[____] [____] [_____] [____] [__] [Index] [Root]

Index C


C

Control-C key (OVERVIEW)

C-key

C

c-key

c range

call

Call by Value Evaluation (MAGMA SEMANTICS)

Expression (OVERVIEW)

Functions (OVERVIEW)

Functions, Procedures, and Mappings (OVERVIEW)

call-by-name

Expression (OVERVIEW)

call-by-value

Call by Value Evaluation (MAGMA SEMANTICS)

Expression (OVERVIEW)

calls

System Calls (INPUT AND OUTPUT)

Cambridge

AlgMat_Cambridge (Example H51E2)

CambridgeMatrix

CambridgeMatrix(t, K, n, Q) : RngIntElt, FldFint, RngIntElt, [ ] -> AlgMatElt

canonical

Canonical Forms (MATRIX ALGEBRAS)

Canonical Forms for Elements (THE MODULES Hom_(R)(M, N) AND End(M))

canonical-form

Canonical Forms (MATRIX ALGEBRAS)

Canonical Forms for Elements (THE MODULES Hom_(R)(M, N) AND End(M))

CanonicalForms

AlgMat_CanonicalForms (Example H51E8)

CanonicalGraph

CanonicalGraph(G: parameters ) : Grph -> Grph

CanonicalHeight

Height(P) : CurveEllPt -> FldPrElt

car

car< R_1, ..., R_k > : Str, ..., Str -> SetCart

cardinality

Groups (OVERVIEW)

Lower Bounds on the Cardinality of a Largest Code (ERROR-CORRECTING CODES)

Rings, Fields, and Algebras (OVERVIEW)

Sets (OVERVIEW)

Upper Bounds on the Cardinality of a Largest Code (ERROR-CORRECTING CODES)

cardinality-lower-bound

Lower Bounds on the Cardinality of a Largest Code (ERROR-CORRECTING CODES)

cardinality-upper-bound

Upper Bounds on the Cardinality of a Largest Code (ERROR-CORRECTING CODES)

CarmichaelLambda

CarmichaelLambda(n) : RngIntElt -> RngIntElt

cartan

Cartan Subalgebra (LIE ALGEBRAS)

CartanSubalgebra

CartanSubalgebra(L) : AlgLie -> AlgLie

AlgLie_CartanSubalgebra (Example H49E4)

Cartesian

The Cartesian Product Constructors (SETS)

cartesian

TUPLES AND CARTESIAN PRODUCTS

Cartesian-product

The Cartesian Product Constructors (SETS)

CartesianPower

CartesianPower(R, k) : Str, RngIntElt -> SetCart

CartesianProduct

CartesianProduct(G, H) : GrphDir, GrphDir -> GrphDir

CartesianProduct(R, S) : Str, ..., Str -> SetCart

Tup_CartesianProduct (Example H9E1)

case

Constructor (OVERVIEW)

The case expression (OVERVIEW)

The Case Expression (STATEMENTS AND EXPRESSIONS)

The case statement (OVERVIEW)

The Case Statement (STATEMENTS AND EXPRESSIONS)

case< | > : ->

case expr : when expr_i : statements end case : ->

State_case (Example H1E12)

case-expression

The Case Expression (STATEMENTS AND EXPRESSIONS)

case-statement

The Case Statement (STATEMENTS AND EXPRESSIONS)

cat

S cat T : List, List -> List

s cat t : MonStgElt, MonStgElt -> MonStgElt

S cat T : SeqEnum, SeqEnum -> SeqEnum

cat:=

S cat:= T : List, List ->

s cat:= t : MonStgElt, MonStgElt -> MonStgElt

Catalan

Catalan(R) : FldRe -> FldReElt

Category

Category(S) : Obj -> Cat

Category(R) : Rng -> Cat

Category(r) : RngElt -> Cat

category

Category (OVERVIEW)

Category and Parent (FUNCTION FIELDS AND THEIR ORDERS)

Category and Parent (NUMBER FIELDS AND THEIR ORDERS)

Magmas (or Structures) (OVERVIEW)

Module Categories (GENERAL MODULES)

Parent and Category (CYCLOTOMIC FIELDS)

Parent and Category (FUNCTION FIELDS AND THEIR ORDERS)

Parent and Category (MULTIVARIATE POLYNOMIAL RINGS)

Parent and Category (NUMBER FIELDS AND THEIR ORDERS)

Parent and Category (POWER SERIES AND LAURENT SERIES)

Parent and Category (QUADRATIC FIELDS)

Parent and Category (UNIVARIATE POLYNOMIAL RINGS)

Parent and Category (VALUATION RINGS)

Taxonomy of Modules (GENERAL MODULES)

The Categories of Algebras (ALGEBRAS)

The Categories of Finite Groups (GROUPS)

The Category of Matrix Groups (MATRIX GROUPS)

The Category of Permutation Groups (PERMUTATION GROUPS)

Transfer Functions Between Group Categories (GROUPS)

Vector Space Categories (VECTOR SPACES)

category-parent

Category and Parent (FUNCTION FIELDS AND THEIR ORDERS)

Category and Parent (NUMBER FIELDS AND THEIR ORDERS)

category-transfer

Transfer Functions Between Group Categories (GROUPS)

cayley

AlgCon_cayley (Example H47E2)

CayleyGraph

CayleyGraph(A) : Grp -> GrphDir

Graph_CayleyGraph (Example H55E8)

Ceiling

Ceiling(q) : FldRatElt -> RngIntElt

Ceiling(r) : FldReElt -> RngIntElt

Ceiling(n) : RngIntElt -> RngIntElt

cent-coll

Plane_cent-coll (Example H57E15)

Center

Centre(G) : GrpAb -> GrpAb

Centre(G) : GrpFin -> GrpFin

Centre(G) : GrpMat -> GrpMat

Centre(G) : GrpPC -> GrpPC

Centre(G) : GrpPerm -> GrpPerm

Centre(R) : Rng -> Rng

central

Central Collineations (FINITE PLANES)

CentralCollineationGroup

CentralCollineationGroup(P, p, l) : Plane, PlanePt, PlaneLn -> GrpPerm, PowMap, Map

CentralEndomorphisms

CentralEndomorphisms(G, n) : GrpMat, RngIntElt -> [ AlgMatElt ]

Centraliser

Centraliser(a) : AlgGrpElt -> AlgGrpSub

Centraliser(S) : AlgGrpSub -> AlgGrpSub

Centraliser(e, f) : SubGrpLatElt, SubGrpLatElt -> SubGrpLatElt

Centralizer(A, S) : AlgAss, AlgAss -> AlgAss

Centralizer(A, s) : AlgAss, AlgAssElt -> AlgAss

Centralizer(G, g) : GrpAb, GrpAbElt -> GrpAb

Centralizer(G, g) : GrpFin, GrpFinElt -> GrpFin

Centralizer(G, g) : GrpPC, GrpPCElt -> GrpPC

Centralizer(G, g) : GrpPerm, GrpPermElt -> GrpPerm

CentralisingMatrix

CentralisingMatrix (G) : GrpMat -> AlgMatElt

Centralizer

Centraliser(a) : AlgGrpElt -> AlgGrpSub

Centraliser(S) : AlgGrpSub -> AlgGrpSub

Centraliser(e, f) : SubGrpLatElt, SubGrpLatElt -> SubGrpLatElt

Centralizer(A, S) : AlgAss, AlgAss -> AlgAss

Centralizer(A, s) : AlgAss, AlgAssElt -> AlgAss

Centralizer(L, K) : AlgLie, AlgLie -> AlgLie

Centralizer(A, S) : AlgMat, AlgMat -> AlgMat

Centralizer(G, g) : GrpAb, GrpAbElt -> GrpAb

Centralizer(G, g) : GrpFin, GrpFinElt -> GrpFin

Centralizer(G, g) : GrpMat, GrpMatElt -> GrpMat

Centralizer(G, g) : GrpPC, GrpPCElt -> GrpPC

Centralizer(G, g) : GrpPerm, GrpPermElt -> GrpPerm

Centre

Centre(A) : AlgAss -> AlgAss

Centre(x) : AlgChtrElt -> Grp

Centre(L) : AlgLie -> AlgLie

Centre(A) : AlgMat -> AlgMat

Centre(G) : GrpAb -> GrpAb

Centre(G) : GrpFin -> GrpFin

Centre(G) : GrpMat -> GrpMat

Centre(G) : GrpPC -> GrpPC

Centre(G) : GrpPerm -> GrpPerm

Centre(R) : Rng -> Rng

CentreOfEndomorphismRing

CentreOfEndomorphismRing(G) : GrpMat -> AlgMat

change

Changing Coefficient Ring (MULTIVARIATE POLYNOMIAL RINGS)

Changing Monomial Order (MULTIVARIATE POLYNOMIAL RINGS)

Changing Rings (ALGEBRAS)

Changing Rings (MATRIX ALGEBRAS)

Changing Rings (MATRIX GROUPS)

Changing Rings (UNIVARIATE POLYNOMIAL RINGS)

change-order

Changing Monomial Order (MULTIVARIATE POLYNOMIAL RINGS)

change-ring

Changing Coefficient Ring (MULTIVARIATE POLYNOMIAL RINGS)

Changing Rings (ALGEBRAS)

Changing Rings (MATRIX ALGEBRAS)

Changing Rings (MATRIX GROUPS)

Changing Rings (UNIVARIATE POLYNOMIAL RINGS)

ChangeBase

ChangeBase(~G, Q) : GrpPerm, [Elt] ->

ChangeDirectory

ChangeDirectory(s) : MonStgElt ->

ChangeOrder

ChangeOrder(I, Q) : RngMPol, RngMPol -> RngMPol, Map

RngMPol_ChangeOrder (Example H29E21)

ChangeRepresentationType

ChangeRepresentationType(A, Rep) : AlgGrp, MonStgElt -> AlgGrp, Map

ChangeRing

ChangeRing(A, S) : AlgGen, Rng -> AlgGen, Map

ChangeRing(A, S) : AlgMat, Rng -> AlgMat, Map

ChangeRing(G, S) : GrpMat, Rng -> GrpMat, Map

ChangeRing(L, S) : Lat, Rng -> Lat, Map

ChangeRing(M, S) : ModRng, Rng -> ModRng, Map

ChangeRing(I, S) : RngMPol, Rng -> RngMPol

ChangeRing(P, S) : RngUPol, Rng -> RngUPol, Map

RngMPol_ChangeRing (Example H29E20)

RngPol_ChangeRing (Example H28E3)

ChangeSupport

ChangeSupport(G, S) : Grph, SetIndx -> Grph, GrphVertSet, GrphEdgeSet

ChangeUniverse

ChangeUniverse(S, V) : SeqEnum, Str ->

ChangeUniverse(~S, V) : SetEnum, Str ->

character

Character Theory (GROUPS)

CHARACTERS OF FINITE GROUPS

Representation Theory (ABELIAN GROUPS)

Representation Theory (GROUPS)

Representation Theory (MATRIX GROUPS)

Representation Theory (PERMUTATION GROUPS)

Representation Theory (SOLUBLE GROUPS)

Rings, Fields, and Algebras (OVERVIEW)

Strings (OVERVIEW)

character-representation

Representation Theory (ABELIAN GROUPS)

Representation Theory (GROUPS)

Representation Theory (MATRIX GROUPS)

Representation Theory (PERMUTATION GROUPS)

Representation Theory (SOLUBLE GROUPS)

Characteristic

Characteristic(R) : Rng -> RngIntElt

characteristic

Characteristic Subgroups and Normal Structure (GROUPS)

Characteristic Subgroups and Normal Structure (MATRIX GROUPS)

Characteristic Subgroups and Normal Structure (PERMUTATION GROUPS)

Minimal and Characteristic Polynomial (FINITE FIELDS)

Normal Structure and Characteristic Subgroups (ABELIAN GROUPS)

Normal Structure and Characteristic Subgroups (SOLUBLE GROUPS)

characteristic-subgroup-normal-structure

Characteristic Subgroups and Normal Structure (GROUPS)

Characteristic Subgroups and Normal Structure (MATRIX GROUPS)

Characteristic Subgroups and Normal Structure (PERMUTATION GROUPS)

Normal Structure and Characteristic Subgroups (ABELIAN GROUPS)

Normal Structure and Characteristic Subgroups (SOLUBLE GROUPS)

CharacteristicPolynomial

CharacteristicPolynomial(a) : FldFinElt -> RngUPolElt

CharacteristicPolynomial(a) : FldNumElt -> RngUPolElt

CharacteristicPolynomial(G) : GrphUnd -> RngUPolElt

CharacteristicPolynomial(a: parameters) : AlgMatElt -> RngUPolElt

CharacteristicPolynomial(g: parameters) : GrpMatElt -> RngPolElt

CharacteristicVector

CharacteristicVector(M, S) : ModRng, { RngIntElt } -> ModRngElt

CharacteristicVector(V, S) : ModTupFld, { RngElt } -> ModTupFldElt

CharacterRing

ClassFunctionSpace(G) : Grp -> AlgChtr

CharacterTable

CharacterTable(G) : Grp -> SeqEnum

CharacterTable(G) : GrpAb -> TabChtr

CharacterTable(G) : GrpFin -> TabChtr

CharacterTable(G) : GrpMat -> TabChtr

CharacterTable(G) : GrpPC -> TabChtr

CharacterTable(G) : GrpPerm -> TabChtr

checking

Checking of Maps (MAPPINGS)

CheckPolynomial

CheckPolynomial(C) : Code -> RngUPolElt

chevalley

Chevalley Groups (MATRIX GROUPS)

ChevalleyGroup

ChevalleyGroup(s, n, K: parameters) : MonStgElt, RngIntElt, FldFin -> GrpMat

ChiefFactors

ChiefFactors(G) : GrpPerm -> [ <RngIntElt, RngIntElt, RngIntElt, RngIntElt> ]

ChiefSeries

ChiefSeries(G) : GrpAb -> [GrpAb]

ChiefSeries(G) : GrpPC -> [GrpPC]

ChiefSeries(G) : GrpPerm -> [ GrpPerm ], [ <RngIntElt, RngIntElt, RngIntElt, RngIntElt> ]

ChienChoyCode

ChienChoyCode(P, G, n, S) : RngUPolElt, RngUPolElt, RngIntElt, FldFin -> Code

ChineseRemainder

ChineseRemainder(I1, I2, e1, e2) : RngOrdIdl, RngOrdIdl, RngOrdElt, RngOrdElt -> RngOrdElt

ChineseRemainderTheorem

ChineseRemainderTheorem(a, b, m) : RngIntElt, RngIntElt, RngIntElt -> RngIntElt

Cholesky

Orthonormalize(F, K) : AlgMatElt, Fld -> AlgMatElt

ChromaticIndex

ChromaticIndex(G) : GrphUnd -> RngIntElt

ChromaticNumber

ChromaticNumber(G) : GrphUnd -> RngIntElt

Graph_ChromaticNumber (Example H55E12)

cInvariants

cInvariants(E) : CurveEll -> [ RngElt ]

circuit

Connectedness, Paths and Circuits (GRAPHS)

CircuitSpace

[Future release] CircuitSpace(G) : GrphUnd -> ModTup

Class

Class(H, g) : GrpAb, GrpAbElt -> { GrpAbElt }

Class(G, H) : GrpFin, GrpFin -> { GrpFin }

Class(H, x) : GrpFin, GrpFinElt -> { GrpFinElt }

Class(H, x) : GrpMat, GrpMatElt -> { GrpMatElt }

Class(H, g) : GrpPC, GrpPCElt -> { GrpPCElt }

Class(H, x) : GrpPerm, GrpPermElt -> { GrpPermElt }

class

Class Information from a Conjugacy Class Poset (GROUPS)

Ideal Class Group (QUADRATIC FIELDS)

Ideal Class Groups (NUMBER FIELDS AND THEIR ORDERS)

Identifier Classes (MAGMA SEMANTICS)

RESIDUE CLASS RINGS

Structure Creation (CHARACTERS OF FINITE GROUPS)

Unit Group (QUADRATIC FIELDS)

class-group

Ideal Class Group (QUADRATIC FIELDS)

Unit Group (QUADRATIC FIELDS)

class-information

Class Information from a Conjugacy Class Poset (GROUPS)

Classes

ConjugacyClasses(G) : GrpAb -> [ <RngIntElt, RngIntElt, GrpAbElt> ]

ConjugacyClasses(G) : GrpPC -> [ <RngIntElt, RngIntElt, GrpPCElt> ]

ConjugacyClasses(G: parameters) : GrpFin -> [ <RngIntElt, RngIntElt, GrpFinElt> ]

ConjugacyClasses(G: parameters) : GrpMat -> [ < RngIntElt, RngIntElt, GrpMatElt > ]

ConjugacyClasses(G: parameters) : GrpPerm -> [ <RngIntElt, RngIntElt, GrpPermElt> ]

GrpPerm_Classes (Example H20E20)

Grp_Classes (Example H15E13)

classes

Conjugacy Classes of Subgroups (GROUPS)

ClassFunctionSpace

ClassFunctionSpace(G) : Grp -> AlgChtr

ClassGroup

ClassGroup(K: parameters) : FldQuad -> GrpAb, Map

ClassGroup(O: parameters) : RngOrd -> GrpAb, Map

ClassGroupStructure

ClassGroupStructure(K: parameters) : FldQuad -> [ RngIntElt ]

ClassGroupStructure(O: parameters) : RngOrd -> [RngIntElt]

classical

Classical Groups (MATRIX GROUPS)

ClassMap

ClassMap(G) : GrpAb -> Map

ClassMap(G) : GrpPC -> Map

ClassMap(G: parameters) : GrpFin -> Map

ClassMap(G: parameters) : GrpMat -> Map

ClassMap(G: parameters) : GrpPerm -> Map

ClassMatrix

ClassMatrix(G, i) : GrpAb, RngIntElt -> AlgMatElt

ClassNumber

ClassNumber(K: parameters) : FldQuad -> RngIntElt

ClassNumber(O: parameters) : RngOrd -> RngIntElt

ClassPowerCharacter

ClassPowerCharacter(x, j) : AlgChtrElt, RngIntElt -> AlgChtrElt

ClassRepresentative

ClassRepresentative(G, x) : GrpAb, GrpAbElt -> GrpAbElt

ClassRepresentative(G, x) : GrpFin, GrpFinElt -> GrpFinElt

ClassRepresentative(G, x) : GrpMat, GrpMatElt -> GrpMatElt

ClassRepresentative(G, x) : GrpPC, GrpPCElt -> GrpPCElt

ClassRepresentative(G, x) : GrpPerm, GrpPermElt -> GrpPermElt

clear

Deleting an identifier (OVERVIEW)

ClearPrevious

ClearPrevious() : ->

ClearVerbose

ClearVerbose() : ->

Clique

Clique(G, n) : GrphUnd, RngIntElt -> { GrphVert }

clique

Independent Sets, Cliques, Colourings (GRAPHS)

CliqueNumber

CliqueNumber(G) : GrphUnd -> RngIntElt

close

Short and Close Vectors (LATTICES)

Closest

Lat_Closest (Example H45E8)

closest

Shortest and Closest Vectors (LATTICES)

ClosestVectors

ClosestVectors(L, w) : Lat, ModTupRngElt -> [ LatElt ], RngElt

ClosestVectorsMatrix

ClosestVectorsMatrix(L, w) : Lat, ModTupRngElt -> ModMatRngElt, RngElt

CloseVectors

CloseVectors(L, w, u) : Lat, ModTupRngElt, RngElt -> [ <LatElt, RngElt> ]

CloseVectorsMatrix

CloseVectorsMatrix(L, w, u) : Lat, ModTupRngElt, RngElt -> ModMatRngElt

CloseVectorsProcess

CloseVectorsProcess(L, w, u) : Lat, ModTupRngElt, RngElt -> LatEnumProc

Closure

[Future release] Closure(r, f) : GrpFPRel, Hom(GrpFP) -> { GrpFPRel }

ClosureGraph

ClosureGraph(P, G) : GrpPerm, GrphUnd -> GrphUnd

cmpeq

x cmpeq y : Elt, Elt -> BoolElt

Co1

GrpFP_Co1 (Example H16E24)

Code

Combinatorial and Geometrical Structures (OVERVIEW)

Lat_Code (Example H45E2)

code

Combinatorial and Geometrical Structures (OVERVIEW)

Construction of Graphs from Groups, Codes and Designs (GRAPHS)

ERROR-CORRECTING CODES

Graphs Constructed from Designs (GRAPHS)

Incidence Structures, Graphs and Codes (INCIDENCE STRUCTURES AND DESIGNS)

Lattices from Linear Codes (LATTICES)

Planes, Graphs and Codes (FINITE PLANES)

code-design

Graphs Constructed from Designs (GRAPHS)

CodeFromMatrix

Code_CodeFromMatrix (Example H58E2)

codes

Plane_codes (Example H57E18)

CodeToString

CodeToString(n) : RngIntElt -> MonStgElt

Codomain

Codomain(f) : Map -> Struct

Codomain(a) : ModMatElt -> ModTupFld

Codomain(S) : ModMatRng -> ModTupRng

CoefficentRing

CoefficentRing(M) : ModMPol -> ModMPol

Coefficient

Coefficient(a, g) : AlgGrpElt, GrpElt -> RngElt

Coefficient(f, i, k) : RngMPolElt, RngIntElt, RngIntElt -> RngElt

Coefficient(f, i) : RngPowSerElt, RngIntElt -> RngElt

Coefficient(p, i) : RngUPolElt, RngIntElt -> RngElt

coefficient

Changing the Coefficient Field (VECTOR SPACES)

Changing the Coefficient Ring (GENERAL MODULES)

Coefficients and Degree (POWER SERIES AND LAURENT SERIES)

Coefficients and Terms (UNIVARIATE POLYNOMIAL RINGS)

Coefficients, Monomials and Terms (MULTIVARIATE POLYNOMIAL RINGS)

coefficient-degree

Coefficients and Degree (POWER SERIES AND LAURENT SERIES)

coefficient-monomial-term

Coefficients, Monomials and Terms (MULTIVARIATE POLYNOMIAL RINGS)

coefficient-term

Coefficients and Terms (UNIVARIATE POLYNOMIAL RINGS)

CoefficientField

CoefficientField(x) : AlgChtrElt -> Rng

CoefficientField(V) : ModTupFld -> Fld

CoefficientRing(R) : RngInvar -> Grp

GroundField(K) : FldNum -> Fld

CoefficientRing

BaseRing(R) : AlgMat -> Rng

BaseRing(F) : FldFun -> Rng

BaseRing(L) : Lat -> Rng

BaseRing(P) : RngMPol -> Rng

BaseRing(O) : RngOrd -> Rng

BaseRing(R) : RngSer -> Rng

BaseRing(P) : RngUPol -> Rng

CoefficientRing(A) : Alg -> Rng

CoefficientRing(A) : AlgGen -> Rng

CoefficientRing(E) : CurveEll -> Rng

CoefficientRing(G) : GrpMat -> Rng

CoefficientRing(M) : ModTupRng -> Rng

CoefficientRing(O) : RngFunOrd -> Rng

CoefficientRing(R) : RngInvar -> Grp

CoefficientRing(Q) : RngMPolRes -> Rng

Coefficients

Coefficients(a) : AlgGrpElt -> SeqEnum

Coefficients(a) : FldLocElt -> [ RngResElt ]

Coefficients(f) : RngMPolElt -> [ RngElt ]

Coefficients(f) : RngPowSerElt -> [ RngElt ]

Coefficients(p) : RngUPolElt -> [ RngElt ]

aInvariants(E) : CurveEll -> [ RngElt ]

RngMPol_Coefficients (Example H29E4)

Coercion

Coercion(D, C) : Struct, Struct -> Map

FldRat_Coercion (Example H26E1)

RngIntRes_Coercion (Example H25E1)

coercion

Coercion (GROUPS)

Coercion (INTRODUCTION [RINGS AND FIELDS])

Coercion (LOCAL FIELDS)

Coercion (PERMUTATION GROUPS)

Coercion (POWER SERIES AND LAURENT SERIES)

Coercion (QUADRATIC FIELDS)

Coercion (RATIONAL FIELD)

Coercion (REAL AND COMPLEX FIELDS)

Coercion (RESIDUE CLASS RINGS)

Coercion (RING OF INTEGERS)

Coercion between Matrix Structures (MATRIX GROUPS)

Coercion Maps (MAPPINGS)

Coercions Between Groups and Subgroups (ABELIAN GROUPS)

Coercions Between Groups and Subgroups (SOLUBLE GROUPS)

Coercions Between Related Groups (BLACKBOX GROUPS)

Magmas (or Structures) (OVERVIEW)

CohomologicalDimension

CohomologicalDimension(G, M, i) : GrpFin, ModRng, RngIntElt -> RngIntElt

CohomologicalDimension(G, M, i) : GrpPerm, ModRng, RngIntElt -> RngIntElt

cohomology

Cohomology (GROUPS)

Cohomology (PERMUTATION GROUPS)

Cokernel

Cokernel(a) : ModMatElt -> ModTupFld

Cokernel(a) : ModMatRngElt -> ModTupRng

Collect

Collect(P, Q) : Process(pQuot), [ <RngIntElt, RngIntElt> ] -> [ RngIntElt ] ->

CollectRelations

CollectRelations(~P) : Process(pQuot) ->

Collineation

Plane_Collineation (Example H57E13)

collineation

The Collineation Group of a Plane (FINITE PLANES)

collineation-group

The Collineation Group of a Plane (FINITE PLANES)

CollineationGroup

CollineationGroup(P) : Plane -> GrpPerm, GSet, GSet, PowMap, Map

CollineationGroupStabilizer

CollineationGroupStabilizer(P, k) : Plane, RngIntElt -> GrpPerm, GSet, GSet, PowMap, Map

CollineationGSet

Plane_CollineationGSet (Example H57E12)

CollineationSubgroup

CollineationSubgroup(P) : Plane -> GrpPerm, GSet, GSet, PowMap, Map

ColonIdeal

ColonIdeal(I, J) : RngMPol, RngMPol -> RngMPol

ColonIdeal(I, J) : RngMPolRes, RngMPolRes -> RngMPolRes

colouring

Independent Sets, Cliques, Colourings (GRAPHS)

column

Row and Column Operations (MATRIX ALGEBRAS)

Row and Column Operations (THE MODULES Hom_(R)(M, N) AND End(M))

Row and Column Operations (VECTOR SPACES)

comb

ENUMERATIVE COMBINATORICS

combinatorial

Combinatorial and Geometrical Structures (OVERVIEW)

combinatorial-geometrical-incidence

Combinatorial and Geometrical Structures (OVERVIEW)

combinatorics

Combinatorial Functions (ENUMERATIVE COMBINATORICS)

Combinatorial Functions (RING OF INTEGERS)

command

Command Line Options (ENVIRONMENT AND OPTIONS)

Performing shell commands from Magma (OVERVIEW)

command-options

Command Line Options (ENVIRONMENT AND OPTIONS)

comment

Comments (OVERVIEW)

Comments and Continuation (STATEMENTS AND EXPRESSIONS)

comment-continuation

Comments and Continuation (STATEMENTS AND EXPRESSIONS)

common

Common Divisors and Common Multiples (UNIVARIATE POLYNOMIAL RINGS)

Greatest Common Divisors (MULTIVARIATE POLYNOMIAL RINGS)

commutative

Groups (OVERVIEW)

commutator

Groups (OVERVIEW)

CommutatorIdeal

CommutatorIdeal(A, B) : AlgAss, AlgAss -> AlgAss

CommutatorModule

CommutatorModule(A, B) : AlgAss, AlgAss -> ModTupRng

CommutatorSubgroup

CommutatorSubgroup(G, H, K) : GrpAb, GrpAb, GrpAb -> GrpAb

CommutatorSubgroup(G, H, K) : GrpFin, GrpFin, GrpFin -> GrpFin

CommutatorSubgroup(G, H, K) : GrpMat, GrpMat, GrpMat -> GrpMat

CommutatorSubgroup(G, H, K) : GrpPC, GrpPC, GrpPC -> GrpPC

CommutatorSubgroup(G, H, K) : GrpPerm, GrpPerm, GrpPerm -> GrpPerm

comp

comp< R | a_1, ..., a_r > : Rng, RngElt, ..., RngElt -> Rng, Map

compact

CompactPresentation (SOLUBLE GROUPS)

compact-presentation

CompactPresentation (SOLUBLE GROUPS)

CompactPresentation

CompactPresentation(G) : GrpPC -> [RngIntElt]

GrpPC_CompactPresentation (Example H19E13)

CompanionMatrix

CompanionMatrix(p) : RngPolElt -> AlgMatElt

CompanionMatrix(p) : RngUPolElt -> AlgMatElt

comparison

Comparison (MATRIX ALGEBRAS)

Comparison (OVERVIEW)

Comparison (RATIONAL FIELD)

Comparison (RING OF INTEGERS)

Comparison of and Membership (REAL AND COMPLEX FIELDS)

Comparison of Ring Elements (INTRODUCTION [RINGS AND FIELDS])

Comparison of Ring Elements (RING OF INTEGERS)

comparisons

Comparisons and Membership Testing (ALGEBRAS)

CompFactors

GrpPerm_CompFactors (Example H20E19)

Complement

Complement(G) : Grph -> Grph

Complement(D) : Inc -> Inc

Complement(V, U) : ModTupFld, ModTupFld -> ModTupFld

complement

Constructing Complements, Line Graphs; Contraction, Switching (GRAPHS)

complement-line-graph-contraction-switching

Constructing Complements, Line Graphs; Contraction, Switching (GRAPHS)

ComplementaryErrorFunction

ComplementaryErrorFunction(r) : FldReElt -> FldReElt

ComplementBasis

ComplementBasis(G) : GrpPC -> [GrpPC]

Complements

Complements(G, H) : GrpPC, GrpPC -> [GrpPC]

Complements(M, S) : ModGrp, ModGrp -> [ ModGrp ]

complements

Complements of Submodules (GENERAL MODULES)

complete

Construction of a Group Algebra (GROUP ALGEBRAS)

Construction of the Complete Matrix Algebra (MATRIX ALGEBRAS)

complete-magma

Construction of a Group Algebra (GROUP ALGEBRAS)

Construction of the Complete Matrix Algebra (MATRIX ALGEBRAS)

CompleteDigraph

CompleteDigraph(p) : RngIntElt -> GrphDir

CompleteGraph

CompleteGraph(p) : RngIntElt -> GrphUnd

CompleteKArc

CompleteKArc(P, k) : Plane, RngIntElt -> SetEnum

CompleteUnion

CompleteUnion(G, H) : GrphDir, GrphDir -> GrphDir

CompleteWeightEnumerator

CompleteWeightEnumerator(C): Code -> RngMPolElt

Completion

Completion(R, P) : Rng, Rng -> Rng, Map

completion

Completion (INTRODUCTION [RINGS AND FIELDS])

complex

REAL AND COMPLEX FIELDS

Real and Complex Valued Functions (NUMBER FIELDS AND THEIR ORDERS)

Rings, Fields, and Algebras (OVERVIEW)

ComplexConjugate

ComplexConjugate(a) : FldCycElt -> FldQuadElt

ComplexConjugate(s) : FldPrElt -> FldPrElt

ComplexConjugate(a) : FldQuadElt -> FldQuadElt

ComplexConjugate(q) : FldRatElt -> FldRatElt

ComplexConjugate(n) : RngIntElt -> RngIntElt

ComplexField

ComplexField(p) : RngIntElt -> FldCom

ComplexToPolar

ComplexToPolar(c) : FldComElt -> FldReElt, FldReElt

Component

Component(u) : GrphVert -> Grph

Component(C, i) : SetCart, RngIntElt -> Str

Components

Components(G) : Grph -> [ { GrphVert } ]

CompositeFields

CompositeFields(K, L) : FldNum, FldNum -> SeqEnum

Composition

f * g : MagFormElt, MagFormElt -> MagFormElt

Composition(f, g) : RngPowElt, RngPowElt -> RngPowElt

Composition(T, q) : [ FldCycElt ], TabChtr -> AlgChtrElt

composition

Composition (MAPPINGS)

Composition and Convolution (POWER SERIES AND LAURENT SERIES)

Composition and Decomposition (CHARACTERS OF FINITE GROUPS)

Composition Series (GENERAL MODULES)

composition-convolution

Composition and Convolution (POWER SERIES AND LAURENT SERIES)

composition-decomposition

Composition and Decomposition (CHARACTERS OF FINITE GROUPS)

composition-series

Composition Series (GENERAL MODULES)

CompositionFactors

CompositionFactors(G) : : GrpFin -> [ <RngIntElt, RngIntElt, RngIntElt> ]

CompositionFactors(G) : : GrpMat -> [ <RngIntElt, RngIntElt, RngIntElt> ]

CompositionFactors(G) : GrpPerm -> [ <RngIntElt, RngIntElt, RngIntElt> ]

CompositionFactors(M) : ModRng -> [ ModRng ]

CompositionSeries

CompositionSeries(A) : AlgGen -> [ AlgGen ], [ AlgGen ], AlgMatElt

CompositionSeries(G) : GrpPC -> [GrpPC]

CompositionSeries(M) : ModRng, ModRng -> [ ModRng ], [ ModRng ], AlgMatElt

Compositum

FldNum_Compositum (Example H36E3)

CompSeries

RMod_CompSeries (Example H42E18)

concatenated

Concatenated and Justensen Codes (ERROR-CORRECTING CODES)

concatenated-justensen

Concatenated and Justensen Codes (ERROR-CORRECTING CODES)

ConcatenatedCode

ConcatenatedCode(O, I) : Code, Code -> Code

concatenation

Strings (OVERVIEW)

condition

The case expression (OVERVIEW)

The case statement (OVERVIEW)

The if statement (OVERVIEW)

The select expression (OVERVIEW)

conditional

Conditional Statements and Expressions (STATEMENTS AND EXPRESSIONS)

The case expression (OVERVIEW)

The case statement (OVERVIEW)

The if statement (OVERVIEW)

The select expression (OVERVIEW)

The Simple Conditional Expression (STATEMENTS AND EXPRESSIONS)

The Simple Conditional Statement (STATEMENTS AND EXPRESSIONS)

conditional-expression

The Simple Conditional Expression (STATEMENTS AND EXPRESSIONS)

conditional-statement

The Simple Conditional Statement (STATEMENTS AND EXPRESSIONS)

conditioned

Conditioned Presentations (SOLUBLE GROUPS)

conditioned-presentation

Conditioned Presentations (SOLUBLE GROUPS)

ConditionedGroup

ConditionedGroup(G) : GrpPC -> GrpPC

Conductor

Conductor(E) : CurveEll -> RngIntElt

Conductor(K) : FldCyc -> RngIntElt

Conductor(K) : FldQuad -> RngIntElt

Conductor(Q) : FldRat -> RngIntElt

Conic

Conic(P, S) : Plane, { PlanePt } -> SetEnum

conjugacy

Groups (OVERVIEW)

ConjugacyClasses

ConjugacyClasses(G) : GrpAb -> [ <RngIntElt, RngIntElt, GrpAbElt> ]

ConjugacyClasses(G) : GrpPC -> [ <RngIntElt, RngIntElt, GrpPCElt> ]

ConjugacyClasses(G: parameters) : GrpFin -> [ <RngIntElt, RngIntElt, GrpFinElt> ]

ConjugacyClasses(G: parameters) : GrpMat -> [ < RngIntElt, RngIntElt, GrpMatElt > ]

ConjugacyClasses(G: parameters) : GrpPerm -> [ <RngIntElt, RngIntElt, GrpPermElt> ]

Conjugate

Conjugate(a, n) : FldCycElt, RngIntElt -> FldCycElt

Conjugate(a, k) : FldNumElt, RngIntElt -> FldPrElt

Conjugate(a) : FldQuadElt -> FldQuadElt

Conjugate(q) : FldRatElt -> FldRatElt

Conjugate(n) : RngIntElt -> RngIntElt

H ^ g : GrpAb, GrpAbElt -> GrpAb

H ^ g : GrpFin, GrpFinElt -> GrpFin

H ^ u : GrpFP, GrpFPElt -> GrpFP

H ^ g : GrpMat, GrpMatElt -> GrpMat

H ^ g : GrpPC, GrpPCElt -> GrpPC

H ^ g : GrpPerm, GrpPermElt -> GrpPerm

conjugate

Conjugacy (ABELIAN GROUPS)

Conjugacy (MATRIX GROUPS)

Conjugacy (PERMUTATION GROUPS)

Conjugacy (SOLUBLE GROUPS)

Conjugacy Classes of Elements (GROUPS)

Conjugates, Norm and Trace (RATIONAL FIELD)

Conjugates, Norm and Trace (RING OF INTEGERS)

Conjugation of Class Functions (CHARACTERS OF FINITE GROUPS)

Groups (OVERVIEW)

Introduction (SOLUBLE GROUPS)

conjugate-norm-trace

Conjugates, Norm and Trace (RATIONAL FIELD)

Conjugates, Norm and Trace (RING OF INTEGERS)

Conjugates

Class(H, g) : GrpAb, GrpAbElt -> { GrpAbElt }

Class(G, H) : GrpFin, GrpFin -> { GrpFin }

Class(H, x) : GrpFin, GrpFinElt -> { GrpFinElt }

Class(H, x) : GrpMat, GrpMatElt -> { GrpMatElt }

Class(H, g) : GrpPC, GrpPCElt -> { GrpPCElt }

Class(H, x) : GrpPerm, GrpPermElt -> { GrpPermElt }

Conjugates(a) : FldNumElt -> [ FldPrElt ]

conjugates

Conjugates, Minimal Polynomial (CYCLOTOMIC FIELDS)

Conjugates, Minimal Polynomial (QUADRATIC FIELDS)

conjugates-norm-trace

Conjugates, Minimal Polynomial (CYCLOTOMIC FIELDS)

conjugation

Groups (OVERVIEW)

connectedness

Connectedness, Paths and Circuits (GRAPHS)

connectedness-path-circuit

Connectedness, Paths and Circuits (GRAPHS)

ConnectionNumber

ConnectionNumber(D, p, B) : Inc, IncPt, IncBlk -> RngIntElt

Consistency

Consistency(~P: parameters) : Process(pQuot) ->

constant

Constants (REAL AND COMPLEX FIELDS)

ConstantWords

ConstantWords(C, i) : Code, RngIntElt -> { ModTupFldElt }

Constituent

Constituent(C, i) : Cop, RngIntElt -> Struct

Constituents

Constituents(M) : ModRng -> [ ModRng ]

ConstituentsWithMultiplicities

ConstituentsWithMultiplicities(M) : ModRng -> [ <ModRng, RngIntElt> ]

ConstructingHomomorphisms

GrpBB_ConstructingHomomorphisms (Example H17E2)

construction

Construction of New Lattices (LATTICES)

Construction of Standard Linear Codes (ERROR-CORRECTING CODES)

Standard Constructions and Conversions (ABELIAN GROUPS)

Standard Constructions of New Lattices (LATTICES)

construction-standard

Construction of Standard Linear Codes (ERROR-CORRECTING CODES)

Constructions

GrpMat_Constructions (Example H21E11)

RMod_Constructions (Example H42E11)

Constructor

GrpMat_Constructor (Example H21E5)

constructor

Construction of Lists (LISTS)

Constructor (OVERVIEW)

Function Expressions (OVERVIEW)

Procedure Expressions (OVERVIEW)

Sequences (OVERVIEW)

Sets (OVERVIEW)

The Map Constructors (MAPPINGS)

Constructors

Design_Constructors (Example H56E1)

Graph_Constructors (Example H55E1)

Graph_Constructors (Example H55E3)

Graph_Constructors (Example H55E4)

Graph_Constructors (Example H55E5)

GrpPerm_Constructors (Example H20E5)

Plane_Constructors (Example H57E1)

ConstructTable

ConstructTable(A) : AlgGrp ->

ContainsQuadrangle

ContainsQuadrangle(P, S) : Plane, { PlanePt } -> BoolElt

Content

Content(f) : RngMPolElt -> RngIntElt

Content(p) : RngUPolElt -> RngIntElt

content

Content and Primitive Part (MULTIVARIATE POLYNOMIAL RINGS)

Content and Primitive Part (UNIVARIATE POLYNOMIAL RINGS)

ContentAndPrimitivePart

ContentAndPrimitivePart(f) : RngMPolElt -> RngIntElt, RngMPolElt

ContentAndPrimitivePart(p) : RngUPolElt -> RngIntElt, RngUPolElt

contents

Contents of Database of Finite Perfect Groups (OVERVIEW)

Contents of Database of Groups of Order Dividing 256 (OVERVIEW)

Contents of Database of Groups of Order Dividing 729 (OVERVIEW)

context

The Initial Context (MAGMA SEMANTICS)

continuation

Comments and Continuation (STATEMENTS AND EXPRESSIONS)

continue

Early Exit from Iterative Statements (STATEMENTS AND EXPRESSIONS)

The continue statement (OVERVIEW)

continue-break

Early Exit from Iterative Statements (STATEMENTS AND EXPRESSIONS)

continued

Continued Fractions (REAL AND COMPLEX FIELDS)

continued-fraction

Continued Fractions (REAL AND COMPLEX FIELDS)

ContinuedFraction

ContinuedFraction(r) : FldPrElt -> [ RngIntElt ]

Contpp

ContentAndPrimitivePart(f) : RngMPolElt -> RngIntElt, RngMPolElt

ContentAndPrimitivePart(p) : RngUPolElt -> RngIntElt, RngUPolElt

Contract

Contract(e) : GrphEdge -> Grph

Contraction

Contraction(D, p) : Inc, IncPt -> Inc

contraction

Constructing Complements, Line Graphs; Contraction, Switching (GRAPHS)

Extension and Contraction of Ideals (MULTIVARIATE POLYNOMIAL RINGS)

control

Control-C key (OVERVIEW)

Controlling selection of a Base (MATRIX GROUPS)

Quitting (OVERVIEW)

control-\-key

<Ctrl>-\

<Ctrl>-\

control-A-key

<Ctrl>-A

control-B-key

<Ctrl>-B

control-C-key

Control-C key (OVERVIEW)

<Ctrl>-C

<Ctrl>-C

control-D-key

Quitting (OVERVIEW)

<Ctrl>-D

quit;

control-E-key

<Ctrl>-E

control-F-key

<Ctrl>-F

control-H-key

<Ctrl>-H

control-I-key

<Ctrl>-I

control-J-key

<Ctrl>-J

control-K-key

<Ctrl>-K

control-L-key

<Ctrl>-L

control-M-key

<Ctrl>-M

control-N-key

<Ctrl>-N

control-P-key

<Ctrl>-P

control-space-key

<Ctrl>- space

control-U-key

<Ctrl>-U

control-V-key

<Ctrl>-V<char>

control-W-key

<Ctrl>-W

control-X-key

<Ctrl>-X

control-Z-key

<Ctrl>-Z

ControlExtn

GrpFP_ControlExtn (Example H16E11)

conv

Design_conv (Example H56E9)

Convergents

Convergents(s) : [ RngIntElt ] -> ModMatRngElt

conversion

Character Conversion (INPUT AND OUTPUT)

Conversion between Categories (SOLUBLE GROUPS)

Conversion Functions (INCIDENCE STRUCTURES AND DESIGNS)

Conversion to a PC-Group (MATRIX GROUPS)

Conversions (REAL AND COMPLEX FIELDS)

Converting between Graphs and Digraphs (GRAPHS)

Creation and Conversion (RING OF INTEGERS)

Element Conversions (RING OF INTEGERS)

Sets from Structures (SETS)

conversion-graph-digraph

Converting between Graphs and Digraphs (GRAPHS)

Convolution

Convolution(f, g) : RngSerElt, RngSerElt -> RngSerElt

convolution

Composition and Convolution (POWER SERIES AND LAURENT SERIES)

ConwayPolynomial

ConwayPolynomial(p, n) : RngIntElt, RngIntElt -> RngUPolElt

Coordelt

CoordinatesToElement(L, C) : Lat, [ RngIntElt ] -> LatElt

CoordinateRing

CoordinateRing(L) : Lat -> RngInt

Coordinates

Coordinates(S, a) : AlgGen, AlgGenElt -> SeqEnum

Coordinates(S, a) : AlgGrpSub, AlgGrpElt -> [ RingElt ]

Coordinates(R, X) : AlgMat, AlgMatElt -> [ RngElt ]

Coordinates(C, u) : Code, ModTupFldElt -> [ FldFinElt ]

Coordinates(v) : LatElt -> [ RngIntElt ]

Coordinates(f, M) : ModMPolElt, ModMPol -> [ RngMPolElt ]

Coordinates(V, v) : ModTupFld, ModTupFldElt -> [FldElt]

Coordinates(M, u) : ModTupRng, ModTupRngElt -> [RngElt]

Coordinates(P, p) : Plane, PlanePt -> [ FldFinElt ]

Coordinates(I, f) : RngMPol, RngMPolElt -> [ RngMPolElt ]

RngMPol_Coordinates (Example H29E13)

CoordinatesToElement

CoordinatesToElement(L, C) : Lat, [ RngIntElt ] -> LatElt

CoordinateVector

CoordinateVector(v) : LatElt -> LatElt

cop

Aggregate (OVERVIEW)

cop< S_1, S_2, ..., S_k > : Struct, Struct, ... -> Cop, [ Map ]

Coproduct_cop (Example H11E1)

CoprimeBasis

CoprimeBasis(S) : [ RngIntElt ] -> [ RngIntElt ]

coproduct

COPRODUCTS

Core

Core(G, H) : GrpAb, GrpAb -> GrpAb

Core(G, H) : GrpFin, GrpFin -> GrpFin

Core(G, H) : GrpFP, GrpFP -> GrpFP

Core(G, H) : GrpMat, GrpMat -> GrpMat

Core(G, H) : GrpPC, GrpPC -> GrpPC

Core(G, H) : GrpPerm, GrpPerm -> GrpPerm

correcting

Combinatorial and Geometrical Structures (OVERVIEW)

ERROR-CORRECTING CODES

Cos

Cos(c) : FldComElt -> FldComElt

Cos(f) : RngSerElt -> RngSerElt

Cosec

Cosec(c) : FldComElt -> FldComElt

Cosech

Cosech(s) : FldPrElt -> FldPrElt

coset

Action on a Coset Space (GROUPS)

Action on a Coset Space (MATRIX GROUPS)

Action on a Coset Space (PERMUTATION GROUPS)

Coset Leaders (ERROR-CORRECTING CODES)

Coset Spaces (ABELIAN GROUPS)

Coset Spaces (SOLUBLE GROUPS)

Coset Spaces and Tables (FINITELY PRESENTED GROUPS)

Coset Spaces: Construction (FINITELY PRESENTED GROUPS)

Coset Tables (FINITELY PRESENTED GROUPS)

coset-leader

Coset Leaders (ERROR-CORRECTING CODES)

coset-space

Coset Spaces (ABELIAN GROUPS)

Coset Spaces (SOLUBLE GROUPS)

Coset Spaces: Construction (FINITELY PRESENTED GROUPS)

coset-space-action

Action on a Coset Space (GROUPS)

Action on a Coset Space (MATRIX GROUPS)

Action on a Coset Space (PERMUTATION GROUPS)

coset-space-table

Coset Spaces and Tables (FINITELY PRESENTED GROUPS)

coset-table

Coset Tables (FINITELY PRESENTED GROUPS)

CosetAction

CosetAction(G, H) : Grp, Grp -> Hom(Grp), Grp, Grp

CosetAction(G, H) : Grp, Grp -> Hom(Grp), GrpPerm, Grp

CosetAction(G, H) : Grp, Grp -> Hom(Grp), GrpPerm, Grp

CosetAction(G, H) : Grp, Grp -> Hom(Grp), GrpPerm, GrpPerm

CosetAction(G, H) : GrpMat, GrpMat -> Hom(Grp), GrpPerm, GrpMat

GrpMat_CosetAction (Example H21E16)

Grp_CosetAction (Example H15E8)

CosetDistanceDistribution

CosetDistanceDistribution(C) : Code -> [ <RngIntElt, RngIntElt> ]

CosetImage

CosetImage(G, H) : Grp, Grp -> Grp

CosetImage(G, H) : Grp, Grp -> GrpPerm

CosetImage(G, H) : Grp, Grp -> GrpPerm

CosetImage(G, H) : Grp, Grp -> GrpPerm

CosetImage(G, H) : GrpMat, GrpMat -> GrpPerm

CosetKernel

CosetKernel(G, H) : Grp, Grp -> Grp

CosetKernel(G, H) : Grp, Grp -> Grp

CosetKernel(G, H) : Grp, Grp -> Grp

CosetKernel(G, H) : GrpFP, GrpFP -> GrpFP

CosetKernel(G, H) : GrpMat, GrpMat -> GrpMat

CosetLeaders

CosetLeaders(C) : Code -> {@ ModTupFldElt @}, Map

Code_CosetLeaders (Example H58E13)

CosetSatisfying

CosetsSatisfying(T, S: parameters) : Map, { GrpFPElt }: -> { GrpFPCosElt }

CosetSpace

CosetSpace(G, H: parameters) : GrpFP, GrpFP: -> GrpFPCos

CosetsSatisfying

CosetsSatisfying(T, S: parameters) : Map, { GrpFPElt }: -> { GrpFPCosElt }

CosetTable

CosetTable(G, H) : Grp, Grp -> Hom(Grp)

CosetTable(G, H) : Grp, Grp -> Map

CosetTable(G, H) : GrpFin, GrpFin -> Map

CosetTable(G, H: parameters) : GrpFP, GrpFP -> Map

CosetTableToPermutationGroup

CosetTableToPermutationGroup(G, T) : GrpFP, Map -> GrpPerm

CosetTableToRepresentation

CosetTableToRepresentation(G, T): GrpFP, Map -> Map, GrpPerm, Grp

Cosh

Cosh(s) : FldPrElt -> FldPrElt

Cosh(f) : RngSerElt -> RngSerElt

Cot

Cot(c) : FldComElt -> FldComElt

Coth

Coth(s) : FldPrElt -> FldPrElt

Covalence

Covalence(D, s) : Dsgn, RngIntElt -> RngIntElt

Covalence(D, S) : Inc, { IncPt } -> RngIntElt

CoveringRadius

CoveringRadius(C) : Code -> RngIntElt

CoveringRadius(L) : Lat -> FldRatElt

Coxeter

Index of a Subgroup: The Todd-Coxeter Algorithm (FINITELY PRESENTED GROUPS)

GrpFP_Coxeter (Example H16E8)

CPU

Timing (OVERVIEW)

Cputime

Timing (OVERVIEW)

Cputime() : -> FldReElt

Create

GrpMat_Create (Example H21E1)

HMod_Create (Example H43E1)

PMod_Create (Example H44E1)

create

Creating Lattices (GENERAL MODULES)

Creating Names (INPUT AND OUTPUT)

Creation of G-Lattices (LATTICES)

create-name

Creating Names (INPUT AND OUTPUT)

CreateA4wrC3

RMod_CreateA4wrC3 (Example H42E7)

CreateA7

RMod_CreateA7 (Example H42E5)

CreateComplexField

FldRe_CreateComplexField (Example H37E3)

CreateElements

FldRe_CreateElements (Example H37E4)

CreateHom

HMod_CreateHom (Example H43E2)

CreateHomGHom

HMod_CreateHomGHom (Example H43E3)

CreateK35

KMod_CreateK35 (Example H41E2)

CreateK6

RMod_CreateK6 (Example H42E2)

CreateL27

RMod_CreateL27 (Example H42E3)

CreateLattice

RMod_CreateLattice (Example H42E21)

CreateM11

RMod_CreateM11 (Example H42E6)

CreateM12

RMod_CreateM12 (Example H42E4)

CreateMatrices

RMod_CreateMatrices (Example H42E8)

CreateQ6

KMod_CreateQ6 (Example H41E1)

CreateSubgroupPoset

Grp_CreateSubgroupPoset (Example H15E15)

CreateZ6

RMod_CreateZ6 (Example H42E1)

Creation

AlgMat_Creation (Example H51E1)

Elcu_Creation (Example H53E1)

FldFunG_Creation (Example H32E1)

FldLoc_Creation (Example H39E1)

FldNum_Creation (Example H36E2)

creation

Cartesian Product Constructor and Functions (TUPLES AND CARTESIAN PRODUCTS)

Constructing the Automorphism Group (INCIDENCE STRUCTURES AND DESIGNS)

Construction of a Base and Strong Generating Set (MATRIX GROUPS)

Construction of a Base and Strong Generating Set (PERMUTATION GROUPS)

Construction of a Blackbox Group and its Elements (BLACKBOX GROUPS)

Construction of a Codeword (ERROR-CORRECTING CODES)

Construction of a Free Algebra (FINITELY PRESENTED ALGEBRAS)

Construction of a General Digraph (GRAPHS)

Construction of a General Graph (GRAPHS)

Construction of a General Group (GROUPS)

Construction of a General Permutation Group (PERMUTATION GROUPS)

Construction of a Matrix (THE MODULES Hom_(R)(M, N) AND End(M))

Construction of a Plane (FINITE PLANES)

Construction of a Vector (VECTOR SPACES)

Construction of a Vector Space (VECTOR SPACES)

Construction of Associative Algebras (ASSOCIATIVE ALGEBRAS)

Construction of Elements (GROUPS)

Construction of Free Abelian Group and its Elements (ABELIAN GROUPS)

Construction of General Algebras and their Elements (ALGEBRAS)

Construction of Group Algebras and their Elements (GROUP ALGEBRAS)

Construction of Hom_(R)(M, N) (THE MODULES Hom_(R)(M, N) AND End(M))

Construction of Incidence Structures and Designs (INCIDENCE STRUCTURES AND DESIGNS)

Construction of Lie Algebras (LIE ALGEBRAS)

Construction of Matrix Algebras and their Elements (MATRIX ALGEBRAS)

Construction of Module Elements (GENERAL MODULES)

Construction of New Ideals (MULTIVARIATE POLYNOMIAL RINGS)

Construction of Structure Constant Algebras and their Elements (STRUCTURE CONSTANT ALGEBRAS)

Creating a G-Set (PERMUTATION GROUPS)

Creating a Record (RECORDS)

Creating Edges and Vertices (GRAPHS)

Creating Point-Sets and Block-Sets (INCIDENCE STRUCTURES AND DESIGNS)

Creating Point-Sets and Line-Sets (FINITE PLANES)

Creating Sequences (SEQUENCES)

Creating Sets (SETS)

Creating the Poset of Subgroup Classes (GROUPS)

Creation (RING OF INTEGERS)

Creation Functions (CHARACTERS OF FINITE GROUPS)

Creation Functions (COPRODUCTS)

Creation Functions (CYCLOTOMIC FIELDS)

Creation Functions (ELLIPTIC CURVES)

Creation Functions (FINITE FIELDS)

Creation Functions (FUNCTION FIELDS AND THEIR ORDERS)

Creation Functions (MAPPINGS)

Creation Functions (NUMBER FIELDS AND THEIR ORDERS)

Creation Functions (POWER SERIES AND LAURENT SERIES)

Creation Functions (QUADRATIC FIELDS)

Creation Functions (RATIONAL FIELD)

Creation Functions (RATIONAL FUNCTION FIELDS)

Creation Functions (REAL AND COMPLEX FIELDS)

Creation Functions (RESIDUE CLASS RINGS)

Creation Functions (RING OF INTEGERS)

Creation Functions (UNIVARIATE POLYNOMIAL RINGS)

Creation Functions (VALUATION RINGS)

Creation of Affine Algebras (MULTIVARIATE POLYNOMIAL RINGS)

Creation of an Elliptic Curve (ELLIPTIC CURVES)

Creation of Booleans (STATEMENTS AND EXPRESSIONS)

Creation of Cyclotomic Fields (CYCLOTOMIC FIELDS)

Creation of Elements (FINITE FIELDS)

Creation of Elements (INTRODUCTION [RINGS AND FIELDS])

Creation of Elements (LOCAL FIELDS)

Creation of Elements (POWER SERIES AND LAURENT SERIES)

Creation of Generic Free Modules (MODULES OVER AFFINE ALGEBRAS)

Creation of Ideals (MULTIVARIATE POLYNOMIAL RINGS)

Creation of Ideals and Quotients (UNIVARIATE POLYNOMIAL RINGS)

Creation of Lattice Elements (LATTICES)

Creation of Lattices (LATTICES)

Creation of New Lists (LISTS)

Creation of Points (ELLIPTIC CURVES)

Creation of Polynomial Rings and Creation of Polynomials (MULTIVARIATE POLYNOMIAL RINGS)

Creation of Strings (INPUT AND OUTPUT)

Creation of Structures (LOCAL FIELDS)

Creation of Subgroups of Elliptic Curves (ELLIPTIC CURVES)

Creation of Subschemes of Elliptic Curves (ELLIPTIC CURVES)

Creation of the General Linear Group and its Elements (MATRIX GROUPS)

Creation of the Symmetric Group and Arithmetic with Permutations (PERMUTATION GROUPS)

Creation of Vector Spaces and Arithmetic with Vectors (VECTOR SPACES)

Defining Ideals and Quotient Rings (INTRODUCTION [RINGS AND FIELDS])

Definition of a Code (ERROR-CORRECTING CODES)

Definition of a Module (GENERAL MODULES)

Definition of Soluble Groups using Power-conjugate Presentations (SOLUBLE GROUPS)

Element Constructors and Selectors (LOCAL FIELDS)

Elementary Creation of Lattices (LATTICES)

General Constructions (MATRIX GROUPS)

Ideal Creation (FUNCTION FIELDS AND THEIR ORDERS)

Ideal Creation (NUMBER FIELDS AND THEIR ORDERS)

New Rings from Old Ones (INTRODUCTION [RINGS AND FIELDS])

Operations on Structure Constant Algebras and their Elements (STRUCTURE CONSTANT ALGEBRAS)

Other Ring Constructions (INTRODUCTION [RINGS AND FIELDS])

Presentation of Lattices (LATTICES)

Specification of a Subgroup (FINITELY PRESENTED GROUPS)

Structure Creation (CHARACTERS OF FINITE GROUPS)

The Automorphism Group Function (GRAPHS)

The Collineation Group Function (FINITE PLANES)

The Construction of a Matrix Group (MATRIX GROUPS)

The Construction of a Permutation Group (PERMUTATION GROUPS)

The Construction of a Vector Space (VECTOR SPACES)

The Construction of Direct Sums and Tensor Products (MATRIX ALGEBRAS)

The Construction of Finitely Presented Groups (FINITELY PRESENTED GROUPS)

The Construction of Finitely Presented Groups (FINITELY PRESENTED GROUPS)

The Construction of Free Semigroups and their Elements (FINITELY PRESENTED SEMIGROUPS)

The Construction of p-Quotients (FINITELY PRESENTED GROUPS)

The Construction of Related Structures (INCIDENCE STRUCTURES AND DESIGNS)

The Record Format Constructor (RECORDS)

The Subcode Constructor (ERROR-CORRECTING CODES)

AlgGrp_creation (Example H50E1)

FldQuad_creation (Example H34E2)

creation-arithmetic

Creation of Vector Spaces and Arithmetic with Vectors (VECTOR SPACES)

creation-class-function-ring

Structure Creation (CHARACTERS OF FINITE GROUPS)

creation-curve

Creation of an Elliptic Curve (ELLIPTIC CURVES)

creation-digraph

Construction of a General Digraph (GRAPHS)

creation-element

Construction of a Matrix (THE MODULES Hom_(R)(M, N) AND End(M))

Construction of a Vector (VECTOR SPACES)

Creation of Elements (INTRODUCTION [RINGS AND FIELDS])

Creation of Elements (LOCAL FIELDS)

Creation of Elements (POWER SERIES AND LAURENT SERIES)

Definition of Soluble Groups using Power-conjugate Presentations (SOLUBLE GROUPS)

Element Constructors and Selectors (LOCAL FIELDS)

creation-format

The Record Format Constructor (RECORDS)

creation-general

Construction of a General Group (GROUPS)

Construction of a General Permutation Group (PERMUTATION GROUPS)

creation-general-linear-group

Creation of the General Linear Group and its Elements (MATRIX GROUPS)

creation-general-matrix-group

General Constructions (MATRIX GROUPS)

creation-graph

Construction of a General Graph (GRAPHS)

creation-ideal

Construction of New Ideals (MULTIVARIATE POLYNOMIAL RINGS)

creation-magma

Construction of a Vector Space (VECTOR SPACES)

creation-module

Definition of a Module (GENERAL MODULES)

creation-other

Other Ring Constructions (INTRODUCTION [RINGS AND FIELDS])

creation-point

Creation of Points (ELLIPTIC CURVES)

creation-record

Creating a Record (RECORDS)

creation-related

The Construction of Related Structures (INCIDENCE STRUCTURES AND DESIGNS)

creation-subgroups

Creation of Subgroups of Elliptic Curves (ELLIPTIC CURVES)

creation-subschemes

Creation of Subschemes of Elliptic Curves (ELLIPTIC CURVES)

creation-symmetric

Construction of Elements (GROUPS)

Creation of the Symmetric Group and Arithmetic with Permutations (PERMUTATION GROUPS)

CRT

ChineseRemainderTheorem(a, b, m) : RngIntElt, RngIntElt, RngIntElt -> RngIntElt

Cunningham

Cunningham(b, k, c) : RngIntElt, RngIntElt, RngIntElt -> SeqEnum

curly

Sets (OVERVIEW)

curly-bracket

Sets (OVERVIEW)

Current

Current(p) : Process -> Grp

Current(p) : Process -> GrpPerm, MonStgElt

CurrentLabel

CurrentLabel(p) : Process -> RngIntElt, RngIntElt

CurrentLabel(p) : Process -> RngIntElt, RngIntElt

curve

Combinatorial and Geometrical Structures (OVERVIEW)

Creation of an Elliptic Curve (ELLIPTIC CURVES)

ELLIPTIC CURVES

CutVertices

CutVertices(G) : Grph -> { GrphVert }

CycleStructure

CycleStructure(g) : GrpPermElt -> [ <RngIntElt, RngIntElt> ]

cyclic

Construction of General Cyclic Codes (ERROR-CORRECTING CODES)

Cyclic6

RngMPol_Cyclic6 (Example H29E10)

CyclicCode

CyclicCode(u) : ModTupFldElt -> Code

Code_CyclicCode (Example H58E6)

CyclicGroup

CyclicGroup(C, n) : Cat, RngIntElt -> GrpFin

CyclicGroup(GrpFP, n) : Cat, RngIntElt -> GrpFP

CyclicGroup(GrpPC, n) : Cat, RngIntElt -> GrpPC

CyclicGroup(GrpPerm, n) : Cat, RngIntElt -> GrpPerm

CyclicSubgroups

CyclicSubgroups(G: parameters) : GrpFin -> [ rec< Grp, RngIntElt, RngIntElt, GrpFP> ]

cyclotomic

CYCLOTOMIC FIELDS

Functions Returning a Scalar (CHARACTERS OF FINITE GROUPS)

Rings, Fields, and Algebras (OVERVIEW)

CyclotomicField

CyclotomicField(m) : RngIntElt -> FldCyc

CyclotomicOrder

CyclotomicOrder(K) : FldCyc -> RngIntElt

CyclotomicPolynomial

CyclotomicPolynomial(m) : RngIntElt -> RngUPolElt


[____] [____] [_____] [____] [__] [Index] [Root]