group.html)
- [Creation Functions](LatticesQuadraticForms/BinaryQuadraticForms/creation.html)
- [Operations on Forms](LatticesQuadraticForms/BinaryQuadraticForms/form-operations.html)
- [Introduction](LatticesQuadraticForms/BinaryQuadraticForms/introduction.html)
- [Class Invariants](LatticesQuadraticForms/BinaryQuadraticForms/invar-2.html)
- [Elliptic and Modular Invariants](LatticesQuadraticForms/BinaryQuadraticForms/invar.html)
- [Basic Invariants](LatticesQuadraticForms/BinaryQuadraticForms/invariants.html)
- [Discrete Logarithms](LatticesQuadraticForms/BinaryQuadraticForms/log.html)
- [Reduced Forms](LatticesQuadraticForms/BinaryQuadraticForms/reduced-forms.html)
- [Attributes of Lattices](LatticesQuadraticForms/Lattices/attributes.html)
- [Creation of Lattices](LatticesQuadraticForms/Lattices/creation-2.html)
- [Presentation of Lattices](LatticesQuadraticForms/Lattices/creation.html)
- [Testing Matrices for Definiteness](LatticesQuadraticForms/Lattices/definite.html)
- [Lattice Elements](LatticesQuadraticForms/Lattices/element.html)
- [Minima and Element Enumeration](LatticesQuadraticForms/Lattices/enumeration.html)
- [Genera and Spinor Genera](LatticesQuadraticForms/Lattices/genus.html)
- [Introduction](LatticesQuadraticForms/Lattices/introduction.html)
- [Database of Lattices](LatticesQuadraticForms/Lattices/latdb.html)
- [Properties of Lattices](LatticesQuadraticForms/Lattices/lattice-properties.html)
- [Construction of New Lattices](LatticesQuadraticForms/Lattices/new-construction.html)
- [Orthogonalization](LatticesQuadraticForms/Lattices/ortho.html)
- [Reduction of Matrices and Lattices](LatticesQuadraticForms/Lattices/reduction.html)
- [Theta Series as Modular Forms](LatticesQuadraticForms/Lattices/theta_modfrm.html)
- [Voronoi Cells, Holes and Covering Radius](LatticesQuadraticForms/Lattices/voronoi.html)
- [Examples](LatticesQuadraticForms/LatticesOverNumberFields/examples.html)
- [Introduction](LatticesQuadraticForms/LatticesOverNumberFields/introduction.html)
- [Lorentzian Lattices](LatticesQuadraticForms/LatticesOverNumberFields/lorentzian-lattices.html)
- [Number Field Lattice Elements](LatticesQuadraticForms/LatticesOverNumberFields/numberfieldlatticeelements.html)
- [Number Field Lattices](LatticesQuadraticForms/LatticesOverNumberFields/numberfieldlattices.html)
- [Lattices from Matrix Groups](LatticesQuadraticForms/LatticesWithGroupAction/G-lattices.html)
- [Automorphism Group and Isometry Testing](LatticesQuadraticForms/LatticesWithGroupAction/auto-isom.html)
- [Introduction](LatticesQuadraticForms/LatticesWithGroupAction/introduction.html)
- [Equivalence](LatticesQuadraticForms/QuadraticForms/Equivalence.html)
- [Constructions and Conversions](LatticesQuadraticForms/QuadraticForms/constructions-conversions.html)
- [Introduction](LatticesQuadraticForms/QuadraticForms/introduction.html)
- [Isotropic Subspaces](LatticesQuadraticForms/QuadraticForms/isotropic.html)
- [Local Invariants](LatticesQuadraticForms/QuadraticForms/local-invariants.html)
- [Automorphisms](LieTheory/ChevalleyGroups/automorphisms.html)
- [Constructing Groups of Lie Type](LieTheory/ChevalleyGroups/construction.html)
- [Building Groups of Lie Type](LieTheory/ChevalleyGroups/create-new-root-datum.html)
- [Curtis–Steinberg–Tits Presentations](LieTheory/ChevalleyGroups/cst-presentations.html)
- [Constructing Elements](LieTheory/ChevalleyGroups/element-construction.html)
- [Operations on Elements](LieTheory/ChevalleyGroups/element-operators.html)
- [Properties of Groups of Lie Type](LieTheory/ChevalleyGroups/element-properties.html)
- [Algebraic Homomorphisms](LieTheory/ChevalleyGroups/homomorphism.html)
- [Introduction](LieTheory/ChevalleyGroups/introduction.html)
- [Properties of Elements](LieTheory/ChevalleyGroups/more-element-operators.html)
- [Operations on Groups of Lie Type](LieTheory/ChevalleyGroups/operations.html)
- [Representations](LieTheory/ChevalleyGroups/representations.html)
- [Roots, Coroots and Weights](LieTheory/ChevalleyGroups/roots-coroots-weights.html)
- [Sylow Subgroups](LieTheory/ChevalleyGroups/sylow-subgroups.html)
- [Twisted Tori](LieTheory/ChevalleyGroups/twisted-tori.html)
- [Standard Action](LieTheory/CoxeterGroups/action-root-coroot-2.html)
- [Root Actions](LieTheory/CoxeterGroups/action-root-coroot.html)
- [Converting Between Types of Coxeter Group](LieTheory/CoxeterGroups/construct-2.html)
- [Constructing Coxeter Groups](LieTheory/CoxeterGroups/construct.html)
- [Braid Groups](LieTheory/CoxeterGroups/group-braid.html)
- [Operations on Elements](LieTheory/CoxeterGroups/group-elt-op.html)
- [Operations on Coxeter Groups](LieTheory/CoxeterGroups/group-op.html)
- [Properties of Coxeter Groups](LieTheory/CoxeterGroups/group-prop.html)
- [\(W\)-graphs](LieTheory/CoxeterGroups/group-wgraphs.html)
- [Introduction](LieTheory/CoxeterGroups/introduction.html)
- [Related Structures](LieTheory/CoxeterGroups/related.html)
- [Roots, Coroots and Reflections](LieTheory/CoxeterGroups/root-data-roots.html)
- [Reflections](LieTheory/CoxeterGroups/rootrefl.html)
- [Reflection Subgroups](LieTheory/CoxeterGroups/subgroups.html)
- [Cartan Matrices](LieTheory/CoxeterSystems/cartanmat.html)
- [Coxeter Graphs](LieTheory/CoxeterSystems/coxetergraph.html)
- [Coxeter Matrices](LieTheory/CoxeterSystems/coxetermat.html)
- [Dynkin Digraphs](LieTheory/CoxeterSystems/dynkindigraph.html)
- [Finite and Affine Coxeter Groups](LieTheory/CoxeterSystems/finiteaffine.html)
- [Introduction](LieTheory/CoxeterSystems/introduction.html)
- [Related Structures](LieTheory/CoxeterSystems/related-2.html)
- [Hyperbolic Groups](LieTheory/CoxeterSystems/related.html)
- [Root Systems and Root Data](LieTheory/Introduction/descriptions-2.html)
- [Lie Algebras and Groups of Lie Type](LieTheory/Introduction/descriptions-3.html)
- [Highest Weight Representations](LieTheory/Introduction/descriptions-4.html)
- [Universal Enveloping Algebras and Quantum Groups](LieTheory/Introduction/descriptions-5.html)
- [Descriptions of Coxeter Groups](LieTheory/Introduction/descriptions.html)
- [Coxeter and Reflection Groups](LieTheory/Introduction/groups.html)
- [Affine Kac–Moody Lie Algebras](LieTheory/KacMoodyLieAlgebras/affine.html)
- [Generalized Cartan Matrices](LieTheory/KacMoodyLieAlgebras/cartan.html)
- [Introduction](LieTheory/KacMoodyLieAlgebras/introduction.html)
- [Lie Algebras Generated by Extremal Elements](LieTheory/LieAlgebras/alglieextr.html)
- [Automorphisms of Classical-type Reductive Algebras](LieTheory/LieAlgebras/automorphisms-classical.html)
- [Constructors for Lie Algebras](LieTheory/LieAlgebras/construct.html)
- [Construction of Elements](LieTheory/LieAlgebras/element-construct.html)
- [Operations on Elements](LieTheory/LieAlgebras/elements.html)
- [Families of Lie Algebras](LieTheory/LieAlgebras/family-construct.html)
- [Finitely Presented Lie Algebras](LieTheory/LieAlgebras/fp-construct.html)
- [Homomorphisms](LieTheory/LieAlgebras/homomorphisms.html)
- [Introduction](LieTheory/LieAlgebras/introduction.html)
- [Operations for Matrix Lie Algebras](LieTheory/LieAlgebras/matrix.html)
- [The Natural Module](LieTheory/LieAlgebras/natural-module.html)
- [Nilpotent Orbits in Simple Lie Algebras](LieTheory/LieAlgebras/nilpotent-orbits.html)
- [Operations on Lie Algebras](LieTheory/LieAlgebras/operation.html)
- [Properties of Lie Algebras and Ideals](LieTheory/LieAlgebras/property.html)
- [Restrictable Lie Algebras](LieTheory/LieAlgebras/restrictable.html)
- [Solvable and Nilpotent Lie Algebras Classification](LieTheory/LieAlgebras/solvable-nilpotent.html)
- [Construction of Subalgebras, Ideals and Quotients](LieTheory/LieAlgebras/sub-construct.html)
- [Semisimple Subalgebras of Simple Lie Algebras](LieTheory/LieAlgebras/sub-sssdb.html)
- [Operations on Subalgebras and Ideals](LieTheory/LieAlgebras/sub.html)
- [Universal Enveloping Algebras](LieTheory/LieAlgebras/universal_enveloping_algebras.html)
- [Automorphisms](LieTheory/QuantumGroups/automorphisms.html)
- [Background](LieTheory/QuantumGroups/background.html)
- [Elements of the Canonical Basis](LieTheory/QuantumGroups/canbas.html)
- [Construction](LieTheory/QuantumGroups/construct.html)
- [Operations on Elements](LieTheory/QuantumGroups/elts-ops.html)
- [Gauss Numbers](LieTheory/QuantumGroups/gauss.html)
- [Hopf Algebra Structure](LieTheory/QuantumGroups/hopf-structure.html)
- [Introduction](LieTheory/QuantumGroups/introduction.html)
- [Kashiwara Operators](LieTheory/QuantumGroups/kashiwara-ops.html)
- [The Path Model](LieTheory/QuantumGroups/path-model.html)
- [Homomorphisms to the Universal Enveloping Algebra](LieTheory/QuantumGroups/q.html)
- [Related Structures](LieTheory/QuantumGroups/rel-struct.html)
- [Representations](LieTheory/QuantumGroups/representations.html)
- [Roots, Coroots and Reflections](LieTheory/ReflectionGroups/action.html)
- [Construction of Finite Complex Reflection Groups](LieTheory/ReflectionGroups/create-group-refl-complex.html)
- [Construction of Real Reflection Groups](LieTheory/ReflectionGroups/create-group-refl-real.html)
- [Construction of Reflection Groups](LieTheory/ReflectionGroups/create-group-refl.html)
- [Introduction](LieTheory/ReflectionGroups/introduction.html)
- [Operations on Reflection Groups](LieTheory/ReflectionGroups/operations.html)
- [Properties of Reflection Groups](LieTheory/ReflectionGroups/properties.html)
- [Construction of Pseudo-reflections](LieTheory/ReflectionGroups/reflections.html)
- [Related Structures](LieTheory/ReflectionGroups/related.html)
- [Other Functions for Representation Decompositions](LieTheory/RepresentationsOfLieGroupsAndAlgebras/representation-other.html)
- [Operations on Weight Multisets](LieTheory/RepresentationsOfLieGroupsAndAlgebras/representation-properties.html)
- [Subgroups of Small Rank](LieTheory/RepresentationsOfLieGroupsAndAlgebras/representation-small-database.html)
- [Constructing Representations](LieTheory/RepresentationsOfLieGroupsAndAlgebras/representations-constructing-2.html)
- [Constructing Weight Multisets](LieTheory/RepresentationsOfLieGroupsAndAlgebras/representations-constructing.html)
- [Introduction](LieTheory/RepresentationsOfLieGroupsAndAlgebras/representations-introduction.html)
- [Operations on Representations](LieTheory/RepresentationsOfLieGroupsAndAlgebras/representations-operations.html)
- [Subalgebras of su(d)](LieTheory/RepresentationsOfLieGroupsAndAlgebras/sub-subsu.html)
- [Constants Associated with Root Data](LieTheory/RootData/constants-root-datum.html)
- [Building Root Data](LieTheory/RootData/create-new-root-datum.html)
- [Constructing Root Data](LieTheory/RootData/create-root-datum.html)
- [Introduction](LieTheory/RootData/introduction.html)
- [Morphisms of Root Data](LieTheory/RootData/morphisms-root-datum.html)
- [Operations on Root Data](LieTheory/RootData/operators-root-dtm.html)
- [Properties of Root Data](LieTheory/RootData/properties-root-datum.html)
- [Related Structures](LieTheory/RootData/related-structures.html)
- [Roots, Coroots and Weights](LieTheory/RootData/roots-coroots-weights.html)
- [Constructing Root Systems](LieTheory/RootSystems/construct-root-system.html)
- [Building Root Systems](LieTheory/RootSystems/create-new-root-system.html)
- [Introduction](LieTheory/RootSystems/introduction.html)
- [Operators on Root Systems](LieTheory/RootSystems/operators-root-sys.html)
- [Properties of Root Systems](LieTheory/RootSystems/properties-root-system.html)
- [Related Structures](LieTheory/RootSystems/related-structures.html)
- [Roots and Coroots](LieTheory/RootSystems/roots-coroots-weights.html)
- [Accessors and Expansion](LocalFields/AlgebraicPowerSeriesRings/accessors.html)
- [Arithmetic](LocalFields/AlgebraicPowerSeriesRings/arith.html)
- [Basics](LocalFields/AlgebraicPowerSeriesRings/basics.html)
- [Constructors](LocalFields/AlgebraicPowerSeriesRings/cons.html)
- [Introduction](LocalFields/AlgebraicPowerSeriesRings/introduction.html)
- [Modifiers](LocalFields/AlgebraicPowerSeriesRings/mods.html)
- [Predicates](LocalFields/AlgebraicPowerSeriesRings/preds.html)
- [Creation Functions](LocalFields/GaloisRings/creation.html)
- [Introduction](LocalFields/GaloisRings/introduction.html)
- [Element Operations](LocalFields/GaloisRings/operation-element.html)
- [Structure Operations](LocalFields/GaloisRings/operation.html)
- [Constructions](LocalFields/GeneralPAdicExtensions/construction.html)
- [Elements Operations](LocalFields/GeneralPAdicExtensions/elements.html)
- [Automorphisms and Galois Theory](LocalFields/GeneralPAdicExtensions/galois.html)
- [Introduction](LocalFields/GeneralPAdicExtensions/introduction.html)
- [Homomorphisms](LocalFields/GeneralPAdicExtensions/maps.html)
- [Maximal Order](LocalFields/GeneralPAdicExtensions/maximal-order.html)
- [Operations with Fields](LocalFields/GeneralPAdicExtensions/operations.html)
- [Polynomial Factorization](LocalFields/GeneralPAdicExtensions/poly_fact.html)
- [Creation of Lazy Series Rings](LocalFields/LazyPowerSeriesRings/creation.html)
- [Elements](LocalFields/LazyPowerSeriesRings/elements.html)
- [Introduction](LocalFields/LazyPowerSeriesRings/introduction.html)
- [Functions on Lazy Series Rings](LocalFields/LazyPowerSeriesRings/ring_ops.html)
- [Arithmetic](LocalFields/LocalGaloisRepresentations/arithmetic.html)
- [Creating Galois Representations](LocalFields/LocalGaloisRepresentations/creating.html)
- [Advanced Examples](LocalFields/LocalGaloisRepresentations/fields-2.html)
- [Changing Fields](LocalFields/LocalGaloisRepresentations/fields.html)
- [Basic Invariants](LocalFields/LocalGaloisRepresentations/invariants.html)
- [Overview](LocalFields/LocalGaloisRepresentations/overview.html)
- [Changing Precision](LocalFields/LocalGaloisRepresentations/precision.html)
- [Introduction](LocalFields/NewtonPolygons/introduction.html)
- [Polynomials Associated with Newton Polygons](LocalFields/NewtonPolygons/newton-polynomials.html)
- [Newton Polygons](LocalFields/NewtonPolygons/newton.html)
- [Using Newton Polygons to Find Roots of Polynomials over Series Rings](LocalFields/NewtonPolygons/poly-ops.html)
- [Finding Valuations of Roots of Polynomials from Newton Polygons](LocalFields/NewtonPolygons/val.html)
- [Automorphisms of Local Rings and Fields](LocalFields/PAdicRingsAndTheirExtensions/autos.html)
- [Background](LocalFields/PAdicRingsAndTheirExtensions/background.html)
- [Class Field Theory](LocalFields/PAdicRingsAndTheirExtensions/class-fields.html)
- [Completions](LocalFields/PAdicRingsAndTheirExtensions/completion.html)
- [Element Constructions and Conversions](LocalFields/PAdicRingsAndTheirExtensions/consconv-element.html)
- [Creation of Local Rings and Fields](LocalFields/PAdicRingsAndTheirExtensions/creation.html)
- [Roots of Elements](LocalFields/PAdicRingsAndTheirExtensions/elt-roots.html)
- [Extensions](LocalFields/PAdicRingsAndTheirExtensions/extensions.html)
- [Introduction](LocalFields/PAdicRingsAndTheirExtensions/introduction.html)
- [Elementary Invariants](LocalFields/PAdicRingsAndTheirExtensions/invariants.html)
- [Linear Algebra](LocalFields/PAdicRingsAndTheirExtensions/lin-alg.html)
- [Operations on Elements](LocalFields/PAdicRingsAndTheirExtensions/operation-element.html)
- [Overview of the \(p\)-adics in Magma](LocalFields/PAdicRingsAndTheirExtensions/overview.html)
- [Polynomials](LocalFields/PAdicRingsAndTheirExtensions/polynomials.html)
- [Operations on Structures](LocalFields/PAdicRingsAndTheirExtensions/structure-operations.html)
- [Exact \(p\)-Adic Rings](LocalFields/PAdicRingsAndTheirExtensions/xpadic.html)
- [Creation Functions](LocalFields/PowerLaurentAndPuiseuxSeries/creation.html)
- [Extensions of Series Rings](LocalFields/PowerLaurentAndPuiseuxSeries/extensions.html)
- [The Hypergeometric Series](LocalFields/PowerLaurentAndPuiseuxSeries/hypergeometric.html)
- [Introduction](LocalFields/PowerLaurentAndPuiseuxSeries/introduction.html)
- [Basic Element Operations](LocalFields/PowerLaurentAndPuiseuxSeries/operation-element.html)
- [Structure Operations](LocalFields/PowerLaurentAndPuiseuxSeries/operation-structure.html)
- [Polynomials over Series Rings](LocalFields/PowerLaurentAndPuiseuxSeries/polynomials.html)
- [Transcendental Functions](LocalFields/PowerLaurentAndPuiseuxSeries/transcendental.html)
- [Introduction](LocalFields/SeriesRingsOverPAdicRings/introduction.html)
- [Matrices and Modules](LocalFields/SeriesRingsOverPAdicRings/matrices-modules.html)
- [Creation Functions](LocalFields/ValuationRings/creation.html)
- [Element Operations](LocalFields/ValuationRings/element.html)
- [Introduction](LocalFields/ValuationRings/introduction.html)
- [Structure Operations](LocalFields/ValuationRings/structure.html)
- [Introduction](MagmaLanguage/DebuggingMagmaCode/introduction.html)
- [Using the Debugger](MagmaLanguage/DebuggingMagmaCode/using-debugger.html)
- [Set and Get](MagmaLanguage/EnvironmentAndOptions/Set-Get.html)
- [Command Line Options](MagmaLanguage/EnvironmentAndOptions/command-options.html)
- [Environment Variables](MagmaLanguage/EnvironmentAndOptions/environment-variable.html)
- [The Magma Help System](MagmaLanguage/EnvironmentAndOptions/help.html)
- [History Files](MagmaLanguage/EnvironmentAndOptions/history-files.html)
- [History](MagmaLanguage/EnvironmentAndOptions/history.html)
- [Other Information Procedures](MagmaLanguage/EnvironmentAndOptions/info.html)
- [Introduction](MagmaLanguage/EnvironmentAndOptions/introduction.html)
- [The Magma Line Editor](MagmaLanguage/EnvironmentAndOptions/line-editor.html)
- [Verbose Levels](MagmaLanguage/EnvironmentAndOptions/verbose.html)
- [Attributes](MagmaLanguage/FunctionsProceduresAndPackages/attribute.html)
- [Functions and Procedures](MagmaLanguage/FunctionsProceduresAndPackages/function-procedure.html)
- [Introduction](MagmaLanguage/FunctionsProceduresAndPackages/introduction.html)
- [Packages](MagmaLanguage/FunctionsProceduresAndPackages/package.html)
- [User-Defined Types](MagmaLanguage/FunctionsProceduresAndPackages/type.html)
- [User-defined Verbose Flags](MagmaLanguage/FunctionsProceduresAndPackages/verbose.html)
- [Asynchronous I/O](MagmaLanguage/InputOutput/asyncio.html)
- [Creating Names](MagmaLanguage/InputOutput/create-name.html)
- [Input](MagmaLanguage/InputOutput/input.html)
- [Introduction](MagmaLanguage/InputOutput/intro.html)
- [Managing Multiple I/O Objects](MagmaLanguage/InputOutput/io-many.html)
- [I/O Operations](MagmaLanguage/InputOutput/io-operations.html)
- [I/O Objects](MagmaLanguage/InputOutput/io.html)
- [Loading Program Files](MagmaLanguage/InputOutput/load.html)
- [Logging a Session](MagmaLanguage/InputOutput/logging.html)
- [Printing](MagmaLanguage/InputOutput/print.html)
- [Character Strings](MagmaLanguage/InputOutput/string.html)
- [System Calls](MagmaLanguage/InputOutput/system-calls-2.html)
- [Memory Usage](MagmaLanguage/InputOutput/system-calls.html)
- [Saving and Restoring Workspaces](MagmaLanguage/InputOutput/workspace.html)
- [Assignment](MagmaLanguage/MagmaSemantics/assignment.html)
- [Terminology](MagmaLanguage/MagmaSemantics/definition.html)
- [Dynamic Typing](MagmaLanguage/MagmaSemantics/dynamic-typing.html)
- [Evaluation in Magma](MagmaLanguage/MagmaSemantics/evaluation.html)
- [Introduction](MagmaLanguage/MagmaSemantics/introduction.html)
- [Appendix B: Reserved Words](MagmaLanguage/MagmaSemantics/precedence-2.html)
- [Appendix A: Precedence](MagmaLanguage/MagmaSemantics/precedence.html)
- [Procedure Expressions](MagmaLanguage/MagmaSemantics/procedure-expression.html)
- [Reference Arguments](MagmaLanguage/MagmaSemantics/reference-argument.html)
- [Scope](MagmaLanguage/MagmaSemantics/scope.html)
- [Traps for Young Players](MagmaLanguage/MagmaSemantics/trap.html)
- [Uninitialized Identifiers](MagmaLanguage/MagmaSemantics/uninitialized-identifier.html)
- [GPUs](MagmaLanguage/Parallelism/GPUs.html)
- [Ideal Class Group of Algebraic Number Fields](MagmaLanguage/Parallelism/classgroup.html)
- [Linear Codes](MagmaLanguage/Parallelism/codes.html)
- [Distributed Computation for Internal Algorithms](MagmaLanguage/Parallelism/distributed.html)
- [Gröbner Bases](MagmaLanguage/Parallelism/groebner-bases.html)
- [Integer Factorisation](MagmaLanguage/Parallelism/integer-factorisation.html)
- [Introduction](MagmaLanguage/Parallelism/intro.html)
- [Magma Kernel Distributed Parallelism](MagmaLanguage/Parallelism/kernel-distributed-parallelism.html)
- [Integral Lattices](MagmaLanguage/Parallelism/lattices.html)
- [Linear Algebra](MagmaLanguage/Parallelism/linear-algebra.html)
- [User-Implemented Distributed Parallelism](MagmaLanguage/Parallelism/par-user.html)
- [Polynomial Rings](MagmaLanguage/Parallelism/poly.html)
- [Polynomial System Solving](MagmaLanguage/Parallelism/polynomial-system-solving.html)
- [Timing](MagmaLanguage/Parallelism/timing.html)
- [Assignment](MagmaLanguage/StatementsAndExpressions/assignment.html)
- [Boolean Values](MagmaLanguage/StatementsAndExpressions/boolean.html)
- [Coercion](MagmaLanguage/StatementsAndExpressions/coercion.html)
- [Comments and Continuation](MagmaLanguage/StatementsAndExpressions/comment-continuation.html)
- [Conditional Statements and Expressions](MagmaLanguage/StatementsAndExpressions/conditional.html)
- [Error Handling Statements](MagmaLanguage/StatementsAndExpressions/error-handling.html)
- [Runtime Evaluation: the eval Expression](MagmaLanguage/StatementsAndExpressions/eval-expression.html)
- [Identifiers](MagmaLanguage/StatementsAndExpressions/identifier.html)
- [Introduction](MagmaLanguage/StatementsAndExpressions/introduction.html)
- [Iterative Statements](MagmaLanguage/StatementsAndExpressions/iteration.html)
- [Miscellaneous](MagmaLanguage/StatementsAndExpressions/misc.html)
- [Random Object Generation](MagmaLanguage/StatementsAndExpressions/random.html)
- [Starting, Interrupting and Terminating](MagmaLanguage/StatementsAndExpressions/startup-interrupt-quit.html)
- [Timing](MagmaLanguage/StatementsAndExpressions/timing.html)
- [Types, Category Names, and Structures](MagmaLanguage/StatementsAndExpressions/type.html)
- [The where \(\ldots\) is Construction](MagmaLanguage/StatementsAndExpressions/where-is.html)
- [Exploring the Call Graph](MagmaLanguage/TheMagmaProfiler/call-graph.html)
- [Introduction](MagmaLanguage/TheMagmaProfiler/intro.html)
- [Profiler Basics](MagmaLanguage/TheMagmaProfiler/profiler-basics.html)
- [Recursion and the Profiler](MagmaLanguage/TheMagmaProfiler/recursion-profiler.html)
- [Elementary Properties](MatricesLinearAlgebra/Matrices/access.html)
- [Elementary Arithmetic](MatricesLinearAlgebra/Matrices/arithmetic.html)
- [Canonical Forms](MatricesLinearAlgebra/Matrices/canonical.html)
- [Changing Ring](MatricesLinearAlgebra/Matrices/change-ring.html)
- [Creation of Matrices](MatricesLinearAlgebra/Matrices/creation.html)
- [Accessing or Modifying Entries](MatricesLinearAlgebra/Matrices/entries.html)
- [Introduction](MatricesLinearAlgebra/Matrices/introduction.html)
- [Building Block Matrices](MatricesLinearAlgebra/Matrices/join.html)
- [Miscellaneous Operations on Matrices](MatricesLinearAlgebra/Matrices/misc.html)
- [Numerical Linear Algebra](MatricesLinearAlgebra/Matrices/numerical-linalg.html)
- [Orders of Invertible Matrices](MatricesLinearAlgebra/Matrices/order.html)
- [Predicates](MatricesLinearAlgebra/Matrices/predicates.html)
- [Minimal and Characteristic Polynomials and Eigenvalues](MatricesLinearAlgebra/Matrices/properties-2.html)
- [Determinant and Other Properties](MatricesLinearAlgebra/Matrices/properties.html)
- [Nullspaces and Solutions of Systems](MatricesLinearAlgebra/Matrices/solution-equation.html)
- [Introduction](MatricesLinearAlgebra/PolarSpaces/Introduction.html)
- [Polar Spaces More Generally](MatricesLinearAlgebra/PolarSpaces/SpcPlr.html)
- [Classical Groups](MatricesLinearAlgebra/PolarSpaces/classical.html)
- [Constructing Polar Spaces](MatricesLinearAlgebra/PolarSpaces/constructions.html)
- [Inner Products](MatricesLinearAlgebra/PolarSpaces/innerprod.html)
- [Invariant Forms](MatricesLinearAlgebra/PolarSpaces/invform.html)
- [Isometries and Similarities](MatricesLinearAlgebra/PolarSpaces/isom-sim.html)
- [Lie Algebras and Bilinear Forms](MatricesLinearAlgebra/PolarSpaces/liealg.html)
- [Reflexive Forms](MatricesLinearAlgebra/PolarSpaces/reflexive-forms.html)
- [The Standard Forms](MatricesLinearAlgebra/PolarSpaces/standard.html)
- [Isotropic and Singular Vectors and Subspaces](MatricesLinearAlgebra/PolarSpaces/structure.html)
- [Wall Forms](MatricesLinearAlgebra/PolarSpaces/wallform.html)
- [Accessing Sparse Matrices](MatricesLinearAlgebra/SparseMatrices/access.html)
- [Elementary Arithmetic](MatricesLinearAlgebra/SparseMatrices/arithmetic.html)
- [Changing Ring](MatricesLinearAlgebra/SparseMatrices/change-ring.html)
- [Conversion to and from Dense Matrices](MatricesLinearAlgebra/SparseMatrices/conversion.html)
- [Creation of Sparse Matrices](MatricesLinearAlgebra/SparseMatrices/creation.html)
- [Determinant and Other Properties](MatricesLinearAlgebra/SparseMatrices/determinant.html)
- [Accessing or Modifying Entries](MatricesLinearAlgebra/SparseMatrices/entries.html)
- [Introduction](MatricesLinearAlgebra/SparseMatrices/introduction.html)
- [Building Block Matrices](MatricesLinearAlgebra/SparseMatrices/join.html)
- [Minimal and Characteristic Polynomials and Eigenvalues](MatricesLinearAlgebra/SparseMatrices/min-char-poly.html)
- [Multiplying Vectors or Matrices by Sparse Matrices](MatricesLinearAlgebra/SparseMatrices/multiply.html)
- [Non-trivial Properties](MatricesLinearAlgebra/SparseMatrices/non-trivial.html)
- [Predicates](MatricesLinearAlgebra/SparseMatrices/predicates.html)
- [Linear Systems (Structured Gaussian Elimination)](MatricesLinearAlgebra/SparseMatrices/solution.html)
- [Bases](MatricesLinearAlgebra/VectorSpaces/basis.html)
- [Creation of Vector Spaces and Arithmetic with Vectors](MatricesLinearAlgebra/VectorSpaces/creation-arithmetic.html)
- [Introduction](MatricesLinearAlgebra/VectorSpaces/introduction.html)
- [Operations with Linear Transformations](MatricesLinearAlgebra/VectorSpaces/linear-transformation.html)
- [Changing the Coefficient Field](MatricesLinearAlgebra/VectorSpaces/modification-coefficient-field.html)
- [Basic Operations](MatricesLinearAlgebra/VectorSpaces/operation.html)
- [Reducing Vectors Relative to a Subspace](MatricesLinearAlgebra/VectorSpaces/reducing-vectors.html)
- [Subspaces, Quotient Spaces and Homomorphisms](MatricesLinearAlgebra/VectorSpaces/subspace-quotient-homomorphism.html)
- [Basic Properties](ModularArithmeticGeometry/AlgebraicModularForms/basic-properties.html)
- [Relation to Other Modular Forms](ModularArithmeticGeometry/AlgebraicModularForms/cmf.html)
- [Creation of Spaces of Algebraic Modular Forms](ModularArithmeticGeometry/AlgebraicModularForms/creation.html)
- [Eigenspace Decomposition and Eigenforms](ModularArithmeticGeometry/AlgebraicModularForms/eigenforms.html)
- [Elements](ModularArithmeticGeometry/AlgebraicModularForms/elements.html)
- [Further Examples](ModularArithmeticGeometry/AlgebraicModularForms/further-examples.html)
- [Introduction](ModularArithmeticGeometry/AlgebraicModularForms/introduction.html)
- [Operators](ModularArithmeticGeometry/AlgebraicModularForms/operators.html)
- [Creation of Subspaces](ModularArithmeticGeometry/AlgebraicModularForms/subspaces.html)
- [Arithmetic Fuchsian Groups](ModularArithmeticGeometry/ArithmeticFuchsianGroupsAndShimuraCurves/ArithmeticFuchsianGroups.html)
- [Fundamental Domains](ModularArithmeticGeometry/ArithmeticFuchsianGroupsAndShimuraCurves/fundamental-domains.html)
- [Triangle Groups](ModularArithmeticGeometry/ArithmeticFuchsianGroupsAndShimuraCurves/triangle-groups.html)
- [Unit Disc](ModularArithmeticGeometry/ArithmeticFuchsianGroupsAndShimuraCurves/unit-disc.html)
- [Subspaces and Decomposition](ModularArithmeticGeometry/BrandtModules/ModBrdt:Subspaces.html)
- [Brandt Module Creation](ModularArithmeticGeometry/BrandtModules/ModBrdt:brandt-modules.html)
- [Dimensions of Spaces](ModularArithmeticGeometry/BrandtModules/ModBrdt:dimension-formulas.html)
- [Brandt Modules Over \(F_q[t]\)](ModularArithmeticGeometry/BrandtModules/ModBrdt:fldfunrat.html)
- [Introduction](ModularArithmeticGeometry/BrandtModules/ModBrdt:introduction.html)
- [Hecke Operators](ModularArithmeticGeometry/BrandtModules/hecke-operators.html)
- [\(q\)-Expansions](ModularArithmeticGeometry/BrandtModules/qexpansions.html)
- [Congruence Subgroups](ModularArithmeticGeometry/CongruenceSubgroupsOfPSL2R/Congruence-subgroups.html)
- [Farey Symbols and Fundamental Domains](ModularArithmeticGeometry/CongruenceSubgroupsOfPSL2R/Farey-Symbols.html)
- [Points and Geodesics](ModularArithmeticGeometry/CongruenceSubgroupsOfPSL2R/Geodesics.html)
- [Elements of \({\operatorname{PSL}}_2({\mathbb{R}})\)](ModularArithmeticGeometry/CongruenceSubgroupsOfPSL2R/GrpPSL2Elt.html)
- [Graphical Output](ModularArithmeticGeometry/CongruenceSubgroupsOfPSL2R/graphics.html)
- [Action of \({\operatorname{PSL}}_2({\mathbb{R}})\) on the Upper Half Plane](ModularArithmeticGeometry/CongruenceSubgroupsOfPSL2R/group-action.html)
- [Introduction](ModularArithmeticGeometry/CongruenceSubgroupsOfPSL2R/introduction.html)
- [Structure of Congruence Subgroups](ModularArithmeticGeometry/CongruenceSubgroupsOfPSL2R/structure-of-congruence-groups.html)
- [The Upper Half Plane](ModularArithmeticGeometry/CongruenceSubgroupsOfPSL2R/upper-plane.html)
- [Basic Properties](ModularArithmeticGeometry/HilbertModularForms/basic-properties.html)
- [Creation of Full Cuspidal Spaces](ModularArithmeticGeometry/HilbertModularForms/creation.html)
- [Eigenspace Decomposition and Eigenforms](ModularArithmeticGeometry/HilbertModularForms/eigenforms.html)
- [Elements](ModularArithmeticGeometry/HilbertModularForms/elements.html)
- [Further Examples](ModularArithmeticGeometry/HilbertModularForms/further-examples.html)
- [Caching Spaces of Modular Forms](ModularArithmeticGeometry/HilbertModularForms/hmf-caching.html)
- [Introduction](ModularArithmeticGeometry/HilbertModularForms/introduction.html)
- [Operators](ModularArithmeticGeometry/HilbertModularForms/operators.html)
- [Creation of Subspaces](ModularArithmeticGeometry/HilbertModularForms/subspaces.html)
- [Arithmetic of Abelian Varieties](ModularArithmeticGeometry/ModularAbelianVarieties/arithabvar.html)
- [Building Blocks](ModularArithmeticGeometry/ModularAbelianVarieties/building-blocks.html)
- [Tamagawa Numbers and Component Groups of Neron Models](ModularArithmeticGeometry/ModularAbelianVarieties/compgrp.html)
- [Orthogonal Complements](ModularArithmeticGeometry/ModularAbelianVarieties/complements.html)
- [Decomposing and Factoring Abelian Varieties](ModularArithmeticGeometry/ModularAbelianVarieties/decomp.html)
- [Elliptic Curves](ModularArithmeticGeometry/ModularAbelianVarieties/ellcrv.html)
- [Elements of Modular Abelian Varieties](ModularArithmeticGeometry/ModularAbelianVarieties/elt.html)
- [Homology](ModularArithmeticGeometry/ModularAbelianVarieties/homology.html)
- [Endomorphism Algebras and Hom Spaces](ModularArithmeticGeometry/ModularAbelianVarieties/homspace.html)
- [Introduction](ModularArithmeticGeometry/ModularAbelianVarieties/introduction.html)
- [\(L\)-series](ModularArithmeticGeometry/ModularAbelianVarieties/lser.html)
- [Creation and Basic Functions](ModularArithmeticGeometry/ModularAbelianVarieties/modabvar.html)
- [Homomorphisms](ModularArithmeticGeometry/ModularAbelianVarieties/morphisms.html)
- [New and Old Subvarieties and Natural Maps](ModularArithmeticGeometry/ModularAbelianVarieties/new_old.html)
- [Hecke and Atkin-Lehner Operators](ModularArithmeticGeometry/ModularAbelianVarieties/operators.html)
- [Complex Period Lattice](ModularArithmeticGeometry/ModularAbelianVarieties/periods.html)
- [Subgroups of Modular Abelian Varieties](ModularArithmeticGeometry/ModularAbelianVarieties/subgrp.html)
- [Rational Torsion Subgroups](ModularArithmeticGeometry/ModularAbelianVarieties/torsion.html)
- [Modular Polynomial Databases](ModularArithmeticGeometry/ModularCurves/attribute-2.html)
- [Class Polynomials](ModularArithmeticGeometry/ModularCurves/attribute-3.html)
- [Invariants](ModularArithmeticGeometry/ModularCurves/attribute.html)
- [Automorphisms](ModularArithmeticGeometry/ModularCurves/automorphisms-2.html)
- [Parametrized Structures](ModularArithmeticGeometry/ModularCurves/automorphisms.html)
- [Creation Functions](ModularArithmeticGeometry/ModularCurves/creation.html)
- [Associated Structures](ModularArithmeticGeometry/ModularCurves/functions.html)
- [Introduction](ModularArithmeticGeometry/ModularCurves/introduction.html)
- [Modular Curves of Given Level and Genus](ModularArithmeticGeometry/ModularCurves/jim_mod_crvs.html)
- [Modular Curves and Quotients (Canonical Embeddings)](ModularArithmeticGeometry/ModularCurves/mod-crv-quotient.html)
- [Bases](ModularArithmeticGeometry/ModularForms/Bases.html)
- [Elliptic Curves](ModularArithmeticGeometry/ModularForms/abelian-varieties.html)
- [Arithmetic](ModularArithmeticGeometry/ModularForms/arithmetic.html)
- [Congruences](ModularArithmeticGeometry/ModularForms/congruences.html)
- [Creation Functions](ModularArithmeticGeometry/ModularForms/creation.html)
- [Eisenstein Series](ModularArithmeticGeometry/ModularForms/eisenstein-series.html)
- [Introduction](ModularArithmeticGeometry/ModularForms/introduction.html)
- [Modular Symbols](ModularArithmeticGeometry/ModularForms/modular-symbols.html)
- [Newforms](ModularArithmeticGeometry/ModularForms/newforms.html)
- [Operators](ModularArithmeticGeometry/ModularForms/operators.html)
- [Overconvergent Modular Forms](ModularArithmeticGeometry/ModularForms/overconvergent.html)
- [Predicates](ModularArithmeticGeometry/ModularForms/predicates.html)
- [Properties](ModularArithmeticGeometry/ModularForms/properties.html)
- [\(q\)-Expansions](ModularArithmeticGeometry/ModularForms/q-expansions.html)
- [Reductions and Embeddings](ModularArithmeticGeometry/ModularForms/reductions-embeddings.html)
- [Algebraic Relations](ModularArithmeticGeometry/ModularForms/relations.html)
- [Subspaces](ModularArithmeticGeometry/ModularForms/subspaces.html)
- [Weight Half Forms](ModularArithmeticGeometry/ModularForms/weight-half-forms.html)
- [Weight One Forms](ModularArithmeticGeometry/ModularForms/weight-one-forms.html)
- [Attributes](ModularArithmeticGeometry/ModularFormsOverImaginaryQuadraticFields/basic-properties.html)
- [New Spaces and Newforms](ModularArithmeticGeometry/ModularFormsOverImaginaryQuadraticFields/bianchi-new.html)
- [Creation](ModularArithmeticGeometry/ModularFormsOverImaginaryQuadraticFields/creation.html)
- [Hecke Operators](ModularArithmeticGeometry/ModularFormsOverImaginaryQuadraticFields/hecke-operators.html)
- [Introduction](ModularArithmeticGeometry/ModularFormsOverImaginaryQuadraticFields/introduction.html)
- [Bases](ModularArithmeticGeometry/ModularSymbols/bases.html)
- [Degeneracy Maps](ModularArithmeticGeometry/ModularSymbols/changing-level.html)
- [The Associated Complex Torus](ModularArithmeticGeometry/ModularSymbols/complex-tori.html)
- [Creation Functions](ModularArithmeticGeometry/ModularSymbols/creation.html)
- [Decomposition](ModularArithmeticGeometry/ModularSymbols/decomposition.html)
- [Dimension Formulas](ModularArithmeticGeometry/ModularSymbols/dimension-formulas.html)
- [Elliptic Curves](ModularArithmeticGeometry/ModularSymbols/elliptic-curves.html)
- [The Hecke Algebra](ModularArithmeticGeometry/ModularSymbols/hecke-algebra.html)
- [The Intersection Pairing](ModularArithmeticGeometry/ModularSymbols/intersection_pairing.html)
- [Basics](ModularArithmeticGeometry/ModularSymbols/introduction-2.html)
- [Introduction](ModularArithmeticGeometry/ModularSymbols/introduction.html)
- [Special Values of \(L\)-functions](ModularArithmeticGeometry/ModularSymbols/l-series.html)
- [Modular Abelian Varieties](ModularArithmeticGeometry/ModularSymbols/modular-abvars.html)
- [Operators](ModularArithmeticGeometry/ModularSymbols/operators.html)
- [\(q\)-Expansions](ModularArithmeticGeometry/ModularSymbols/qexpansions.html)
- [Subspaces](ModularArithmeticGeometry/ModularSymbols/subspaces.html)
- [Twists](ModularArithmeticGeometry/ModularSymbols/twists.html)
- [Associated Vector Space](ModularArithmeticGeometry/ModularSymbols/underlying-representation.html)
- [Attributes of Admissible Representations](ModularArithmeticGeometry/RepresentationsOfLocalFields/attributes.html)
- [Creation of Admissible Representations](ModularArithmeticGeometry/RepresentationsOfLocalFields/creation.html)
- [Examples](ModularArithmeticGeometry/RepresentationsOfLocalFields/examples.html)
- [Local Galois Representations](ModularArithmeticGeometry/RepresentationsOfLocalFields/galois.html)
- [Introduction](ModularArithmeticGeometry/RepresentationsOfLocalFields/introduction.html)
- [Structure of Admissible Representations](ModularArithmeticGeometry/RepresentationsOfLocalFields/structure.html)
- [Automorphisms](ModularArithmeticGeometry/SmallModularCurves/auts_small_mod_crv.html)
- [Small Modular Curve Models](ModularArithmeticGeometry/SmallModularCurves/create_small_mod_crv.html)
- [Cusps and Rational Points](ModularArithmeticGeometry/SmallModularCurves/cusps_small_mod_crv.html)
- [Standard Functions and Forms](ModularArithmeticGeometry/SmallModularCurves/fns_frms_small_mod_crv.html)
- [Introduction](ModularArithmeticGeometry/SmallModularCurves/introduction.html)
- [Parametrized Structures](ModularArithmeticGeometry/SmallModularCurves/isogs_sm_mod_crvs.html)
- [Projection Maps](ModularArithmeticGeometry/SmallModularCurves/prj_mp_small_mod_crv.html)
- [Modular Generators and \(q\)-Expansions](ModularArithmeticGeometry/SmallModularCurves/q_exps_sm_mod_crvs.html)
- [Extended Example](ModularArithmeticGeometry/SmallModularCurves/sm_mod_crvs_big_ex.html)
- [Arithmetic](ModularArithmeticGeometry/SupersingularDivisorsOnModularCurves/arithmetic.html)
- [Associated Spaces](ModularArithmeticGeometry/SupersingularDivisorsOnModularCurves/associated-spaces.html)
- [Basis](ModularArithmeticGeometry/SupersingularDivisorsOnModularCurves/basis.html)
- [Creation Functions](ModularArithmeticGeometry/SupersingularDivisorsOnModularCurves/creation.html)
- [Introduction](ModularArithmeticGeometry/SupersingularDivisorsOnModularCurves/introduction.html)
- [The Monodromy Pairing](ModularArithmeticGeometry/SupersingularDivisorsOnModularCurves/monodromy-pairing.html)
- [Operators](ModularArithmeticGeometry/SupersingularDivisorsOnModularCurves/operators.html)
- [Predicates](ModularArithmeticGeometry/SupersingularDivisorsOnModularCurves/predicates.html)
- [Properties](ModularArithmeticGeometry/SupersingularDivisorsOnModularCurves/properties.html)
- [Chain Maps](Modules/ChainComplexes/chainmaps.html)
- [Complexes of Modules](Modules/ChainComplexes/complexes.html)
- [Accessing Module Information](Modules/FreeModules/access.html)
- [Bases](Modules/FreeModules/basis.html)
- [Definition of a Module](Modules/FreeModules/creation-module.html)
- [Construction of Elements](Modules/FreeModules/creation.html)
- [Homomorphisms](Modules/FreeModules/homomorphisms.html)
- [Introduction](Modules/FreeModules/introduction.html)
- [Standard Constructions](Modules/FreeModules/operation.html)
- [Quotient Modules](Modules/FreeModules/quotient.html)
- [Submodules](Modules/FreeModules/submodule.html)
- [General Modules](Modules/IntroductionToModules/definition.html)
- [Overview](Modules/IntroductionToModules/overview.html)
- [The Presentation of Submodules](Modules/IntroductionToModules/presentation.html)
- [Basis of a Module](Modules/ModulesOverDedekindDomains/basis.html)
- [Creation of Modules](Modules/ModulesOverDedekindDomains/creation.html)
- [Elementary Functions](Modules/ModulesOverDedekindDomains/elementary-functions.html)
- [Elements of Modules](Modules/ModulesOverDedekindDomains/elements.html)
- [Homomorphisms between Modules](Modules/ModulesOverDedekindDomains/homomorphisms.html)
- [Introduction](Modules/ModulesOverDedekindDomains/introduction.html)
- [Arithmetic with Modules](Modules/ModulesOverDedekindDomains/module-arith.html)
- [Predicates on Modules](Modules/ModulesOverDedekindDomains/ops.html)
- [Other Functions on Modules](Modules/ModulesOverDedekindDomains/other.html)
- [Pseudo Matrices](Modules/ModulesOverDedekindDomains/pmat.html)
- [Linear Invariants of Tensors](Modules/MultilinearAlgebra/Linear-invariants-of-tensors.html)
- [Some Extended Examples](Modules/MultilinearAlgebra/Some_examples.html)
- [Tensor Categories](Modules/MultilinearAlgebra/Tensor_categories.html)
- [Introduction](Modules/MultilinearAlgebra/intro.html)
- [Tensor Spaces](Modules/MultilinearAlgebra/tensor_spaces.html)
- [Tensors](Modules/MultilinearAlgebra/tensors.html)
- [Creation of LP objects](Optimization/LinearProgramming/creation.html)
- [Explicit LP Solving Functions](Optimization/LinearProgramming/instant-lp.html)
- [Introduction](Optimization/LinearProgramming/introduction.html)
- [Operations on LP objects](Optimization/LinearProgramming/operations.html)
- [Brauer Characters](RepresentationTheory/CharactersOfFiniteGroups/brauer-characters.html)
- [Constructions for Characters](RepresentationTheory/CharactersOfFiniteGroups/constructing-characters.html)
- [Creation Functions](RepresentationTheory/CharactersOfFiniteGroups/creation.html)
- [Element Operations](RepresentationTheory/CharactersOfFiniteGroups/element.html)
- [The Table of Irreducible Characters](RepresentationTheory/CharactersOfFiniteGroups/irreducible.html)
- [Database of Character Tables](RepresentationTheory/CharactersOfFiniteGroups/ring-2.html)
- [Character Ring Operations](RepresentationTheory/CharactersOfFiniteGroups/ring.html)
- [The Schur Index](RepresentationTheory/CharactersOfFiniteGroups/schur-index.html)
- [Basic Properties](RepresentationTheory/GroupRepresentations/basic-properties.html)
- [Creation of Group Representations](RepresentationTheory/GroupRepresentations/creation.html)
- [Elements of Group Representations](RepresentationTheory/GroupRepresentations/elements.html)
- [Introduction](RepresentationTheory/GroupRepresentations/introduction.html)
- [Homomorphisms of Group Representations](RepresentationTheory/GroupRepresentations/morphisms.html)
- [Operations on Group Representations](RepresentationTheory/GroupRepresentations/ops.html)
- [Examples](RepresentationTheory/ModPGaloisRepresentations/Examples.html)
- [Introduction](RepresentationTheory/ModPGaloisRepresentations/Introduction.html)
- [\(\varphi\)-modules and Galois Representations in Magma](RepresentationTheory/ModPGaloisRepresentations/modules-Galois-representations.html)
- [Constructions for \(A\)-Modules](RepresentationTheory/ModulesOverAnAlgebraAndGroupRepresentations/A-module.html)
- [Constructions for \(K[G]\)-Modules](RepresentationTheory/ModulesOverAnAlgebraAndGroupRepresentations/K[G]-module.html)
- [Accessing Module Information](RepresentationTheory/ModulesOverAnAlgebraAndGroupRepresentations/access.html)
- [Bimodules](RepresentationTheory/ModulesOverAnAlgebraAndGroupRepresentations/bimodules.html)
- [Cohomology and Extensions](RepresentationTheory/ModulesOverAnAlgebraAndGroupRepresentations/cohomology-extensions.html)
- [Enumerating All Irreducible Modules](RepresentationTheory/ModulesOverAnAlgebraAndGroupRepresentations/construct-irreds.html)
- [Constructing All Irreducible \(K[G]\)-Modules](RepresentationTheory/ModulesOverAnAlgebraAndGroupRepresentations/constructing-all-irred.html)
- [Module Elements](RepresentationTheory/ModulesOverAnAlgebraAndGroupRepresentations/element.html)
- [Characters and Character Tables](RepresentationTheory/ModulesOverAnAlgebraAndGroupRepresentations/enum-irreducibles.html)
- [Homomorphisms](RepresentationTheory/ModulesOverAnAlgebraAndGroupRepresentations/homomorphism.html)
- [Introduction](RepresentationTheory/ModulesOverAnAlgebraAndGroupRepresentations/introduction.html)
- [Properties of a Module](RepresentationTheory/ModulesOverAnAlgebraAndGroupRepresentations/module-props.html)
- [Modules over a General Algebra](RepresentationTheory/ModulesOverAnAlgebraAndGroupRepresentations/modules-matrix-algebra.html)
- [New Modules from Old](RepresentationTheory/ModulesOverAnAlgebraAndGroupRepresentations/operation.html)
- [Projective Indecomposable Modules](RepresentationTheory/ModulesOverAnAlgebraAndGroupRepresentations/projective-indecomposable-modules.html)
- [Group Representations](RepresentationTheory/ModulesOverAnAlgebraAndGroupRepresentations/representation.html)
- [Structure of a Module](RepresentationTheory/ModulesOverAnAlgebraAndGroupRepresentations/structure.html)
- [Lattice of Submodules](RepresentationTheory/ModulesOverAnAlgebraAndGroupRepresentations/submodule-lattice.html)
- [Submodules and Quotient Modules](RepresentationTheory/ModulesOverAnAlgebraAndGroupRepresentations/submodules.html)
- [Vertex and Source of an Indecomposable Module](RepresentationTheory/ModulesOverAnAlgebraAndGroupRepresentations/vertex-source.html)
- [Characters of the Alternating Group](RepresentationTheory/RepresentationsOfSymmetricGroups/charalt.html)
- [Characters of the Symmetric Group](RepresentationTheory/RepresentationsOfSymmetricGroups/charsym.html)
- [Introduction](RepresentationTheory/RepresentationsOfSymmetricGroups/introduction.html)
- [Representations of the Alternating Group](RepresentationTheory/RepresentationsOfSymmetricGroups/repalt.html)
- [Representations of the Symmetric Group](RepresentationTheory/RepresentationsOfSymmetricGroups/repsym.html)
- [Iteration](SetsSequencesMappings/AssociativeArrays/Iteration.html)
- [Introduction](SetsSequencesMappings/AssociativeArrays/introduction.html)
- [Operations](SetsSequencesMappings/AssociativeArrays/operations.html)
- [Accessing Functions](SetsSequencesMappings/Coproducts/access.html)
- [Creation Functions](SetsSequencesMappings/Coproducts/creation.html)
- [Flattening](SetsSequencesMappings/Coproducts/flat.html)
- [Introduction](SetsSequencesMappings/Coproducts/introduction.html)
- [Retrieve](SetsSequencesMappings/Coproducts/retrieve.html)
- [Universal Map](SetsSequencesMappings/Coproducts/universal.html)
- [Dual iterators in constructors](SetsSequencesMappings/IntroductionToAggregates/dual-iterators.html)
- [Introduction](SetsSequencesMappings/IntroductionToAggregates/introduction.html)
- [Nested Aggregates](SetsSequencesMappings/IntroductionToAggregates/nesting.html)
- [Restrictions on Sets and Sequences](SetsSequencesMappings/IntroductionToAggregates/restriction.html)
- [Iteration](SetsSequencesMappings/Lists/Iteration.html)
- [Access Functions](SetsSequencesMappings/Lists/access.html)
- [Assignment Operator](SetsSequencesMappings/Lists/assignment.html)
- [Construction of Lists](SetsSequencesMappings/Lists/constructor.html)
- [Creation of New Lists](SetsSequencesMappings/Lists/creation.html)
- [Introduction](SetsSequencesMappings/Lists/introduction.html)
- [Creation Functions](SetsSequencesMappings/Mappings/creation.html)
- [Images and Preimages](SetsSequencesMappings/Mappings/image-preimage.html)
- [Introduction](SetsSequencesMappings/Mappings/introduction.html)
- [Operations on Mappings](SetsSequencesMappings/Mappings/operation.html)
- [Parents of Maps](SetsSequencesMappings/Mappings/parents.html)
- [Access and Modification Functions](SetsSequencesMappings/Records/access-modification.html)
- [The Record Format Constructor](SetsSequencesMappings/Records/creation-format.html)
- [Creating a Record](SetsSequencesMappings/Records/creation-record.html)
- [Introduction](SetsSequencesMappings/Records/introduction.html)
- [Predicates on Sequences](SetsSequencesMappings/Sequences/Boolean.html)
- [Creating Sequences](SetsSequencesMappings/Sequences/creation.html)
- [Introduction](SetsSequencesMappings/Sequences/introduction.html)
- [Operators on Sequences](SetsSequencesMappings/Sequences/operation.html)
- [Power Sequences](SetsSequencesMappings/Sequences/power-sequence.html)
- [Recursion, Reduction, and Iteration](SetsSequencesMappings/Sequences/recursion-reduction-iteration.html)
- [Accessing and Modifying Sets](SetsSequencesMappings/Sets/access-modification.html)
- [Sets from Structures](SetsSequencesMappings/Sets/conversion.html)
- [Creating Sets](SetsSequencesMappings/Sets/creation.html)
- [Introduction](SetsSequencesMappings/Sets/introduction.html)
- [Operations on Sets](SetsSequencesMappings/Sets/operation.html)
- [Power Sets](SetsSequencesMappings/Sets/power-set.html)
- [Quantifiers](SetsSequencesMappings/Sets/quantifier.html)
- [Reduction and Iteration](SetsSequencesMappings/Sets/reduction-iteration.html)
- [Equality](SetsSequencesMappings/TuplesCartesianProducts/Boolean.html)
- [Iteration](SetsSequencesMappings/TuplesCartesianProducts/Iteration.html)
- [Other Operations](SetsSequencesMappings/TuplesCartesianProducts/Other.html)
- [Cartesian Product Constructor and Functions](SetsSequencesMappings/TuplesCartesianProducts/creation.html)
- [Introduction](SetsSequencesMappings/TuplesCartesianProducts/introduction.html)
- [Tuple Access Functions](SetsSequencesMappings/TuplesCartesianProducts/tuple-access.html)
- [Creating and Modifying Tuples](SetsSequencesMappings/TuplesCartesianProducts/tuple.html)
- [Homology Computation](Topology/SimplicialHomology/homology-computation.html)
- [Introduction](Topology/SimplicialHomology/introduction.html)
- [Simplicial Complexes](Topology/SimplicialHomology/simplicial-complexes.html)
- [Magma Handbook](index.html)
- [Preface](preface.html)