Index C

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

Index C

C

C-key

c-key

CanContinueEnumeration

CanContinueEnumeration(P) : GrpFPCosetEnumProc -> BoolElt

Canonical

CanonicalDivisor(C) : Crv -> DivCrvElt
D ! 0 : DivCrv,RngIntElt -> DivCrvElt
CalculateCanonicalClass(~g) : GrphRes ->
CanonicalClass(g) : GrphRes -> SeqEnum
CanonicalDivisor(F) : FldFun -> DivFunElt
CanonicalGraph(G : parameters ) : Grph -> Grph
CanonicalInvolution(X) : CrvMod -> MapSch
CanonicalMap(C) : Crv -> MapSch
CanonicalModularEquation(N) : RngIntElt -> RngMPolElt
Height(P: parameters) : PtEll -> FldPrElt
Height(P: Precision) : JacHypPt -> FldPrElt
IsCanonical(D) : DivCrvElt -> BoolElt,DiffFunElt
IsCanonical(D) : DivFunElt -> BoolElt, DiffFunElt
IsCanonical(D) : DivFunElt -> BoolElt, DiffFunElt

canonical

Canonical Forms (MATRICES)
Canonical Forms (MATRIX ALGEBRAS)
Canonical Forms over Euclidean Domains (MATRICES)
Canonical Forms over Fields (MATRICES)
Canonical Forms over General Rings (MATRICES)

canonical-euclidean

Canonical Forms over Euclidean Domains (MATRICES)

canonical-field

Canonical Forms over Fields (MATRICES)

canonical-form

Canonical Forms (MATRIX ALGEBRAS)

canonical-map

Crv_canonical-map (Example H82E20)

canonical_divisor

Crv_canonical_divisor (Example H82E18)

CanonicalClass

CanonicalClass(g) : GrphRes -> SeqEnum

CanonicalDivisor

CanonicalDivisor(C) : Crv -> DivCrvElt
D ! 0 : DivCrv,RngIntElt -> DivCrvElt
CanonicalDivisor(F) : FldFun -> DivFunElt

CanonicalForms

AlgMat_CanonicalForms (Example H72E8)
Mat_CanonicalForms (Example H62E9)

CanonicalGraph

CanonicalGraph(G : parameters ) : Grph -> Grph

CanonicalHeight

CanonicalHeight(P: parameters) : PtEll -> FldPrElt
Height(P: parameters) : PtEll -> FldPrElt
Height(P: Precision) : JacHypPt -> FldPrElt

CanonicalInvolution

AtkinLehnerInvolution(X,N) : CrvMod, RngIntElt -> MapSch
CanonicalInvolution(X) : CrvMod -> MapSch

CanonicalMap

CanonicalMap(C) : Crv -> MapSch

CanonicalModularEquation

CanonicalModularEquation(N) : RngIntElt -> RngMPolElt

CanRedoEnumeration

CanRedoEnumeration(P) : GrpFPCosetEnumProc -> BoolElt

car

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

Card-Best-Comparison

CodeFld_Card-Best-Comparison (Example H97E39)

cardinality

Bounds on the Cardinality of a Largest Code (LINEAR CODES OVER FINITE FIELDS)
Groups (OVERVIEW)
Rings, Fields, and Algebras (OVERVIEW)
Sets (OVERVIEW)

Carmichael

CarmichaelLambda(n) : RngIntElt -> RngIntElt
FactoredCarmichaelLambda(n) : RngIntElt -> RngIntEltFact

CarmichaelLambda

CarmichaelLambda(n) : RngIntElt -> RngIntElt

Cartan

LieConstant_A( RD, r, s) : RootDtm, RngIntElt, RngIntElt -> RngIntElt
CartanInteger( RD, r, s) : RootDtm, RngIntElt, RngIntElt -> RngIntElt
CartanMatrix( W ) : GrpCox -> AlgMatElt
CartanMatrix(g) : GrphRes -> Mtrx
CartanMatrix( G ) : GrpLie -> AlgMatElt
CartanMatrix( t ) : MonStgElt -> AlgMatElt
CartanMatrix( RD ) : RootDtm -> AlgMatElt
CartanName( C ) : AlgMatElt -> List
CartanName( G ) : GrpLie -> MonStgElt
CartanSubalgebra(L) : AlgLie -> AlgLie
IsCartanIrreducible( C ) : AlgMatElt -> BoolElt
IsCartanMatrix( M ) : AlgMatElt -> BoolElt

cartan

Cartan matrices (ROOT DATA FOR LIE THEORY)
Cartan Subalgebra (LIE ALGEBRAS)

cartan-matrices-and-types

Cartan matrices (ROOT DATA FOR LIE THEORY)

CartanInteger

LieConstant_A( RD, r, s) : RootDtm, RngIntElt, RngIntElt -> RngIntElt
CartanInteger( RD, r, s) : RootDtm, RngIntElt, RngIntElt -> RngIntElt

CartanMatrices

RootDtm_CartanMatrices (Example H35E1)

CartanMatrix

CartanMatrix( W ) : GrpCox -> AlgMatElt
CartanMatrix(g) : GrphRes -> Mtrx
CartanMatrix( G ) : GrpLie -> AlgMatElt
CartanMatrix( t ) : MonStgElt -> AlgMatElt
CartanMatrix( RD ) : RootDtm -> AlgMatElt

CartanMatrixFunctions

RootDtm_CartanMatrixFunctions (Example H35E2)

CartanName

CartanName( C ) : AlgMatElt -> List
CartanName( G ) : GrpLie -> MonStgElt

CartanSubalgebra

CartanSubalgebra(L) : AlgLie -> AlgLie
AlgLie_CartanSubalgebra (Example H75E4)

Cartesian

The Cartesian Product Constructors (SETS)
CartesianPower(R, k) : Str, RngIntElt -> SetCart
CartesianProduct(G, H) : GrphDir, GrphDir -> GrphDir
CartesianProduct(R, S) : Str, ..., Str -> SetCart

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)

Cartier

Cartier(a) : DiffFunElt -> DiffFunElt
Cartier(b) : DiffFunElt -> DiffFunElt
CartierRepresentation(F) : FldFunG -> AlgMatElt, SeqEnum[DiffFunElt]

CartierRepresentation

CartierRepresentation(F) : FldFunG -> AlgMatElt, SeqEnum[DiffFunElt]

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

C1 cat C2 : Code,Code -> Code
C1 cat C2 : Code,Code -> Code
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

categories-verbose

Categories and Verbose Output (MODULAR FORMS)

category-transfer

Transfer Functions Between Group Categories (GROUPS)

Cayley

UnlabelledCayleyGraph(A) : Grp -> GrphDir
CayleyGraph(A) : Grp -> GrphDir

cayley

AlgCon_cayley (Example H69E2)

CayleyGraph

UnlabelledCayleyGraph(A) : Grp -> GrphDir
CayleyGraph(A) : Grp -> GrphDir
Graph_CayleyGraph (Example H93E8)

Ceiling

Ceiling(q) : FldRatElt -> RngIntElt
Ceiling(r) : FldReElt -> RngIntElt
Ceiling(n) : RngIntElt -> RngIntElt

Cell

VoronoiCell(L) : Lat -> [ ModTupFldElt ], SetEnum , [ ModTupFldElt ]

cent-coll

Plane_cent-coll (Example H95E15)

Center

Center(G) : GrpAb -> GrpAb
Centre(G) : GrpAb -> GrpAb
Centre(G) : GrpFin -> GrpFin
Centre(G) : GrpGPC -> GrpGPC
Centre(G) : GrpMat -> GrpMat
Centre(G) : GrpPC -> GrpPC
Centre(G) : GrpPerm -> GrpPerm
Centre(R) : Rng -> Rng
CentreDensity(L) : Lat -> FldReElt

CenterDensity

CenterDensity(L) : Lat -> FldReElt
CentreDensity(L) : Lat -> FldReElt

Central

central

Central Collineations (FINITE PLANES)
Central Extensions (FINITE SOLUBLE GROUPS)

central-extensions

Central Extensions (FINITE SOLUBLE GROUPS)

CentralCollineationGroup

CentralEndomorphisms

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

CentralExtension

CentralExtension (G, U, A) : GrpPC, GrpPC, AlgMatElt -> GrpPC
GrpPC_CentralExtension (Example H25E28)

CentralExtensionProcess

CentralExtensionProcess (G, U) : GrpPC, GrpPC -> Proc

CentralExtensions

CentralExtensions (G, U, Q) : GrpPC, GrpPC, [AlgMatElt] -> [GrpPC]

Centraliser

Centralizer(a) : AlgGrpElt -> AlgGrpSub
Centraliser(a) : AlgGrpElt -> AlgGrpSub
Centraliser(S) : AlgGrpSub -> AlgGrpSub
Centraliser(S, a) : AlgGrpSub, AlgGrpElt -> AlgGrpSub
Centraliser(G, H) : GrpGPC, GrpGPC -> GrpGPC
Centraliser(G, g) : GrpGPC, GrpGPCElt -> GrpGPC
Centraliser(e, f) : SubGrpLatElt, SubGrpLatElt -> SubGrpLatElt
Centralizer(A, S) : AlgAss, AlgAss -> AlgAss
Centralizer(A, s) : AlgAss, AlgAssElt -> AlgAss
Centralizer(G, H) : GrpAb, GrpAb -> GrpAb
Centralizer(G, g) : GrpAb, GrpAbElt -> GrpAb
Centralizer(G, H) : GrpFin, GrpFin -> GrpFin
Centralizer(G, g) : GrpFin, GrpFinElt -> GrpFin
Centralizer(G, H) : GrpPC, GrpPC -> GrpPC
Centralizer(G, g) : GrpPC, GrpPCElt -> GrpPC
Centralizer(G, H) : GrpPerm, GrpPerm -> GrpPerm
Centralizer(G, g) : GrpPerm, GrpPermElt -> GrpPerm
SectionCentraliser(G, H, K) : GrpPerm, GrpPerm, GrpPerm -> GrpPerm

Centralising

CentralisingMatrix(G) : GrpMat -> AlgMatElt

CentralisingMatrix

CentralisingMatrix(G) : GrpMat -> AlgMatElt

Centralizer

Centralizer(a) : AlgGrpElt -> AlgGrpSub
Centraliser(a) : AlgGrpElt -> AlgGrpSub
Centraliser(S) : AlgGrpSub -> AlgGrpSub
Centraliser(S, a) : AlgGrpSub, AlgGrpElt -> AlgGrpSub
Centraliser(G, H) : GrpGPC, GrpGPC -> GrpGPC
Centraliser(G, g) : GrpGPC, GrpGPCElt -> GrpGPC
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, H) : GrpAb, GrpAb -> GrpAb
Centralizer(G, g) : GrpAb, GrpAbElt -> GrpAb
Centralizer(G, H) : GrpFin, GrpFin -> GrpFin
Centralizer(G, g) : GrpFin, GrpFinElt -> GrpFin
Centralizer(G, H) : GrpMat, GrpMat -> GrpMat
Centralizer(G, g) : GrpMat, GrpMatElt -> GrpMat
Centralizer(G, H) : GrpPC, GrpPC -> GrpPC
Centralizer(G, g) : GrpPC, GrpPCElt -> GrpPC
Centralizer(G, H) : GrpPerm, GrpPerm -> GrpPerm
Centralizer(G, g) : GrpPerm, GrpPermElt -> GrpPerm
CentralizerOfNormalSubgroup(G, H) : GrpPerm, GrpPerm -> GrpPerm
SectionCentraliser(G, H, K) : GrpPerm, GrpPerm, GrpPerm -> GrpPerm

CentralizerOfNormalSubgroup

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

Centralizing

GHomOverCentralizingField(M, N) : ModGrp, ModGrp -> ModMatGrp

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) : GrpGPC -> GrpGPC
Centre(G) : GrpMat -> GrpMat
Centre(G) : GrpPC -> GrpPC
Centre(G) : GrpPerm -> GrpPerm
Centre(R) : Rng -> Rng
CentreDensity(L) : Lat -> FldReElt
CentreOfEndomorphismRing(G) : GrpMat -> AlgMat
DimensionOfCentreOfEndomorphismRing(G) : GrpMat -> RngIntElt
HasCentreType(X,i) : VSrfK3,RngIntElt -> BoolElt

CentreDensity

CenterDensity(L) : Lat -> FldReElt
CentreDensity(L) : Lat -> FldReElt

CentreOfEndomorphismRing

CentreOfEndomorphismRing(G) : GrpMat -> AlgMat

Centres

Centres(X) : VSrfK3 -> SeqEnum
Centres(~X,DB) : VSrfK3,SeqEnum ->

Certificate

HasSolubilityCertificate(C) : CrvCon -> BoolElt, SeqEnum
HasSolubilityCertificate(S) : SeqEnum[RngIntElt] -> BoolElt, SeqEnum
SolubilityCertificate(C) : CrvCon -> SeqEnum

Chabauty

Chabauty(P, p: Precision) : JacHypPt, RngIntElt -> SetIndx

chabauty

Chabauty's Method (HYPERELLIPTIC CURVES)

chabauty-method

Chabauty's Method (HYPERELLIPTIC CURVES)

Chabauty0

Chabauty0(J) : JacHyp -> SetIndx

Chain

BasicStabiliserChain(G) : GrpMat -> [GrpMat]
BasicStabilizerChain(G) : GrpMat -> [GrpMat]
BasicStabilizerChain(G) : GrpPerm -> [GrpPerm]
ChainMap(Q, C, D, n) : SeqEnum, ModCpx, ModCpx, RngIntElt -> ModMatCpxElt
CohomologyGeneratorToChainMap(P,Q,C,n) : ModCpx, ModCpx, Tup, RngIntElt -> MapChn
CohomologyGeneratorToChainMap(P,C,n) : ModCpx, Tup, RngIntElt -> MapChn
Homology(C) : ModCpx -> SeqEnum
IsChainMap(L, C, D, n) : List, ModCpx, ModCpx, RngIntElt -> BoolElt
IsChainMap(f) : MapChn -> BoolElt
IsProperChainMap(f) : MapChn -> BoolElt
ZeroChainMap(C, D) : ModCpx -> ModMatCpxElt

ChainCyclic

CodeFld_ChainCyclic (Example H97E25)

ChainMap

ChainMap(Q, C, D, n) : SeqEnum, ModCpx, ModCpx, RngIntElt -> ModMatCpxElt

Chainmaps

ModCpx_Chainmaps (Example H80E2)

chainmaps

Chain Maps (CHAIN COMPLEXES)

Chains

ProjectionChains(X,DB) : VSrfK3,SeqEnum -> SeqEnum
UnprojectionChains(X,DB) : VSrfK3,SeqEnum -> SeqEnum

Chang

ChangGraphs() : -> [GrpUnd, GrpUnd, GrpUnd]

Change

BaseExtend(E, h) : CrvEll, Map -> CrvEll
BaseChange(E, h) : CrvEll, Map -> CrvEll
BaseChange(E, K) : CrvEll, Rng -> CrvEll
BaseChange(E, n) : CrvEll, RngIntElt -> CrvEll
BaseChange(J, j) : JacHyp, Map -> JacHyp
BaseChange(J, F) : JacHyp, Rng -> JacHyp
BaseChange(J, n) : JacHyp, RngIntElt -> JacHyp
BaseChange(C, K) : Sch, Fld -> Sch
BaseChange(A,m) : Sch, Map -> Sch
BaseChange(C, j) : Sch, Map -> Sch
BaseChange(C, n) : Sch, RngIntElt -> Sch
BaseChange(C, n) : Sch, RngIntElt -> Sch
BaseChange(X, n) : Sch, RngIntElt -> Sch
BaseChange(C,m) : Sch,Map -> Sch
BaseChange(A,K) : Sch,Rng -> Sch
BaseChange(C,K) : Sch,Rng -> Sch
BaseChange(C,A) : Sch,Sch -> Sch
BaseChange(X,A) : Sch,Sch -> Sch
BaseChange(F,K) : SeqEnum,Rng -> SeqEnum
BaseChange(K, j) : SrfKum, Map -> SrfKum
BaseChange(K, F) : SrfKum, Rng -> SrfKum
BaseChange(K, n): SrfKum, RngIntElt -> SrfKum
BaseChangeMatrix(A) : AlgBas -> ModAlg
CanChangeUniverse(S, V) : SeqEnum, Str -> Bool, SeqEnum
CanChangeUniverse(S, V) : SetEnum, Str -> Bool, SeqEnum
ChangeBase(~G, Q) : GrpPerm, [Elt] ->
ChangeDirectory(s) : MonStgElt ->
ChangeOrder(I, order) : RngMPol, ..., -> RngMPol, Map
ChangeOrder(I, Q) : RngMPol, RngMPol -> RngMPol, Map
ChangePrecision(L, r) : RngLoc, RngIntElt -> RngLoc
ChangePrecision(P, r) : RngLoc, RngIntElt -> RngLoc
ChangePrecision(x, m) : RngLocElt, RngIntElt -> RngLocElt
ChangeRepresentationType(A, Rep) : AlgGrp, MonStgElt -> AlgGrp, Map
ChangeRing(A, S) : AlgGen, Rng -> AlgGen, Map
ChangeRing(A, S, f) : AlgGen, Rng, Map -> AlgGen, Map
ChangeRing(A, S) : AlgMat, Rng -> AlgMat, Map
ChangeRing(A, S, f) : AlgMat, Rng, Map -> AlgMat, Map
ChangeRing(E, K) : CrvEll, Rng -> CrvEll
ChangeRing(G, S) : GrpMat, Rng -> GrpMat, Map
ChangeRing(G, S, f) : GrpMat, Rng, Map -> GrpMat, Map
ChangeRing(L, S) : Lat, Rng -> Lat, Map
BaseExtend(L, S) : Lat, Rng -> Lat, Map
ChangeRing(M, S) : ModRng, Rng -> ModRng, Map
ChangeRing(M, S) : ModRng, Rng -> ModRng, Map
ChangeRing(M, S, f) : ModRng, Rng, Map -> ModRng, Map
ChangeRing(M, S, f) : ModRng, Rng, Map -> ModRng, Map
ChangeRing(A, R) : Mtrx, Ring -> Mtrx
ChangeRing(I, S) : RngMPol, Rng -> RngMPol
ChangeRing(P, S) : RngMPol, Rng -> RngMPol
ChangeRing(P, S) : RngUPol, Rng -> RngUPol, Map
ChangeRing(P, S, f) : RngUPol, Rng, Map -> RngUPol, Map
ChangeRing(C, K) : Sch, Rng -> Sch
ChangeSupport(~G, S) : Grph, SetIndx ->
ChangeSupport(G, S) : Grph, SetIndx -> Grph, GrphVertSet, GrphEdgeSet
ChangeUniverse(S, V) : SeqEnum, Str ->
ChangeUniverse(~S, V) : SetEnum, Str ->

change

Base Change (PLANE ALGEBRAIC CURVES)
Base Change for Schemes (SCHEMES)
Changing Coefficient Ring (IDEAL THEORY AND GRÖBNER BASES)
Changing Coefficient Ring (MULTIVARIATE POLYNOMIAL RINGS)
Changing Monomial Order (IDEAL THEORY AND GRÖBNER BASES)
Changing Ring (MATRICES)
Changing Rings (ALGEBRAS)
Changing Rings (MATRIX ALGEBRAS)
Changing Rings (MATRIX GROUPS)
Changing Rings (UNIVARIATE POLYNOMIAL RINGS)

change-order

Changing Monomial Order (IDEAL THEORY AND GRÖBNER BASES)

change-ring

Changing Coefficient Ring (IDEAL THEORY AND GRÖBNER BASES)
Changing Coefficient Ring (MULTIVARIATE POLYNOMIAL RINGS)
Changing Ring (MATRICES)
Changing Rings (ALGEBRAS)
Changing Rings (MATRIX ALGEBRAS)
Changing Rings (MATRIX GROUPS)
Changing Rings (UNIVARIATE POLYNOMIAL RINGS)

change_ring

Changing the Base Ring (ELLIPTIC CURVES)

ChangeBase

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

ChangeDirectory

ChangeDirectory(s) : MonStgElt ->

ChangeOrder

ChangeOrder(I, order) : RngMPol, ..., -> RngMPol, Map
ChangeOrder(I, Q) : RngMPol, RngMPol -> RngMPol, Map
GB_ChangeOrder (Example H50E16)

ChangePrecision

ChangePrecision(L, r) : RngLoc, RngIntElt -> RngLoc
ChangePrecision(P, r) : RngLoc, RngIntElt -> RngLoc
ChangePrecision(x, m) : RngLocElt, RngIntElt -> RngLocElt

ChangeRepresentationType

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

ChangeRing

ChangeRing(A, S) : AlgGen, Rng -> AlgGen, Map
ChangeRing(A, S, f) : AlgGen, Rng, Map -> AlgGen, Map
ChangeRing(A, S) : AlgMat, Rng -> AlgMat, Map
ChangeRing(A, S, f) : AlgMat, Rng, Map -> AlgMat, Map
ChangeRing(E, K) : CrvEll, Rng -> CrvEll
ChangeRing(G, S) : GrpMat, Rng -> GrpMat, Map
ChangeRing(G, S, f) : GrpMat, Rng, Map -> GrpMat, Map
ChangeRing(L, S) : Lat, Rng -> Lat, Map
ChangeRing(M, S) : ModRng, Rng -> ModRng, Map
ChangeRing(M, S) : ModRng, Rng -> ModRng, Map
ChangeRing(M, S, f) : ModRng, Rng, Map -> ModRng, Map
ChangeRing(M, S, f) : ModRng, Rng, Map -> ModRng, Map
ChangeRing(A, R) : Mtrx, Ring -> Mtrx
ChangeRing(I, S) : RngMPol, Rng -> RngMPol
ChangeRing(P, S) : RngMPol, Rng -> RngMPol
ChangeRing(P, S) : RngUPol, Rng -> RngUPol, Map
ChangeRing(P, S, f) : RngUPol, Rng, Map -> RngUPol, Map
ChangeRing(C, K) : Sch, Rng -> Sch
GB_ChangeRing (Example H50E15)
RngPol_ChangeRing (Example H44E3)

ChangeSupport

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

ChangeUniverse

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

ChangGraphs

ChangGraphs() : -> [GrpUnd, GrpUnd, GrpUnd]

changing

Changing Basis (MODULES OVER A MATRIX ALGEBRA)
Changing the Coefficient Ring (MODULES OVER A MATRIX ALGEBRA)
Degeneracy Maps (MODULAR SYMBOLS)

changing-basis

Changing Basis (MODULES OVER A MATRIX ALGEBRA)

changing-level

Degeneracy Maps (MODULAR SYMBOLS)

changing-ring

Changing the Coefficient Ring (MODULES OVER A MATRIX ALGEBRA)

Char

EulerFactorModChar(J) : JacHyp -> RngUPolElt

Character

CharacterDegrees(G) : GrpFin -> [ RngIntElt ]
CharacterDegrees(G) : GrpFin -> [ RngIntElt ]
CharacterTable(G) : Grp -> SeqEnum
CharacterTable(G) : GrpAb -> TabChtr
CharacterTable(G) : GrpFin -> TabChtr
CharacterTable(G) : GrpMat -> TabChtr
CharacterTable(G) : GrpPC -> TabChtr
CharacterTable(G) : GrpPerm -> TabChtr
ClassFunctionSpace(G) : Grp -> AlgChtr
ClassPowerCharacter(x, j) : AlgChtrElt, RngIntElt -> AlgChtrElt
Id(R) : AlgChtr -> AlgChtrElt
IsCharacter(x) : AlgChtrElt -> BoolElt
IsGeneralizedCharacter(x) : AlgChtrElt -> BoolElt
KroneckerCharacter(D) :RngIntElt -> GrpDrchElt
KroneckerCharacter(D, R) : RngIntElt, Rng -> GrpDrchElt
LiftCharacter(x, f, G) : AlgChtrElt, MapHom, Grp -> AlgChtrElt
PermutationCharacter(G, H) : Grp, Grp -> AlgChtrElt
PermutationCharacter(G, H) : GrpFin, GrpFin -> AlgChtrElt
PermutationCharacter(G, H) : GrpMat, GrpMat -> AlgChtrElt
PermutationCharacter(G) : GrpPerm -> AlgChtrElt
PermutationCharacter(G) : GrpPerm -> AlgChtrElt
PermutationCharacter(G) : GrpPerm -> AlgChtrElt
PermutationCharacter(G, H) : GrpPerm, GrpPerm -> AlgChtrElt

character

Character Theory (GROUPS)
Characters and Representations (GROUPS)
CHARACTERS OF FINITE GROUPS
Representation Theory (ABELIAN GROUPS)
Representation Theory (FINITE SOLUBLE GROUPS)
Representation Theory (FINITELY PRESENTED GROUPS)
Representation Theory (MATRIX GROUPS)
Representation Theory (PERMUTATION GROUPS)
Rings, Fields, and Algebras (OVERVIEW)
Strings (OVERVIEW)

character-representation

Characters and Representations (GROUPS)
Representation Theory (ABELIAN GROUPS)
Representation Theory (FINITE SOLUBLE GROUPS)
Representation Theory (FINITELY PRESENTED GROUPS)
Representation Theory (MATRIX GROUPS)
Representation Theory (PERMUTATION GROUPS)

CharacterDegrees

CharacterDegrees(G) : GrpFin -> [ RngIntElt ]
CharacterDegrees(G) : GrpFin -> [ RngIntElt ]

Characteristic

AbsoluteCharacteristicPolynomial(a) : FldAlgElt -> RngUPolElt
BerlekampMassey(S) : SeqEnum -> RngUPolElt, RngIntElt
Characteristic(F) : FldFun -> RngIntElt
Characteristic(R) : Rng -> RngIntElt
Characteristic(O) : RngFunOrd -> RngIntElt
Characteristic(R) : RngGal -> RngIntElt
Characteristic(L) : RngLoc -> RngIntElt
Characteristic(P) : RngLoc -> RngIntElt
CharacteristicPolynomial(x) : AlgQuatElt -> RngUPolElt
CharacteristicPolynomial(a) : FldAlgElt -> RngUPolElt
CharacteristicPolynomial(a) : FldFinElt -> RngUPolElt
CharacteristicPolynomial(a, E) : FldFinElt, FldFin -> RngUPolElt
CharacteristicPolynomial(G) : GrphUnd -> RngUPolElt
CharacteristicPolynomial(a: parameters) : AlgMatElt -> RngUPolElt
CharacteristicPolynomial(g: parameters) : GrpMatElt -> RngPolElt
CharacteristicPolynomial(A: parameters) : Mtrx -> RngUPolElt
CharacteristicSeries(A) : GrpAuto -> SeqEnum
CharacteristicVector(M, S) : ModRng, { RngIntElt } -> ModRngElt
CharacteristicVector(V, S) : ModTupFld, { RngElt } -> ModTupFldElt
EulerCharacteristic(s) : GrphSpl -> RngIntElt
FactoredCharacteristicPolynomial(A: parameters) : Mtrx -> [ <RngUPolElt, RngIntElt>]
FactoredMinimalAndCharacteristicPolynomials(A: parameters) : Mtrx -> [<RngUPolElt, RngIntElt>], [<RngUPolElt, RngIntElt>]
MinimalAndCharacteristicPolynomials(A: parameter) : Mtrx -> RngUPolElt, RngUPolElt

characteristic

Characteristic Subgroups (FINITE SOLUBLE GROUPS)
Characteristic Subgroups and Normal Structure (GROUPS)
Minimal and Characteristic Polynomial (FINITE FIELDS)
Normal and Subnormal Subgroups (MATRIX GROUPS)
Normal and Subnormal Subgroups (PERMUTATION GROUPS)
Normal Structure and Characteristic Subgroups (ABELIAN GROUPS)
Normal Structure and Characteristic Subgroups (POLYCYCLIC GROUPS)

characteristic-subgroup-normal-structure

Characteristic Subgroups and Normal Structure (GROUPS)
Normal and Subnormal Subgroups (MATRIX GROUPS)
Normal and Subnormal Subgroups (PERMUTATION GROUPS)
Normal Structure and Characteristic Subgroups (ABELIAN GROUPS)
Normal Structure and Characteristic Subgroups (POLYCYCLIC GROUPS)

characteristic-subgroups

Characteristic Subgroups (FINITE SOLUBLE GROUPS)

CharacteristicPolynomial

CharacteristicSeries

CharacteristicSeries(A) : GrpAuto -> SeqEnum

characteristicsubgps

GrpAuto_characteristicsubgps (Example H29E2)

CharacteristicVector

CharacteristicVector(M, S) : ModRng, { RngIntElt } -> ModRngElt
CharacteristicVector(V, S) : ModTupFld, { RngElt } -> ModTupFldElt

CharacterRing

CharacterRing(G) : Grp -> AlgChtr
ClassFunctionSpace(G) : Grp -> AlgChtr

Characters

DirichletCharacters(M) : ModFrm -> [GrpDrchElt]
LiftCharacters(T, f, G) : AlgChtrElt, MapHom, Grp -> AlgChtrElt
LinearCharacters(G): Grp -> SeqEnum
LinearCharacters(G) : GrpMat -> [ Chtr ]
ReduceCharacters(I, C) : [ AlgChtrElt ], [ AlgChtrElt ] -> [ AlgChtrElt ], [ AlgChtrElt ]
SpinorCharacters(G) : SymGen -> [ GrpDrchElt ]

CharacterTable

Basis(R) : AlgChtr -> SeqEnum
CharacterTable(G) : Grp -> SeqEnum
CharacterTable(G) : GrpAb -> TabChtr
CharacterTable(G) : GrpFin -> TabChtr
CharacterTable(G) : GrpMat -> TabChtr
CharacterTable(G) : GrpPC -> TabChtr
CharacterTable(G) : GrpPerm -> TabChtr

Chebyshev

ChebyshevT(n) : RngIntElt -> RngUPolElt
ChebyshevFirst(n) : RngIntElt -> RngUPolElt
ChebyshevSecond(n) : RngIntElt -> RngUPolElt

ChebyshevFirst

ChebyshevT(n) : RngIntElt -> RngUPolElt
ChebyshevFirst(n) : RngIntElt -> RngUPolElt

ChebyshevSecond

ChebyshevU(n) : RngIntElt -> RngUPolElt
ChebyshevSecond(n) : RngIntElt -> RngUPolElt

ChebyshevT

ChebyshevT(n) : RngIntElt -> RngUPolElt
ChebyshevFirst(n) : RngIntElt -> RngUPolElt

ChebyshevU

ChebyshevU(n) : RngIntElt -> RngUPolElt
ChebyshevSecond(n) : RngIntElt -> RngUPolElt

Check

CheckPolynomial(C) : Code -> RngUPolElt
ParityCheckMatrix(C) : Code -> ModMatFldElt
ParityCheckMatrix(C) : Code -> ModMatRngElt

check

Automorphism Group and Isomorphism Testing (HYPERELLIPTIC CURVES)

checking

Checking of Maps (MAPPINGS)

CheckPolynomial

CheckPolynomial(C) : Code -> RngUPolElt

Chevalley

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

chevalley

Chevalley Groups (MATRIX GROUPS)

ChevalleyGroup

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

Chief

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

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> ]

Chien

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

ChienChoyCode

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

Child

GetChild(SQP, i) : SQProc, RngIntElt -> List

Children

DisownChildren(M) : ModSym ->
GetChildren(SQP) : SQProc -> List

Chinese

ChineseRemainderTheorem(I1, L1, e1, L2) : RngOrdIdl, [RngIntElt], RngOrdElt, [RngIntElt] -> RngOrdElt
ClassRepresentative(I) : RngOrdFracIdl -> RngOrdFracIdl
CRT(I1, L1, e1, L2) : RngOrdIdl, [RngIntElt], RngOrdElt, [RngIntElt] -> RngOrdElt
ChineseRemainderTheorem(I, J, a, b) : RngInt, RngInt, RngIntElt, RngIntElt -> RngIntElt
ChineseRemainderTheorem(I1, I2, e1, e2) : RngOrdIdl, RngOrdIdl, RngOrdElt, RngOrdElt -> RngOrdElt
ChineseRemainderTheorem(X, N) : [RngIntElt], [RngIntElt] -> RngIntElt

ChineseRemainderTheorem

ChineseRemainderTheorem(I1, L1, e1, L2) : RngOrdIdl, [RngIntElt], RngOrdElt, [RngIntElt] -> RngOrdElt
ClassRepresentative(I) : RngOrdFracIdl -> RngOrdFracIdl
CRT(I1, L1, e1, L2) : RngOrdIdl, [RngIntElt], RngOrdElt, [RngIntElt] -> RngOrdElt
ChineseRemainderTheorem(I, J, a, b) : RngInt, RngInt, RngIntElt, RngIntElt -> RngIntElt
ChineseRemainderTheorem(I1, I2, e1, e2) : RngOrdIdl, RngOrdIdl, RngOrdElt, RngOrdElt -> RngOrdElt
ChineseRemainderTheorem(X, N) : [RngIntElt], [RngIntElt] -> RngIntElt

Cholesky

Cholesky(L) : Lat -> AlgMatElt
Orthonormalize(L) : Lat -> AlgMatElt
Orthonormalize(M, K) : MtrxSpcElt, Fld -> AlgMatElt

Choy

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

Chromatic

ChromaticIndex(G) : GrphUnd -> RngIntElt
ChromaticNumber(G) : GrphUnd -> RngIntElt
ChromaticPolynomial(G) : GrphUnd -> RngUPolElt

ChromaticIndex

ChromaticIndex(G) : GrphUnd -> RngIntElt

ChromaticNumber

ChromaticNumber(G) : GrphUnd -> RngIntElt
Graph_ChromaticNumber (Example H93E12)

ChromaticPolynomial

ChromaticPolynomial(G) : GrphUnd -> RngUPolElt

cInvariants

cInvariants(E) : CrvEll -> [ RngElt ]

Circuit

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

circuit

Connectedness, Paths and Circuits (GRAPHS)

CircuitSpace

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

Circulant

BorderedDoublyCirculantQRCode(p,a,b) : RngIntElt, RngElt, RngElt -> Code
DoublyCirculantQRCode(p) : RngIntElt -> Code

Class

ChineseRemainderTheorem(I1, L1, e1, L2) : RngOrdIdl, [RngIntElt], RngOrdElt, [RngIntElt] -> RngOrdElt
ClassRepresentative(I) : RngOrdFracIdl -> RngOrdFracIdl
CRT(I1, L1, e1, L2) : RngOrdIdl, [RngIntElt], RngOrdElt, [RngIntElt] -> RngOrdElt
CalculateCanonicalClass(~g) : GrphRes ->
CanonicalClass(g) : GrphRes -> SeqEnum
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 }
ClassFunctionSpace(G) : Grp -> AlgChtr
ClassGroup(F : parameters) : FldFun -> GrpAb, Map
ClassGroup(Q: parameters) : QuadBin -> GrpAb, Map
ClassGroup(C) : Crv -> GrpAb, Map
ClassGroup(K) : FldQuad -> GrpAb, Map
ClassGroup(Q) : FldRat -> GrpAb, Map
ClassGroup(F : parameters) : FldFun -> GrpAb, Map
ClassGroup(O: parameters) : RngOrd -> GrpAb, Map
ClassGroup(O) : RngFunOrd -> GrpAb, Map
ClassGroup(Z) : RngInt -> GrpAb, Map
ClassGroupAbelianInvariants(F : parameters) : FldFun -> SeqEnum
ClassGroupAbelianInvariants(F : parameters) : FldFun -> SeqEnum
ClassGroupAbelianInvariants(O) : RngFunOrd -> SeqEnum
ClassGroupCyclicFactorGenerators(O) : RngOrd -> ModHomElt
ClassGroupExactSequence(F) : FldFun -> Map, Map, Map
ClassGroupExactSequence(O) : RngFunOrd -> Map, Map, Map
ClassGroupGenerationBound(F) : FldFun -> RngIntElt
ClassGroupGenerationBound(q, g) : RngIntElt, RngIntElt -> RngIntElt
ClassGroupPRank(F) : FldFunG -> RngIntElt
ClassGroupPRank(F) : FldFunG -> RngIntElt
ClassGroupStructure(Q: parameters) : QuadBin -> [ RngIntElt ]
ClassImage(A) : GrpAuto -> GrpPerm
ClassMap(G) : GrpAb -> Map
ClassMap(G) : GrpPC -> Map
ClassMap(G: parameters) : GrpFin -> Map
ClassMap(G: parameters) : GrpMat -> Map
ClassMap(G: parameters) : GrpPerm -> Map
ClassMatrix(G, i) : GrpAb, RngIntElt -> AlgMatElt
ClassNumber(F) : FldFun -> RngIntElt
ClassNumber(F) : FldFun -> RngIntElt
ClassNumber(K) : FldQuad -> RngIntElt
ClassNumber(Q: parameters) : QuadBin -> RngIntElt
ClassNumber(O: parameters) : RngOrd -> RngIntElt
ClassNumber(O) : RngFunOrd -> RngIntElt
ClassNumberApproximation(F, e) : FldFun, FldPrElt -> FldReElt
ClassNumberApproximationBound(q, g, e) : RngIntElt, RngIntElt, -> RngIntElt
ClassPowerCharacter(x, j) : AlgChtrElt, RngIntElt -> AlgChtrElt
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
ClassRepresentative(I) : RngInt -> RngInt
ClassTwo (p, d : parameters) : RngIntElt, RngIntElt -> SeqEnum
ClassUnion(A) : GrpAuto -> SetIndx
ConditionalClassGroup(O) : RngOrd -> GrpAb, Map
Degree(I) : RngFunOrdIdl -> RngIntElt
HasParallelClass(D) : Inc -> BoolElt, { IncBlk }
HilbertClassPolynomial(D) : RngIntElt -> RngUPolElt
HilbertClassPolynomial(D) : RngIntElt -> RngUPolElt
InertiaDegree(P) : PlcFunElt -> RngIntElt
IsParallelClass(D, B, C) : Inc, IncBlk, IncBlk -> BoolElt, { IncBlk }
NextClass(~P : parameters) : Process(pQuot) ->
NilpotencyClass(G) : GrpAb -> RngIntElt
NilpotencyClass(G) : GrpFin -> RngIntElt
NilpotencyClass(G) : GrpMat -> RngIntElt
NilpotencyClass(G) : GrpPC -> RngIntElt
NilpotencyClass(G) : GrpPerm -> RngIntElt
NilpotencyClass(G) : GrpGPC -> RngIntElt
PCClass(x) : GrpPCElt -> RngIntElt
ParallelClass(P, l) : Plane, PlaneLn -> { PlaneLn }
PermutationRepresentation(A) : GrpAuto -> Map, GrpPerm, SetIndx
RayClassField(m) : Map -> FldAb
RayClassGroup(I) : RngOrdIdl -> GrpAb, Map
ResidueClassField(P) : PlcFunElt -> Rng
ResidueClassField(R, I) : Rng, Rng -> Fld, Map
ResidueClassField(I) : RngFunOrdIdl -> Rng, Map
ResidueClassField(L) : RngLoc -> FldFin, Map
ResidueClassField(P) : RngLoc -> FldFin, Map
ResidueClassField(O, I) : RngOrd, RngOrdIdl -> FldFin, Map
ResidueClassRing(m) : RngIntElt -> RngIntRes
ResidueClassRing(Q) : RngIntEltFact -> RngIntRes
RevertClass(~P) : Process(pQuot) ->
StartNewClass (~P: parameters) : Process(pQuot) ->
WeberClassPolynomial(D) : RngIntElt -> RngUPolElt
WeberClassPolynomial(D) : RngIntElt -> RngUPolElt

class

Class Field Theory (ORDERS AND ALGEBRAIC FIELDS)
Class Group (BINARY QUADRATIC FORMS)
Class Information from a Conjugacy Class Poset (GROUPS)
Functions related to Divisor Class Groups of Global Function Fields (ALGEBRAIC FUNCTION FIELDS)
Ideal Class Group (QUADRATIC FIELDS)
Ideal Class Groups (ORDERS AND ALGEBRAIC FIELDS)
Identifier Classes (MAGMA SEMANTICS)
Linear Equivalence and Class Group (PLANE ALGEBRAIC CURVES)
Ray Class Group (ORDERS AND ALGEBRAIC FIELDS)
Residue Class Rings (RING OF INTEGERS)
Structure Creation (CHARACTERS OF FINITE GROUPS)

class-field

RngOrd_class-field (Example H53E25)

class-field-theory

Class Field Theory (ORDERS AND ALGEBRAIC FIELDS)

class-group

Class Group (BINARY QUADRATIC FORMS)
Ideal Class Group (QUADRATIC FIELDS)
Linear Equivalence and Class Group (PLANE ALGEBRAIC CURVES)

class-information

Class Information from a Conjugacy Class Poset (GROUPS)

class_map

GrpPC_class_map (Example H25E12)

ClassAction

ClassAction(A) : GrpAuto -> Map, GrpPerm, SetIndx
PermutationRepresentation(A) : GrpAuto -> Map, GrpPerm, SetIndx

Classes

AllParallelClasses(D) : Inc -> SeqEnum
AutomorphousClasses(L,p) : Lat, RngIntElt -> RngIntElt
Classes(D) : DB -> SeqEnum
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> ]
ExtensionClasses(D, Q) : DB, MonStgElt -> SetEnum
LeftIdealClasses(S) : AlgQuatOrd -> [AlgQuatOrd]
NumberOfClasses(D) : DB -> RngIntElt
NumberOfClasses(G) : GrpAb -> RngIntElt
NumberOfClasses(G) : GrpFin -> RngIntElt
NumberOfClasses(G) : GrpMat -> RngIntElt
NumberOfClasses(G) : GrpPC -> RngIntElt
NumberOfClasses(G) : GrpPerm -> RngIntElt
NumberOfIsogenyClasses(D, N) : DB, RngIntElt -> RngIntElt
NumberOfNewformClasses(M : parameters) : ModFrm -> RngIntElt
ParallelClasses(P) : PlaneAff -> { { PlaneLn } }
RightIdealClasses(S) : AlgQuatOrd -> [AlgQuatOrd]
SubgroupClasses(G) : GrpPC -> SeqEnum
SubgroupClasses(G: parameters) : GrpFin -> [ rec< Grp, RngIntElt, RngIntElt, GrpFP> ]
SubgroupClasses(G: parameters) : GrpPerm -> [ rec< GrpPerm, RngIntElt, RngIntElt, GrpFP> ]
TwoSidedIdealClasses(S) : AlgQuatOrd -> [AlgQuatOrd]
GrpPerm_Classes (Example H20E11)
Grp_Classes (Example H19E14)

classes

Conjugacy Classes of Subgroups (FINITE SOLUBLE GROUPS)
Conjugacy Classes of Subgroups (GROUPS)
Enumeration of Ideal Classes (QUATERNION ALGEBRAS)

ClassFunctionSpace

CharacterRing(G) : Grp -> AlgChtr
ClassFunctionSpace(G) : Grp -> AlgChtr

ClassGroup

ClassGroup(F : parameters) : FldFun -> GrpAb, Map
ClassGroup(Q: parameters) : QuadBin -> GrpAb, Map
ClassGroup(C) : Crv -> GrpAb, Map
ClassGroup(K) : FldQuad -> GrpAb, Map
ClassGroup(Q) : FldRat -> GrpAb, Map
ClassGroup(F : parameters) : FldFun -> GrpAb, Map
ClassGroup(O: parameters) : RngOrd -> GrpAb, Map
ClassGroup(O) : RngFunOrd -> GrpAb, Map
ClassGroup(Z) : RngInt -> GrpAb, Map
RngOrd_ClassGroup (Example H53E18)

ClassGroupAbelianInvariants

ClassGroupAbelianInvariants(F : parameters) : FldFun -> SeqEnum
ClassGroupAbelianInvariants(F : parameters) : FldFun -> SeqEnum
ClassGroupAbelianInvariants(O) : RngFunOrd -> SeqEnum

ClassGroupCyclicFactorGenerators

ClassGroupCyclicFactorGenerators(O) : RngOrd -> ModHomElt

ClassGroupExactSequence

ClassGroupExactSequence(F) : FldFun -> Map, Map, Map
ClassGroupExactSequence(O) : RngFunOrd -> Map, Map, Map

ClassGroupGenerationBound

ClassGroupGenerationBound(F) : FldFun -> RngIntElt
ClassGroupGenerationBound(q, g) : RngIntElt, RngIntElt -> RngIntElt

ClassGroupPRank

ClassGroupPRank(F) : FldFunG -> RngIntElt
ClassGroupPRank(F) : FldFunG -> RngIntElt

ClassGroupStructure

ClassGroupStructure(Q: parameters) : QuadBin -> [ RngIntElt ]

Classical

ClassicalForms(G): GrpMat -> BoolElt
ClassicalModularEquation(N) : RngIntElt -> RngMPolElt
ClassicalPeriod(M, j, prec) : ModSym, RngIntElt, RngIntElt -> FldPrElt
ClassicalType(G) : GrpMat -> MonStgElt
RecognizeClassical( G : parameters): GrpMat -> BoolElt

classical

Classical Groups (MATRIX GROUPS)

ClassicalForms

ClassicalForms(G): GrpMat -> BoolElt
GrpMat_ClassicalForms (Example H21E29)

classicalforms

Classical forms (MATRIX GROUPS)

ClassicalModularEquation

ClassicalModularEquation(N) : RngIntElt -> RngMPolElt

ClassicalPeriod

ClassicalPeriod(M, j, prec) : ModSym, RngIntElt, RngIntElt -> FldPrElt

ClassicalType

ClassicalType(G) : GrpMat -> MonStgElt

classification

Classification of root data (ROOT DATA FOR LIE THEORY)

classification-root-data

Classification of root data (ROOT DATA FOR LIE THEORY)

ClassImage

ClassImage(A) : GrpAuto -> GrpPerm

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(F) : FldFun -> RngIntElt
ClassNumber(F) : FldFun -> RngIntElt
ClassNumber(K) : FldQuad -> RngIntElt
ClassNumber(Q: parameters) : QuadBin -> RngIntElt
ClassNumber(O: parameters) : RngOrd -> RngIntElt
ClassNumber(O) : RngFunOrd -> RngIntElt

ClassNumberApproximation

ClassNumberApproximation(F, e) : FldFun, FldPrElt -> FldReElt

ClassNumberApproximationBound

ClassNumberApproximationBound(q, g, e) : RngIntElt, RngIntElt, -> RngIntElt

ClassPowerCharacter

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

ClassRepresentative

ClassTwo

ClassTwo (p, d : parameters) : RngIntElt, RngIntElt -> SeqEnum
GrpPGp_ClassTwo (Example H26E6)

ClassUnion

ClassUnion(A) : GrpAuto -> SetIndx

Clear

ClearPrevious() : ->
ClearVerbose() : ->

clear

Deleting an identifier (OVERVIEW)

ClearPrevious

ClearPrevious() : ->

ClearVerbose

ClearVerbose() : ->

Clebsch

ShrikhandeGraph() : -> GrphUnd
GewirtzGraph() : -> GrphUnd
ClebschGraph() : -> GrphUnd
ClebschInvariants(C) : CrvHyp -> SeqEnum
ClebschInvariants(f) : RngUPolElt -> SeqEnum
ClebschToIgusaClebsch(Q) : SeqEnum -> SeqEnum
IgusaClebschInvariants(C: parameters) : CrvHyp -> SeqEnum
IgusaClebschInvariants(f: parameters) : RngUPolElt -> SeqEnum
IgusaClebschInvariants(h, f) : RngUPolElt, RngUPolElt -> SeqEnum
IgusaClebschToIgusa(S) : SeqEnum -> SeqEnum

ClebschGraph

ShrikhandeGraph() : -> GrphUnd
GewirtzGraph() : -> GrphUnd
ClebschGraph() : -> GrphUnd

ClebschInvariants

ClebschInvariants(C) : CrvHyp -> SeqEnum
ClebschInvariants(f) : RngUPolElt -> SeqEnum

ClebschToIgusaClebsch

ClebschToIgusaClebsch(Q) : SeqEnum -> SeqEnum

Clique

CliqueNumber(G: parameters) : GrphUnd -> RngIntElt
HasClique(G, k) : GrphUnd, RngIntEl -> BoolElt, { GrphVert }
HasClique(G, k, m: parameters) : GrphUnd, RngIntEl, BoolElt -> BoolElt, { GrphVert }
HasClique(G, k, m, f: parameters) : GrphUnd, RngIntEl, BoolElt, RngIntEl -> BoolElt, { GrphVert }
MaximumClique(G: parameters) : GrphUnd -> { GrphVert }

clique

Cliques, Independent Sets (GRAPHS)

clique-independent-set

Cliques, Independent Sets (GRAPHS)

CliqueNumber

CliqueNumber(G: parameters) : GrphUnd -> RngIntElt

Cliques

AllCliques(G) : GrphUnd -> SeqEnum
AllCliques(G, k) : GrphUnd, RngIntEl -> SeqEnum
AllCliques(G, k, m: parameters) : GrphUnd, RngIntElt, BoolElt -> SeqEnum
Graph_Cliques (Example H93E13)

Close

CloseSmallGroupDatabase(~D) DB : ->
CloseVectors(L, w, u) : Lat, ModTupRngElt, RngElt -> [ <LatElt, RngElt> ]
CloseVectorsMatrix(L, w, u) : Lat, ModTupRngElt, RngElt -> ModMatRngElt
CloseVectorsProcess(L, w, u) : Lat, ModTupRngElt, RngElt -> LatEnumProc

close

Short and Close Vectors (LATTICES)

Closed

HasCompleteCosetTable(P) : GrpFPCosetEnumProc -> BoolElt
HasClosedCosetTable(P) : GrpFPCosetEnumProc -> BoolElt

closed

ALGEBRAICALLY CLOSED FIELDS

CloseSmallGroupDatabase

CloseSmallGroupDatabase(~D) DB : ->

Closest

ClosestVectors(L, w) : Lat, ModTupRngElt -> [ LatElt ], RngElt
ClosestVectorsMatrix(L, w) : Lat, ModTupRngElt -> ModMatRngElt, RngElt
Lat_Closest (Example H66E7)

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

AlgebraicClosure() : -> FldAC
ClosureGraph(P, G) : GrpPerm, GrphUnd -> GrphUnd
IntegralClosure(R, F) : Rng, FldFun -> RngFunOrd
IntegralClosure(R, F) : Rng, FldFun -> RngFunOrd
MakeProjectiveClosureMap(A, P, S) : Aff,Prj,SeqEnum ->
NeighbourClosure(L, p) : Lat, RngIntElt -> Lat
NormalClosure(G, H) : GrpAb, GrpAb -> GrpAb
OrbitClosure(G, S) : GrpMat, { Elt } -> GSet
OrbitClosure(G, Y, S) : GrpPerm, GSet, { Elt } -> GSet
ProjectiveClosure(f) : MapSch -> MapSch
ProjectiveClosure(A): Sch -> Sch
ProjectiveClosure(C) : Sch -> Sch
ProjectiveClosure(X) : Sch -> Sch
ProjectiveClosureMap(A) : Aff -> MapSch
VarietySizeOverAlgebraicClosure(I) : RngMPol -> RngIntElt
H ^ G : GrpFin -> GrpFin
H ^ G : GrpFin, GrpFin -> GrpFin
H ^ G : GrpFP, GrpFP -> GrpFP
H ^ G : GrpGPC, GrpGPC -> GrpGPC
H ^ G : GrpMat -> GrpMat
H ^ G : GrpMat, GrpMat -> GrpMat
H ^ G : GrpPC, GrpPC -> GrpPC
H ^ G : GrpPerm, GrpPerm -> GrpPerm

closure

Maps and Closure (SCHEMES)
Projective Closure (PLANE ALGEBRAIC CURVES)
Projective Closure (SCHEMES)
Projective Closure and Affine Patches (PLANE ALGEBRAIC CURVES)
Projective Closure and Affine Patches (SCHEMES)

closure-crvpl

Projective Closure and Affine Patches (PLANE ALGEBRAIC CURVES)

ClosureGraph

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

Cluster

IsCluster(X) : Sch -> BoolElt,Clstr
Scheme(p) : Pt -> Sch
Scheme(X,f) : Sch,RngMPolElt -> Sch

cluster-degree5

Scheme_cluster-degree5 (Example H81E7)

clusters

Zero-dimensional Schemes (SCHEMES)

cmpeq

x cmpeq y : Elt, Elt -> BoolElt

cmpne

x cmpne y : Elt, Elt -> BoolElt

Co1

GrpFP_1_Co1 (Example H22E52)

cocycle

Lifting a Quotient by Choosing an Individual Cocycle (FP GROUPS - ADVANCED FEATURES)

Cocycles

RepresentativeCocycles (G, U, Ext, Hom) : GrpPC, GrpPC, [AlgMatElt], [AlgMatElt]-> [AlgMatElt]

Code

code

Combinatorial and Geometrical Structures (OVERVIEW)
Construction of Graphs from Groups, Codes and Designs (GRAPHS)
Graphs Constructed from Designs (GRAPHS)
Incidence Structures, Graphs and Codes (INCIDENCE STRUCTURES AND DESIGNS)
Lattices from Linear Codes (LATTICES)
LINEAR CODES OVER FINITE FIELDS
LINEAR CODES OVER FINITE RINGS
Planes, Graphs and Codes (FINITE PLANES)
The Code Space (LINEAR CODES OVER FINITE FIELDS)

code-design

Graphs Constructed from Designs (GRAPHS)

code-subspace

The Code Space (LINEAR CODES OVER FINITE FIELDS)

CodeComplement

CodeComplement(C,C1) : Code, Code -> Code

CodeFromMatrix

CodeFld_CodeFromMatrix (Example H97E2)
CodeRng_CodeFromMatrix (Example H98E2)

CodeJuxtaposition

CodeJuxtaposition(C1, C2) : Code,Code -> Code

codes

Algebraic Geometric Codes (LINEAR CODES OVER FINITE FIELDS)
Best Known Linear Codes (LINEAR CODES OVER FINITE FIELDS)
Combining Codes (LINEAR CODES OVER FINITE FIELDS)
Combining Codes (LINEAR CODES OVER FINITE RINGS)
Geometric Codes (PLANE ALGEBRAIC CURVES)
Maximum Distance Separable Codes (LINEAR CODES OVER FINITE FIELDS)
Plane_codes (Example H95E18)

CodeToString

CodeToString(n) : RngIntElt -> MonStgElt

Codimension

ApparentCodimension(X) : VSrfK3 -> RngIntElt
Codimension(X) : Sch -> RngIntElt
Codimension(X) : VSrfK3 -> RngIntElt

Codomain

Codomain(f) : Map -> Grp
Codomain(f) : Map -> Grp
Codomain(f) : Map -> Grp
Codomain(f) : Map -> Struct
Codomain(f) : MapCrvHyp -> CrvHyp
Codomain(f) : MapSch -> Sch
Codomain(a) : ModMatElt -> ModTupFld
Codomain(f) : ModMatFldElt -> ModAlg
Codomain(S) : ModMatRng -> ModTupRng
Codomain(a) : ModMatRngElt -> ModTupRng

coeff

Coefficient Arithmetic (PLANE ALGEBRAIC CURVES)

Coefficient

coefficient

KSpace(V, F) : ModTupFld, Fld -> ModTupFld, Map
KMatrixSpace(V, F) : ModTupFld, Fld -> ModTupFld, Map
KModule(V, F) : ModTupFld, Fld -> ModTupFld, Map
Changing the Coefficient Field (VECTOR SPACES)
Changing the Coefficient Ring (FREE MODULES)
Coefficients and Degree (POWER, LAURENT AND PUISEUX SERIES)
Coefficients and Terms (UNIVARIATE POLYNOMIAL RINGS)
Coefficients, Monomials and Terms (MULTIVARIATE POLYNOMIAL RINGS)

coefficient-degree

Coefficients and Degree (POWER, LAURENT AND PUISEUX SERIES)

coefficient-monomial-term

Coefficients, Monomials and Terms (MULTIVARIATE POLYNOMIAL RINGS)

coefficient-term

Coefficients and Terms (UNIVARIATE POLYNOMIAL RINGS)

CoefficientField

BaseField(F) : Fld -> Rng
CoefficientRing(F) : FldFun -> Rng
CoefficientField(F) : FldFun -> Rng
BaseRing(F) : Fld -> Rng
CoefficientField(x) : AlgChtrElt -> Rng
CoefficientField(V) : ModTupFld -> Fld
CoefficientRing(R) : RngInvar -> Grp
CoefficientRing(X) : Sch -> Fld
GroundField(F) : FldAlg -> Fld

CoefficientMap

CoefficientMap(L) : LinSys -> ModTupFldElt

CoefficientRing

Coefficients

Coefficients(a) : AlgGrpElt -> SeqEnum
Coefficients(x) : RngLocElt -> [ RngLocElt ]
Coefficients(x) : RngLocElt -> [ RngLocElt ]
Coefficients(f) : RngMPolElt -> [ RngElt ]
Coefficients(f, i) : RngMPolElt, RngIntElt -> [ RngElt ]
Coefficients(f) : RngSerElt -> [ RngElt ], RngIntElt, RngIntElt
Coefficients(p) : RngUPolElt -> [ RngElt ]
HilbertCoefficients(X,n) : VSrfK3,RngIntElt -> SeqEnum
aInvariants(E) : CrvEll -> [ RngElt ]
RngMPol_Coefficients (Example H45E4)

CoefficientSpace

CoefficientSpace(L) : LinSys -> ModTupFld

coerce-quo

ModOrd_coerce-quo (Example H65E4)

Coercible

IsCoercible(X,Q) : Sch,SeqEnum -> BoolElt,Pt
IsCoercible(S, x) : Str, Elt -> Bool, Elt

Coercion

Bang(D, C) : Struct, Struct -> Map
Coercion(D, C) : Struct, Struct -> Map
FldRat_Coercion (Example H41E1)
RngInt_Coercion (Example H40E5)

coercion

Coercion (ALGEBRAICALLY CLOSED FIELDS)
Coercion (GROUPS)
Coercion (INTRODUCTION [BASIC RINGS])
Coercion (PERMUTATION GROUPS)
Coercion (RATIONAL FIELD)
Coercion (REAL AND COMPLEX FIELDS)
Coercion (RING OF INTEGERS)
Coercion (RING OF INTEGERS)
Coercion (STATEMENTS AND EXPRESSIONS)
Coercion between Matrix Structures (MATRIX GROUPS)
Coercion Maps (MAPPINGS)
Coercions Between Groups and Subgroups (ABELIAN GROUPS)
Coercions Between Groups and Subgroups (POLYCYCLIC GROUPS)
Coercions Between Related Groups (GROUPS WHOSE ELEMENTS ARE STRAIGHT-LINE PROGRAMS)
Magmas (or Structures) (OVERVIEW)
Membership and Coercion (FINITE SOLUBLE GROUPS)
Predicates for Permutations (PERMUTATION GROUPS)
Properties of Permutations (PERMUTATION GROUPS)
GrpPC_coercion (Example H25E14)

Coercion-spaces

ModSym_Coercion-spaces (Example H88E10)

coercions

Class Groups Coercions (BINARY QUADRATIC FORMS)

Cohen

IsCohenMacaulay(R) : RngInvar -> BoolElt

Cohomological

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

CohomologicalDimension

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

Cohomology

CohomologyGeneratorToChainMap(P,Q,C,n) : ModCpx, ModCpx, Tup, RngIntElt -> MapChn
CohomologyGeneratorToChainMap(P,C,n) : ModCpx, Tup, RngIntElt -> MapChn
CohomologyLeftModuleGenerators(P, CP, Q) : Tup, Tup, Tup -> Tup
CohomologyRightModuleGenerators(P, Q, CQ) : Tup, Tup, Tup -> Tup
CohomologyRingGenerators(P) : Tup -> Tup
DegreesOfCohomologyGenerators(C) : Tup -> SeqEnum
SimpleCohomologyDimensions(M) : ModAlg -> SeqEnum
AlgBas_Cohomology (Example H79E5)
GrpPerm_Cohomology (Example H20E30)

cohomology

Cohomology (BASIC ALGEBRAS)
Cohomology (GROUPS)
Cohomology (PERMUTATION GROUPS)

CohomologyGeneratorToChainMap

CohomologyGeneratorToChainMap(P,Q,C,n) : ModCpx, ModCpx, Tup, RngIntElt -> MapChn
CohomologyGeneratorToChainMap(P,C,n) : ModCpx, Tup, RngIntElt -> MapChn

CohomologyLeftModuleGenerators

CohomologyLeftModuleGenerators(P, CP, Q) : Tup, Tup, Tup -> Tup

CohomologyRightModuleGenerators

CohomologyRightModuleGenerators(P, Q, CQ) : Tup, Tup, Tup -> Tup

CohomologyRingGenerators

CohomologyRingGenerators(P) : Tup -> Tup

Coisogeny

CoisogenyGroup( G ) : GrpLie -> RootDtm
CoisogenyGroup( RD ) : RootDtm -> GrpAb

CoisogenyGroup

CoisogenyGroup( G ) : GrpLie -> RootDtm
CoisogenyGroup( RD ) : RootDtm -> GrpAb

Cokernel

Cokernel(f) : ModMatCpxElt -> ModCpx, ModMatCpxElt
Cokernel(a) : ModMatElt -> ModTupFld
Cokernel(f) : ModMatFldElt -> ModAlg,ModMatFldElt
Cokernel(a) : ModMatRngElt -> ModTupRng

Collect

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

Collector

DeleteSplitCollector (SQP) : SQProc, RngIntElt ->
DeleteNonsplitCollector (SQP) : SQProc, RngIntElt ->
DeleteCollector (SQP) : SQProc, RngIntElt ->
DeleteNonsplitCollector (SQP) : SQProc, RngIntElt ->
DeleteCollector (SQP, p) : SQProc, RngIntElt ->
DeleteNonsplitCollector (SQP, p) : SQProc, RngIntElt ->
NonsplitCollector(SQP, p) : SQProc, RngIntElt ->
PrintCollector (SQP : parameters) : SQProc ->

collector

DeleteSplitCollector (SQP) : SQProc, RngIntElt ->
DeleteNonsplitCollector (SQP) : SQProc, RngIntElt ->
Symbolic Collector (FP GROUPS - ADVANCED FEATURES)

CollectRelations

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

Collinear

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

Collineation

CentralCollineationGroup(P, l) : Plane, PlaneLn -> GrpPerm, PowMap, Map
CentralCollineationGroup(P, p) : Plane, PlanePt -> GrpPerm, PowMap, Map
CentralCollineationGroup(P, p, l) : Plane, PlanePt, PlaneLn -> GrpPerm, PowMap, Map
CollineationGroup(P) : Plane -> GrpPerm, GSet, GSet, PowMap, Map
CollineationGroupStabilizer(P, k) : Plane, RngIntElt -> GrpPerm, GSet, GSet, PowMap, Map
CollineationSubgroup(P) : Plane -> GrpPerm, GSet, GSet, PowMap, Map
IsCentralCollineation(P, g) : Plane, GrpPermElt -> BoolElt, PlanePt, PlaneLn
Plane_Collineation (Example H95E13)

collineation

The Collineation Group of a Plane (FINITE PLANES)

collineation-group

The Collineation Group of a Plane (FINITE PLANES)

CollineationGroup

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

CollineationGroupStabilizer

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

CollineationGSet

Plane_CollineationGSet (Example H95E12)

CollineationSubgroup

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

Colon

IdealQuotient(I, J) : RngMPol, RngMPol -> RngMPol
ColonIdeal(I, J) : RngMPol, RngMPol -> RngMPol
ColonIdeal(I, f) : RngMPol, RngMPolElt -> RngMPol, RngIntElt
ColonIdeal(I, J) : RngMPolRes, RngMPolRes -> RngMPolRes
ColonIdeal(I, J) : RngOrdIdl, RngOrdIdl -> RngOrdIdl

ColonIdeal

Colouring

OptimalEdgeColouring(G) : GrphUnd -> SeqEnum
OptimalVertexColouring(G) : GrphUnd -> SeqEnum

colouring

Colourings (GRAPHS)

Column

AddColumn(~a, u, i, j) : AlgMatElt, RngElt, RngIntElt, RngIntElt ->
AddColumn(A, c, i, j) : Mtrx, RngElt, RngIntElt, RngIntElt -> Mtrx
ColumnSkewLength(t, j) : Tableau,RngIntElt -> RngIntElt
ColumnSubmatrix(A, i) : Mtrx, RngIntElt -> Mtrx
ColumnSubmatrix(A, i, k) : Mtrx, RngIntElt, RngIntElt -> Mtrx
ColumnSubmatrixRange(A, i, j) : Mtrx, RngIntElt, RngIntElt -> Mtrx
ColumnWord(t) : Tableau -> SeqEnum
FirstColumnEntry(t, j) : Tableau,RngIntElt -> RngIntElt
HadamardColumnDesign(H, i) : AlgMatElt, RngIntElt -> Dsgn
LastColumnEntry(t, j) : Tableau,RngIntElt -> RngIntElt
MultiplyColumn(~a, u, i) : AlgMatElt, RngElt, RngIntElt ->
MultiplyColumn(A, c, i) : Mtrx, RngElt, RngIntElt -> Mtrx

column

Row and Column Operations (MATRICES)
Row and Column Operations (MATRIX ALGEBRAS)

ColumnLength

ColumnLength(t, j): Tableau,RngIntElt -> RnfIntElt
LastColumnEntry(t, j) : Tableau,RngIntElt -> RngIntElt

Columns

NFSCharacterColumns(n, F, tuple) : RngIntElt, RngMPolElt, Tup -> .
NumberOfColumns(a) : AlgMatElt -> RngIntElt
NumberOfColumns(u) : ModTupFldElt -> RngIntElt
NumberOfColumns(A) : Mtrx -> RngIntElt
SetAutoColumns(b) : BoolElt ->
SetColumns(n) : RngIntElt ->
SwapColumns(~a, i, j) : AlgMatElt, RngIntElt, RngIntElt ->
SwapColumns(A, i, j) : Mtrx, RngIntElt, RngIntElt -> Mtrx

ColumnSkewLength

ColumnSkewLength(t, j) : Tableau,RngIntElt -> RngIntElt

ColumnSubmatrix

ColumnSubmatrix(A, i) : Mtrx, RngIntElt -> Mtrx
ColumnSubmatrix(A, i, k) : Mtrx, RngIntElt, RngIntElt -> Mtrx

ColumnSubmatrixRange

ColumnSubmatrixRange(A, i, j) : Mtrx, RngIntElt, RngIntElt -> Mtrx

ColumnWord

ColumnWord(t) : Tableau -> SeqEnum

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)

combining

Combining Codes (LINEAR CODES OVER FINITE FIELDS)
Combining Codes (LINEAR CODES OVER FINITE RINGS)

combining-codes

Combining Codes (LINEAR CODES OVER FINITE FIELDS)
Combining Codes (LINEAR CODES OVER FINITE RINGS)

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

Contpp(p) : RngUPolElt -> RngIntElt, RngUPolElt
Common Divisors and Common Multiples (UNIVARIATE POLYNOMIAL RINGS)
Greatest Common Divisors (MULTIVARIATE POLYNOMIAL RINGS)
Greatest Common Divisors (QUADRATIC FIELDS)

CommonZeros

CommonZeros(L) : SeqEnum[ FldFunElt ] -> SeqEnum[ PlcFunElt ]

Commutative

IsCommutative(A) : AlgGen -> BoolElt
IsCommutative(R) : Rng -> BoolElt

commutative

Groups (OVERVIEW)

Commutator

CommutatorIdeal(A, B) : AlgAss, AlgAss -> AlgAss
CommutatorIdeal(S) : AlgQuatOrd -> AlgQuatOrd
CommutatorModule(A, B) : AlgAss, AlgAss -> ModTupRng
CommutatorSubgroup(G, H, K) : GrpAb, GrpAb, GrpAb -> GrpAb
CommutatorSubgroup(G, H, K) : GrpFin, GrpFin, GrpFin -> GrpFin
CommutatorSubgroup(G, H, K) : GrpGPC, GrpGPC, GrpGPC -> GrpGPC
CommutatorSubgroup(G, H, K) : GrpMat, GrpMat, GrpMat -> GrpMat
CommutatorSubgroup(G) : GrpPC -> GrpPC
CommutatorSubgroup(G, H, K) : GrpPC, GrpPC, GrpPC -> GrpPC
CommutatorSubgroup(G, H, K) : GrpPerm, GrpPerm, GrpPerm -> GrpPerm

commutator

Groups (OVERVIEW)

CommutatorIdeal

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

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) : GrpGPC, GrpGPC, GrpGPC -> GrpGPC
CommutatorSubgroup(G, H, K) : GrpMat, GrpMat, GrpMat -> GrpMat
CommutatorSubgroup(G) : GrpPC -> GrpPC
CommutatorSubgroup(G, H, K) : GrpPC, GrpPC, GrpPC -> GrpPC
CommutatorSubgroup(G, H, K) : GrpPerm, GrpPerm, GrpPerm -> GrpPerm

comp

comp<K|P> : FldAlg, RngOrdIdl -> FldLoc, Map
Completion(K, P) : FldAlg, RngOrdIdl -> FldLoc, Map
comp< R | a_1, ..., a_r > : Rng, RngElt, ..., RngElt -> Rng, Map

Compact

CompactInjectiveResolution(M, n) : ModAlg, RngIntElt -> List, ModMatFldElt
CompactPresentation(G) : GrpPC -> [RngIntElt]
CompactProjectiveResolution(M, n) : ModAlg, RngIntElt -> Tup
SetAutoCompact(b) : BoolElt ->

compact

CompactPresentation (FINITE SOLUBLE GROUPS)

compact-presentation

CompactPresentation (FINITE SOLUBLE GROUPS)

CompactInjectiveResolution

CompactInjectiveResolution(M, n) : ModAlg, RngIntElt -> List, ModMatFldElt

CompactPresentation

CompactPresentation(G) : GrpPC -> [RngIntElt]
GrpPC_CompactPresentation (Example H25E25)

CompactProjectiveResolution

CompactProjectiveResolution(M, n) : ModAlg, RngIntElt -> Tup

Companion

CompanionMatrix(p) : RngPolElt -> AlgMatElt
CompanionMatrix(f) : RngUPolElt -> AlgMatElt

CompanionMatrix

CompanionMatrix(p) : RngPolElt -> AlgMatElt
CompanionMatrix(f) : 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 [BASIC RINGS])
Comparison of Ring Elements (RING OF INTEGERS)

comparisons

Comparisons and Membership Testing (ALGEBRAS)

CompFactors

GrpPerm_CompFactors (Example H20E25)

compgrp

Tamagawa Numbers and Orders of Component Groups (MODULAR SYMBOLS)

Complement

CodeComplement(C,C1) : Code, Code -> Code
Complement(G) : Grph -> Grph
Complement(D) : Inc -> Inc
Complement(L,K) : LinSys,LinSys -> LinSys
Complement(L,X) : LinSys,Sch -> LinSys
Complement(M) : ModSym -> ModSym
Complement(V, U) : ModTupFld, ModTupFld -> ModTupFld
ComplementBasis(G) : GrpPC -> [GrpPC]
HasComplement(G, M) : GrpPerm, GrpPerm -> BoolElt, GrpPerm
HasComplement(M, S) : ModGrp, ModGrp -> BoolElt, ModGrp
OrthogonalComplement(M) : ModBrdt -> ModBrdt

complement

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

complement-line-graph-contraction-switching

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

Complementary

ComplementaryDivisor(D,p) : DivCrvElt,Pt -> DivCrvElt
ComplementaryDivisor(D) : DivFunElt -> DivFunElt
ComplementaryErrorFunction(r) : FldReElt -> FldReElt

ComplementaryDivisor

ComplementaryDivisor(D,p) : DivCrvElt,Pt -> DivCrvElt
ComplementaryDivisor(D) : DivFunElt -> DivFunElt

ComplementaryErrorFunction

Erfc(r) : FldReElt -> FldReElt
ComplementaryErrorFunction(r) : FldReElt -> FldReElt

ComplementBasis

ComplementBasis(G) : GrpPC -> [GrpPC]

Complements

Complements(G, N) : GrpPC, GrpPC -> SeqEnum
Complements(G, M) : GrpPerm, GrpPerm -> [ GrpPerm ]
Complements(G, M, N) : GrpPerm, GrpPerm, GrpPerm -> [ GrpPerm ]
Complements(M, S) : ModGrp, ModGrp -> [ ModGrp ]
NormalComplements(G, H, N) : GrpPC, GrpPC -> SeqEnum
NormalComplements(G, N) : GrpPC, GrpPC -> SeqEnum
GrpPerm_Complements (Example H20E28)

complements

Complements and Supplements (PERMUTATION GROUPS)
Decomposabilty and Complements (MODULES OVER A MATRIX ALGEBRA)

Complete

CompleteDigraph(p) : RngIntElt -> GrphDir
CompleteGraph(p) : RngIntElt -> GrphUnd
CompleteKArc(P, k) : Plane, RngIntElt -> SetEnum
CompleteUnion(G, H) : GrphDir, GrphDir -> GrphDir
CompleteWeightEnumerator(C): Code -> RngMPolElt
CompleteWeightEnumerator(C): Code -> RngMPolElt
CompleteWeightEnumerator(C, u): Code, ModTupFldElt -> RngMPolElt
HasClosedCosetTable(P) : GrpFPCosetEnumProc -> BoolElt
IsComplete(V) : GrpFPCos -> BoolElt
IsComplete(G) : Grph -> BoolElt
IsComplete(D) : Inc -> BoolElt
IsComplete(L) : LinSys -> BoolElt
IsComplete(P, A) : Plane, { PlanePt } -> BoolElt
IsComplete(S) : SeqEnum -> BoolElt

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
CompleteWeightEnumerator(C): Code -> RngMPolElt
CompleteWeightEnumerator(C, u): Code, ModTupFldElt -> RngMPolElt

Completion

comp<K|P> : FldAlg, RngOrdIdl -> FldLoc, Map
Completion(K, P) : FldAlg, RngOrdIdl -> FldLoc, Map
Completion(Q, P) : FldRat, RngInt -> FldLoc, Map
Completion(R, P) : Rng, Rng -> Rng, Map
Completion(P, n) : RngOrdIdl, RngIntElt -> RngLoc, Map

completion

Completion (INTRODUCTION [BASIC RINGS])
Completions (LOCAL RINGS AND FIELDS)

Complex

Complex(L, d) : List, RngIntElt -> ModCpx
Complex(f, d) : Map, RngIntElt -> ModCpx
ComplexConjugate(a) : FldCycElt -> FldCycElt
ComplexConjugate(s) : FldPrElt -> FldPrElt
ComplexConjugate(a) : FldQuadElt -> FldQuadElt
ComplexConjugate(q) : FldRatElt -> FldRatElt
ComplexConjugate(n) : RngIntElt -> RngIntElt
ComplexEmbeddings(f) : ModFrmElt -> List
ComplexField() : Null -> FldPr
ComplexField(p) : RngIntElt -> FldCom
ComplexToPolar(c) : FldComElt -> FldReElt, FldReElt
ComplexValue(x) : SpcHypElt) -> FldPrElt
Homology(C) : ModCpx -> SeqEnum
IsZeroComplex(C) : ModCpx -> BoolElt
PolarToComplex(m, a) : FldReElt, FldReElt -> FldComElt
ZeroComplex(A, m, n) : AlgBas, RngIntElt, RngIntElt -> ModCpx

complex

REAL AND COMPLEX FIELDS
Real and Complex Valued Functions (ORDERS AND ALGEBRAIC FIELDS)
Rings, Fields, and Algebras (OVERVIEW)
The Associated Complex Torus (MODULAR SYMBOLS)

complex-tori

The Associated Complex Torus (MODULAR SYMBOLS)

ComplexConjugate

ComplexEmbeddings

ComplexEmbeddings(f) : ModFrmElt -> List

Complexes

ModCpx_Complexes (Example H80E1)

complexes

CHAIN COMPLEXES
Complexes of Modules over Basic Algebras (CHAIN COMPLEXES)

ComplexField

ComplexField() : Null -> FldPr
ComplexField(p) : RngIntElt -> FldCom

ComplexToPolar

ComplexToPolar(c) : FldComElt -> FldReElt, FldReElt

ComplexValue

ComplexValue(x) : SpcHypElt) -> FldPrElt

Component

BaseComponent(L) : LinSys -> SchProj
Component(v) : GrphResVert -> GrphRes
Component(u) : GrphVert -> Grph
Component(C, i) : SetCart, RngIntElt -> Str
ComponentGroupOrder(M, p) : ModSym, RngIntElt -> RngIntElt
HomogeneousComponent(f, d) : RngMPolElt, RngIntElt -> RngMPolElt
OrthogonalComponent(x, p) : AlgChtrElt, [ RngIntElt ] -> AlgChtrElt
SymplecticComponent(x, p) : AlgChtrElt, [ RngIntElt ] -> AlgChtrElt
pPrimaryComponent(A, p) : GrpAb, RngIntElt -> GrpAb

ComponentGroupOrder

ComponentGroupOrder(M, p) : ModSym, RngIntElt -> RngIntElt

Components

Components(A) : FldAb -> [RngOrd]
Components(G) : Grph -> [ { GrphVert } ]
HomogeneousComponents(f) : RngMPolElt -> [ RngMPolElt ]
NumberOfComponents(C) : SetCart -> RngIntElt
OrthogonalComponents(x, n) : AlgChtrElt, RngIntElt -> SetEnum
PrimaryComponents(X) : Sch -> SeqEnum
PrimeComponents(X) : Sch -> SeqEnum
SymmetricComponents(x, n) : AlgChtrElt, RngIntElt -> SetEnum
SymplecticComponents(x, n) : AlgChtrElt, RngIntElt -> SetEnum

Compose

ComposeQuotients(SQ1, SQ2, SQ3: parameter) : SQProc, SQProc, SQProc -> BoolElt, SQProc

ComposeQuotients

ComposeQuotients(SQ1, SQ2, SQ3: parameter) : SQProc, SQProc, SQProc -> BoolElt, SQProc

Composite

Composite(I,J) : AlgQuatOrd, AlgQuatOrd -> AlgQuatOrd
I * J : AlgQuatOrd, AlgQuatOrd -> AlgQuatOrd
MergeFields(F, L) : FldAlg, FldAlg -> SeqEnum

CompositeFields

CompositeFields(F, L) : FldAlg, FldAlg -> SeqEnum
MergeFields(F, L) : FldAlg, FldAlg -> SeqEnum
RngOrd_CompositeFields (Example H53E2)

Composition

Composition(f,g) : MapCrvHyp, MapCrvHyp -> MapCrvHyp
f * g : MapCrvHyp, MapCrvHyp -> MapCrvHyp
f * g : QuadBinElt, QuadBinElt -> QuadBinElt
Composition(f, g) : RngSerElt, RngSerElt -> RngSerElt
Composition(T, q) : [ FldCycElt ], TabChtr -> AlgChtrElt
CompositionFactors(G) : : GrpFin -> [ <RngIntElt, RngIntElt, RngIntElt> ]
CompositionFactors(G) : : GrpMat -> [ <RngIntElt, RngIntElt, RngIntElt> ]
CompositionFactors(G) : GrpPC -> SeqEnum
CompositionFactors(G) : GrpPerm -> [ <RngIntElt, RngIntElt, RngIntElt> ]
CompositionFactors(M) : ModRng -> [ ModRng ]
CompositionSeries(A) : AlgGen -> [ AlgGen ], [ AlgGen ], AlgMatElt
CompositionSeries(G) : GrpPC -> [GrpPC]
CompositionSeries(G, i) : GrpPC, RngIntElt -> [GrpPC]
CompositionSeries(M) : ModRng, ModRng -> [ ModRng ], [ ModRng ], AlgMatElt

composition

Composition (MAPPINGS)
Composition and Chief Series (PERMUTATION GROUPS)
Composition and Decomposition (CHARACTERS OF FINITE GROUPS)
Composition and Reversion (POWER, LAURENT AND PUISEUX SERIES)
Composition Factors (MATRIX GROUPS)
Composition Series (MODULES OVER A MATRIX ALGEBRA)

composition-decomposition

Composition and Decomposition (CHARACTERS OF FINITE GROUPS)

composition-factors

Composition Factors (MATRIX GROUPS)

composition-reversion

Composition and Reversion (POWER, LAURENT AND PUISEUX SERIES)

composition-series

Composition and Chief Series (PERMUTATION GROUPS)
Composition Series (MODULES OVER A MATRIX ALGEBRA)

CompositionFactors

CompositionFactors(G) : : GrpFin -> [ <RngIntElt, RngIntElt, RngIntElt> ]
CompositionFactors(G) : : GrpMat -> [ <RngIntElt, RngIntElt, RngIntElt> ]
CompositionFactors(G) : GrpPC -> SeqEnum
CompositionFactors(G) : GrpPerm -> [ <RngIntElt, RngIntElt, RngIntElt> ]
CompositionFactors(M) : ModRng -> [ ModRng ]
GrpMat_CompositionFactors (Example H21E27)

CompositionReversion

RngSer_CompositionReversion (Example H60E2)

CompositionSeries

CompositionSeries(A) : AlgGen -> [ AlgGen ], [ AlgGen ], AlgMatElt
CompositionSeries(G) : GrpPC -> [GrpPC]
CompositionSeries(G, i) : GrpPC, RngIntElt -> [GrpPC]
CompositionSeries(M) : ModRng, ModRng -> [ ModRng ], [ ModRng ], AlgMatElt

Compositum

RngOrd_Compositum (Example H53E9)

CompSeries

ModAlg_CompSeries (Example H76E16)

Computable

HasComputableLCS(G) : GrpGPC -> BoolElt

computation

Structure Computation (GENERIC ABELIAN GROUPS)

Concatenated

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

ConcatenatedCode

ConcatenatedCode(O, I) : Code, Code -> Code
CodeFld_ConcatenatedCode (Example H97E32)

concatenation

Strings (OVERVIEW)

Concurrent

IsConcurrent(P, R) : Plane, { PlaneLn } -> BoolElt, PlanePt

condition

The case expression (OVERVIEW)
The case statement (OVERVIEW)
The if statement (OVERVIEW)
The select expression (OVERVIEW)

Conditional

ConditionalClassGroup(O) : RngOrd -> GrpAb, Map

conditional

Classes of Subgroups Satisfying a Condition (PERMUTATION GROUPS)
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)

ConditionalClassGroup

ConditionalClassGroup(O) : RngOrd -> GrpAb, Map

Conditioned

ConditionedGroup(G) : GrpPC -> GrpPC
IsConditioned(G) : GrpPC -> BoolElt

conditioned

Conditioned Presentations (FINITE SOLUBLE GROUPS)

conditioned-presentation

Conditioned Presentations (FINITE SOLUBLE GROUPS)

ConditionedGroup

ConditionedGroup(G) : GrpPC -> GrpPC

conditions

Point conditions (SCHEMES)

Conductor

Conductor(E) : CrvEll -> RngIntElt
Conductor(A) : FldAb -> RngOrdIdl, [RngIntElt]
Conductor(K) : FldCyc -> RngIntElt
Conductor(K) : FldQuad -> RngIntElt
Conductor(Q) : FldRat -> RngIntElt
Conductor(M) : ModBrdt -> RngIntElt
Conductor(O) : RngOrd -> RngOrdIdl
Conductor(O) : RngQuad -> RngIntElt
ConductorRange(D) : DB -> RngIntElt, RngIntElt
LargestConductor(D) : DB -> RngIntElt

ConductorRange

ConductorRange(D) : DB -> RngIntElt, RngIntElt

Cone

TangentCone(p) : Crv,Pt -> Crv
TangentCone(p) : Sch,Pt -> Sch

Confluent

IsConfluent(G) : GrpAtc -> BoolElt
IsConfluent(G) : GrpRWS -> BoolElt
IsConfluent(M) : MonRWS -> BoolElt

Congruence

Congruence Subgroups (SUBGROUPS OF PSL_2(R))
CongruenceGroup(M1, M2, prec) : ModFrm, ModFrm, RngIntElt -> GrpAb
CongruenceGroup(M : parameters) : ModSym -> GrpAb
CongruenceModulus(M : parameters) : ModSym -> RngIntElt
CongruenceSubgroup(N) : RngIntElt -> GrpPSL2
CongruenceSubgroup(i,N) : RngIntElt, RngIntElt -> GrpPSL2
CongruenceSubgroup([N,M,P]) : SeqEnum -> GrpPSL2
IsCongruence(G) : GrpPSL2 -> BoolElt

congruence

Structure of congruence subgroups (SUBGROUPS OF PSL_2(R))

Congruence-subgroups

Congruence Subgroups (SUBGROUPS OF PSL_2(R))

CongruenceGroup

CongruenceGroup(M1, M2, prec) : ModFrm, ModFrm, RngIntElt -> GrpAb
CongruenceGroup(M : parameters) : ModSym -> GrpAb

CongruenceModulus

CongruenceModulus(M : parameters) : ModSym -> RngIntElt

Congruences

ModForm_Congruences (Example H90E17)

congruences

Congruences (MODULAR FORMS)

CongruenceSubgroup

CongruenceSubgroup(N) : RngIntElt -> GrpPSL2
CongruenceSubgroup(i,N) : RngIntElt, RngIntElt -> GrpPSL2
CongruenceSubgroup([N,M,P]) : SeqEnum -> GrpPSL2

Conic

Combinatorial and Geometrical Structures (OVERVIEW)
Conic(X,f:parameters) : Sch, RngMPolElt -> CrvCon
Conic(P, S) : Plane, { PlanePt } -> SetEnum
Conic(P,S) : Prj, Pt -> Crv
IsConic(X) : Sch -> BoolElt, CrvCon
IsConic(X) : Sch -> BoolElt,CrvCon

conic

RATIONAL CURVES AND CONICS

conic_curve

CrvCon_conic_curve (Example H84E2)

conics

Conic Curves (RATIONAL CURVES AND CONICS)

Conjugacy

Classes(G) : GrpAb -> [ <RngIntElt, RngIntElt, GrpAbElt> ]
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> ]
GrpGPC_Conjugacy (Example H24E12)

conjugacy

Conjugacy (FINITE SOLUBLE GROUPS)
Groups (OVERVIEW)

ConjugacyClasses

Conjugate

conjugate

Conjugacy (ABELIAN GROUPS)
Conjugacy (MATRIX GROUPS)
Conjugacy (PERMUTATION GROUPS)
Conjugacy (POLYCYCLIC 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)

Conjugate(f)

Conjugate(f) : QuadBinElt -> QuadBinElt

conjugate-norm-trace

Conjugates, Norm and Trace (RATIONAL FIELD)
Conjugates, Norm and Trace (RING OF INTEGERS)

ConjugatePartition

ConjugatePartition(P) : SeqEnum -> SeqEnum

Conjugates

Conjugates(H, g) : GrpAb, GrpAbElt -> { GrpAbElt }
g ^ H : GrpAbElt, GrpAb -> { GrpAbElt }
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) : FldACElt -> [ FldACElt ]
Conjugates(a) : FldAlgElt -> [ FldPrElt ]
ExcludedConjugate(P) : GrpFPCosetEnumProc -> GrpFPElt
ExcludedConjugates(V) : GrpFPCos -> { GrpFPElt }

conjugates

Conjugates (CYCLOTOMIC FIELDS)
Conjugates (QUADRATIC FIELDS)

conjugation

Groups (OVERVIEW)

Connect

Connect(v,w) : GrphResVert,GrphResVert -> GrphRes

Connected

IsConnected(G) : GrphUnd -> BoolElt
IsResiduallyConnected(C) : CosetGeom -> BoolElt
IsResiduallyConnected(D) : IncGeom -> BoolElt
IsSimplyConnected( G ) : GrpLie-> BoolElt
IsSimplyConnected( RD ) : RootDtm-> BoolElt
IsStronglyConnected(G) : GrphDir -> BoolElt
IsWeaklyConnected(G) : GrphDir -> BoolElt

connectedness

Connectedness, Paths and Circuits (GRAPHS)

connectedness-path-circuit

Connectedness, Paths and Circuits (GRAPHS)

Connecting

ConnectingHomomorphism(f,g,n) : MapChn, MapChn, RngIntElt -> ModMatFldElt

ConnectingHomomorphism

ConnectingHomomorphism(f,g,n) : MapChn, MapChn, RngIntElt -> ModMatFldElt

Connection

ConnectionNumber

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

ConnectionPolynomial

ConnectionPolynomial(S) : SeqEnum -> RngUPolElt, RngIntElt
CharacteristicPolynomial(S) : SeqEnum -> RngUPolElt, RngIntElt
BerlekampMassey(S) : SeqEnum -> RngUPolElt, RngIntElt

cons

Constructions (p-ADIC RINGS AND FIELDS)

consconv

Element Constructions and Conversions (LOCAL RINGS AND FIELDS)

consconv-element

Element Constructions and Conversions (LOCAL RINGS AND FIELDS)

Consecutive

RandomConsecutiveBits(n, a, b) : RngIntElt, RngIntElt -> RngIntElt

Consistency

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

Consistent

IsConsistent(G) : GrpPC -> BoolElt
IsConsistent(G) : GrpGPC -> BoolElt
IsConsistent(A, w) : ModMatRngElt, ModTupRng -> BoolElt, ModTupRngElt, ModTupRng
IsConsistent(A, W) : ModMatRngElt, [ ModTupRng ] -> BoolElt, [ ModTupRngElt ], ModTupRng
IsConsistent(A, W) : Mtrx, Mtrx -> BoolElt, Mtrx, ModTupRng
IsConsistent(A, Q) : Mtrx, [ ModTupRng ] -> BoolElt, [ ModTupRngElt ], ModTupRng

Constant

constant

Constants (REAL AND COMPLEX FIELDS)

ConstantField

DefiningConstantField(F) : FldFun -> Rng
ConstantField(F) : FldFun -> Rng

ConstantMap

map< X -> Y | Q > : Sch,Sch,SeqEnum -> MapSch
ConstantMap(X,Y,p) : Sch,Sch,Pt -> MapSch

Constants

StructureConstants( RD ) : RootDtm -> RngIntElt

constants

Constants associated with crystallographic root data (ROOT DATA FOR LIE THEORY)

constants-root-datum

Constants associated with crystallographic root data (ROOT DATA FOR LIE THEORY)

ConstantWords

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

Constituent

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

Constituents

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

ConstituentsWithMultiplicities

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

constr

Miscellaneous Graph Constructions (GRAPHS)

constr-misc

Miscellaneous Graph Constructions (GRAPHS)

constr_elt

Constructions (LOCAL RINGS AND FIELDS)

Constraint

Constraint(L, n) : LP, RngIntElt -> Mtrx, Mtrx, RngIntElt
RemoveConstraint(L, n) : LP, RngIntElt ->

Constraints

AddConstraints(L, lhs, rhs) : LP, Mtrx, Mtrx ->
NumberOfConstraints(L) : LP -> RngIntElt

Construct

ConstructTable(A) : AlgGrp ->

construct

Element Constructions and Conversions (p-ADIC RINGS AND FIELDS)

construct-element

Element Constructions and Conversions (p-ADIC RINGS AND FIELDS)

ConstructingHomomorphisms

GrpSLP_ConstructingHomomorphisms (Example H32E2)

Construction

Construction(D, i): DB, RngIntElt -> MonStgElt, Rng
Construction(D, d, i): DB, RngIntElt, RngIntElt -> MonStgElt, Rng
ConstructionX(C1, C2, C3) : Code, Code, Code -> Code
ConstructionX3(C1,C2,C3,D1,D2) : Code,Code,Code -> Code,Map
ConstructionXX(C1,C2,C3,D2,D3) : Code,Code,Code,Code,Code -> Code
ConstructionY1(C) : Code -> Code
ConstructionY1(C, w) : Code, RngIntElt -> Code

construction

Abelian and p-Quotients (FINITE SOLUBLE GROUPS)
Abelian, Nilpotent and Soluble Quotients (MATRIX GROUPS)
Abelian, Nilpotent and Soluble Quotients (PERMUTATION GROUPS)
Constructing and Modifying a Coset Enumeration Process (FP GROUPS - ADVANCED FEATURES)
Constructing elements (GROUPS OF LIE TYPE)
Constructing groups of Lie type (GROUPS OF LIE TYPE)
Construction (FP GROUPS - ADVANCED FEATURES)
Construction (MODULES OVER A MATRIX ALGEBRA)
Construction Functions (FINITE SOLUBLE GROUPS)
Construction of a Base and Strong Generating Set (PERMUTATION GROUPS)
Construction of a Subgroup (PERMUTATION GROUPS)
Construction of an FP-Group (FINITELY PRESENTED GROUPS)
Construction of Coxeter groups (COXETER GROUPS)
Construction of New Lattices (LATTICES)
Construction of Quotient Groups (FINITE SOLUBLE GROUPS)
Construction of Quotient Groups (MATRIX GROUPS)
Construction of Quotient Groups (PERMUTATION GROUPS)
Construction of Subgroups (MATRIX GROUPS)
Construction of Words (FINITELY PRESENTED GROUPS)
Some Basic Families of Codes (LINEAR CODES OVER FINITE FIELDS)
Standard Constructions and Conversions (ABELIAN GROUPS)
Standard Constructions of New Lattices (LATTICES)
Standard Subgroups (PERMUTATION GROUPS)

construction-base-strong-generator

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

construction-functions

Construction Functions (FINITE SOLUBLE GROUPS)

construction-quotient

Construction of Quotient Groups (FINITE SOLUBLE GROUPS)
Construction of Quotient Groups (MATRIX GROUPS)
Construction of Quotient Groups (PERMUTATION GROUPS)

construction-special-quotient

Abelian and p-Quotients (FINITE SOLUBLE GROUPS)
Abelian, Nilpotent and Soluble Quotients (MATRIX GROUPS)
Abelian, Nilpotent and Soluble Quotients (PERMUTATION GROUPS)

construction-standard

Some Basic Families of Codes (LINEAR CODES OVER FINITE FIELDS)

construction-standard-subgroup

Standard Subgroups (PERMUTATION GROUPS)

construction-subgroup

Construction of a Subgroup (PERMUTATION GROUPS)
Construction of Subgroups (MATRIX GROUPS)

Constructions

GrpMat_Constructions (Example H21E10)

constructions

Point computations (SCHEMES)
Standard Subgroup Constructions (FINITE SOLUBLE GROUPS)
Standard Subgroups (MATRIX GROUPS)

ConstructionX

ConstructionX(C1, C2, C3) : Code, Code, Code -> Code

constructionX

CodeFld_constructionX (Example H97E33)

ConstructionX3

ConstructionX3(C1,C2,C3,D1,D2) : Code,Code,Code -> Code,Map

ConstructionXX

ConstructionXX(C1,C2,C3,D2,D3) : Code,Code,Code,Code,Code -> Code

ConstructionY1

ConstructionY1(C) : Code -> Code
ConstructionY1(C, w) : Code, RngIntElt -> Code

Constructor

GrpGPC_Constructor (Example H24E1)
GrpMat_Constructor (Example H21E3)

constructor

Construction from a Finite Permutation or Matrix Group (FINITELY PRESENTED GROUPS)
Construction of Lists (LISTS)
Constructor (OVERVIEW)
Definition by Presentation (FINITE SOLUBLE GROUPS)
Function Expressions (OVERVIEW)
Procedure Expressions (OVERVIEW)
Sequences (OVERVIEW)
Sets (OVERVIEW)
The FP-Group Constructor (FINITELY PRESENTED GROUPS)
The Map Constructors (MAPPINGS)

Constructors

ConstructTable

ConstructTable(A) : AlgGrp ->

consts

RootDtm_consts (Example H35E17)

Containing

FacesContaining(N,p) : NwtnPgon,Tup -> SeqEnum

Contains

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

ContainsQuadrangle

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

Content

Content(L) : Lat -> RngElt
Content(f) : RngMPolElt -> RngIntElt
Content(I) : RngOrdFracIdl -> RngIntElt
Content(I) : RngQuadFracIdl -> RngQuadFracIdl
Content(p) : RngUPolElt -> RngIntElt
Content(w) : SeqEnum -> SeqEnum
Content(t) : Tableau -> SeqEnum
ContentAndPrimitivePart(f) : RngMPolElt -> RngIntElt, RngMPolElt
ContentAndPrimitivePart(p) : RngUPolElt -> RngIntElt, RngUPolElt

content

Contpp(f) : RngMPolElt -> RngIntElt, RngMPolElt
Content and Primitive Part (MULTIVARIATE POLYNOMIAL RINGS)
Content and Primitive Part (UNIVARIATE POLYNOMIAL RINGS)

content-primitive

Contpp(f) : RngMPolElt -> RngIntElt, RngMPolElt
Content and Primitive Part (MULTIVARIATE POLYNOMIAL RINGS)

ContentAndPrimitivePart

Contpp(f) : RngMPolElt -> RngIntElt, RngMPolElt
ContentAndPrimitivePart(f) : RngMPolElt -> RngIntElt, RngMPolElt
ContentAndPrimitivePart(p) : RngUPolElt -> RngIntElt, RngUPolElt

context

The Initial Context (MAGMA SEMANTICS)

continuation

Comments and Continuation (STATEMENTS AND EXPRESSIONS)

Continue

CanContinueEnumeration(P) : GrpFPCosetEnumProc -> BoolElt
ContinueEnumeration(~P: parameters) : GrpFPCosetEnumProc ->

continue

Early Exit from Iterative Statements (STATEMENTS AND EXPRESSIONS)
The continue statement (OVERVIEW)

continue-break

Early Exit from Iterative Statements (STATEMENTS AND EXPRESSIONS)

Continued

ContinuedFraction(r) : FldPrElt -> [ RngIntElt ]

continued

Continued Fractions (REAL AND COMPLEX FIELDS)

continued-fraction

Continued Fractions (REAL AND COMPLEX FIELDS)

ContinuedFraction

ContinuedFraction(r) : FldPrElt -> [ RngIntElt ]

ContinueEnumeration

ContinueEnumeration(~P: parameters) : GrpFPCosetEnumProc ->

Contpp

Contpp(f) : RngMPolElt -> RngIntElt, RngMPolElt
ContentAndPrimitivePart(f) : RngMPolElt -> RngIntElt, RngMPolElt
ContentAndPrimitivePart(p) : RngUPolElt -> RngIntElt, RngUPolElt

Contract

Contract(e) : GrphEdge -> Grph
Contract(u, v) : GrphVert, GrphVert -> Grph
Contract(S) : { GrphVert } -> Grph

Contraction

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

contraction

Constructing Complements, Line Graphs; Contraction, Switching (GRAPHS)
Extension and Contraction of Ideals (IDEAL THEORY AND GRÖBNER BASES)

Contribution

GenusContribution(g) : GrphRes -> RngIntElt

control

Control-C key (OVERVIEW)
Controlling Selection of a Base (MATRIX GROUPS)
Quitting (OVERVIEW)

control--key

<Ctrl>-\
<Ctrl>-\

control-_-key

<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

control-W-key

<Ctrl>-W

control-X-key

<Ctrl>-X

control-Y-key

<Ctrl>-Y

control-Z-key

<Ctrl>-Z

ControlExtn

GrpFP_1_ControlExtn (Example H22E15)

conv

Design_conv (Example H94E10)

Convergents

Convergents(s) : [ RngIntElt ] -> ModMatRngElt

Conversion

GrpAtc_Conversion (Example H31E9)
GrpRWS_Conversion (Example H30E8)
MonRWS_Conversion (Example H18E8)

conversion

Character Conversion (INPUT AND OUTPUT)
Construction of the Standard Presentation for a Coxeter Group (FINITELY PRESENTED GROUPS)
Conversion between Categories (POLYCYCLIC GROUPS)
Conversion from a Special Form of FP-Group (FINITELY PRESENTED GROUPS)
Conversion Functions (INCIDENCE STRUCTURES AND DESIGNS)
Conversion to a Finitely Presented Group (AUTOMATIC GROUPS)
Conversion to a Finitely Presented Group (GROUPS DEFINED BY REWRITE SYSTEMS)
Conversion to a Finitely Presented Monoid (MONOIDS GIVEN BY REWRITE SYSTEMS)
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 conversion functions (COXETER GROUPS)
Element Conversions (RING OF INTEGERS)
Sets from Structures (SETS)

conversion-graph-digraph

Converting between Graphs and Digraphs (GRAPHS)

Convert

ConvertFromManinSymbol(M, x) : ModSym, Tup -> ModSymElt

convert

Conversion (COXETER GROUPS)

ConvertFromManinSymbol

ConvertFromManinSymbol(M, x) : ModSym, Tup -> ModSymElt

Convolution

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

Conway

ConwayPolynomial(p, n) : RngIntElt, RngIntElt -> RngUPolElt
ExistsConwayPolynomial(p, n) : RngIntElt, RngIntElt -> BoolElt, RngUPolElt
IsConway(F) : FldFin -> BoolElt

conway

Conway Polynomials (FINITE FIELDS)

ConwayPolynomial

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

Coordelt

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

Coordinate

CoordinateLattice(L) : Lat -> Lat
CoordinateRing(L) : Lat -> RngInt
CoordinateRing(A) : Sch -> Rng
CoordinateRing(C) : Sch -> Rng
CoordinateRing(A) : Sch -> RngMPol
CoordinateRing(X) : Sch -> RngMPol
CoordinateSpace(L) : Lat -> ModTupFld, Map
CoordinateVector(L, v) : LatElt -> LatElt
CoordinateVector(v) : LatElt -> LatElt
p[i] : Pt, RngIntElt -> RngElt
p[i] : Pt, RngIntElt -> RngElt

CoordinateLattice

CoordinateLattice(L) : Lat -> Lat

CoordinateRing

CoordinateRing(L) : Lat -> RngInt
CoordinateRing(A) : Sch -> Rng
CoordinateRing(C) : Sch -> Rng
CoordinateRing(A) : Sch -> RngMPol
CoordinateRing(X) : Sch -> RngMPol

Coordinates

Coordinates(S, a) : AlgGen, AlgGenElt -> SeqEnum
Coordinates(S, a) : AlgGrpSub, AlgGrpElt -> [ RingElt ]
Coordinates(R, X) : AlgMat, AlgMatElt -> [ RngElt ]
Coordinates(C, u) : Code, ModTupRngElt -> [ RngFinElt ]
Coordinates(C, u) : Code, ModTupRngElt -> [ RngFinElt ]
Coordinates(L, v) : LatElt -> [ RngIntElt ]
Coordinates(v) : LatElt -> [ RngIntElt ]
Coordinates(f, M) : ModMPolElt, ModMPol -> [ RngMPolElt ]
Coordinates(V, v) : ModTupFld, ModTupFldElt -> [FldElt]
Coordinates(M, u) : ModTupRng, ModTupRngElt -> [RngElt]
Coordinates(P, l) : Plane, PlaneLn -> [ FldFinElt ]
Coordinates(P, p) : Plane, PlanePt -> [ FldFinElt ]
Coordinates(p) : Pt -> SeqEnum
Coordinates(p) : Pt -> SeqEnum
Coordinates(p) : Pt -> SeqEnum
Coordinates(I, f) : RngMPol, RngMPolElt -> [ RngMPolElt ]
CoordinatesToElement(L, C) : Lat, [ RngIntElt ] -> LatElt
ElementToSequence(x) : AlgQuatOrdElt -> SeqEnum
IdentityAutomorphism(A) : Sch -> AutSch
NumberOfCoordinates(X) : Sch -> RngIntElt
CodeFld_Coordinates (Example H97E12)
GB_Coordinates (Example H50E7)

CoordinateSpace

CoordinateSpace(L) : Lat -> ModTupFld, Map

CoordinatesToElement

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

CoordinateVector

CoordinateVector(L, v) : LatElt -> LatElt
CoordinateVector(v) : LatElt -> LatElt

coords

Choosing Coordinates (PLANE ALGEBRAIC CURVES)
Function Fields and Divisors (PLANE ALGEBRAIC CURVES)

cop

Aggregate (OVERVIEW)
cop< S_1, S_2, ..., S_k > : Struct, Struct, ... -> Cop, [ Map ]
Coproduct_cop (Example H11E1)

Coprime

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

CoprimeBasis

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

coproduct

COPRODUCTS

Cordaro

CordaroWagnerCode(n) : RngIntElt -> Code

CordaroWagnerCode

CordaroWagnerCode(n) : RngIntElt -> Code

Core

Core(G, H) : GrpFP, GrpFP -> GrpFP
Core(G, H) : GrpAb, GrpAb -> GrpAb
Core(G, H) : GrpFin, GrpFin -> GrpFin
Core(G, H) : GrpGPC, GrpGPC -> GrpGPC
Core(G, H) : GrpMat, GrpMat -> GrpMat
Core(G, H) : GrpPC, GrpPC -> GrpPC
Core(G, H) : GrpPerm, GrpPerm -> GrpPerm

Coreflection

CoreflectionGroup( W ) : GrpCox -> GrpMat, Map
ReflectionGroup( W ) : GrpCox -> GrpMat, Map
ReflectionMatrices( RD ) : RootDtm -> []
ReflectionMatrix( RD, r ) : RootDtm, RngIntElt -> []
SimpleReflectionMatrices( RD ) : RootDtm -> []

CoreflectionGroup

CoreflectionGroup( W ) : GrpCox -> GrpMat, Map
ReflectionGroup( W ) : GrpCox -> GrpMat, Map

CoreflectionMatrices

CoreflectionMatrices( RD ) : RootDtm -> []
ReflectionMatrices( RD ) : RootDtm -> []

CoreflectionMatrix

CoreflectionMatrix( RD, r ) : RootDtm, RngIntElt -> []
ReflectionMatrix( RD, r ) : RootDtm, RngIntElt -> []

Coroot

Coroot( W, r ) : GrpCox, RngIntElt -> {@@}
Root( W, r ) : GrpCox, RngIntElt -> {@@}
Root( G, r ) : GrpLie, RngIntElt -> {@@}
Root( RD, r ) : RootDtm, RngIntElt -> {@@}
RootAction( W ) : GrpCox -> Map
RootAction( F ) : GrpFP -> Map
RootGSet( W ) : GrpCox -> GSet
RootHeight( RD, r ) : RootDtm, RngIntElt -> RngIntElt
RootNorm( RD, r ) : RootDtm, RngIntElt -> RngIntElt
RootNorms( RD ) : RootDtm -> [RngIntElt]
RootPosition( W, v ) : GrpCox, . -> {@@}
RootPosition( G, v ) : GrpLie, . -> {@@}
RootPosition( RD, v ) : RootDtm, . -> {@@}
RootSpace( W ) : GrpCox -> .
RootSpace( RD ) : RootDtm -> .
WordOnRootSpace( W, v, w ) : GrpCox, ., . -> .

coroot

Actions on roots and coroots (COXETER GROUPS)
Operations and properties for (co)roots (ROOT DATA FOR LIE THEORY)

CorootAction

CorootAction( W ) : GrpCox -> Map
RootAction( W ) : GrpCox -> Map
RootAction( F ) : GrpFP -> Map
GrpCox_CorootAction (Example H36E10)

CorootGSet

CorootGSet( W ) : GrpCox -> GSet
RootGSet( W ) : GrpCox -> GSet

CorootHeight

CorootHeight( RD, r ) : RootDtm, RngIntElt -> RngIntElt
RootHeight( RD, r ) : RootDtm, RngIntElt -> RngIntElt

CorootNorm

CorootNorm( RD, r ) : RootDtm, RngIntElt -> RngIntElt
RootNorm( RD, r ) : RootDtm, RngIntElt -> RngIntElt

CorootNorms

CorootNorms( RD ) : RootDtm -> [RngIntElt]
RootNorms( RD ) : RootDtm -> [RngIntElt]

CorootPosition

CorootPosition( W, v ) : GrpCox, . -> {@@}
RootPosition( W, v ) : GrpCox, . -> {@@}
RootPosition( G, v ) : GrpLie, . -> {@@}
RootPosition( RD, v ) : RootDtm, . -> {@@}

Coroots

PositiveCoroots( W ) : GrpCox -> {@@}
PositiveRoots( W ) : GrpCox -> {@@}
PositiveRoots( G ) : GrpLie -> {@@}
PositiveRoots( RD ) : RootDtm -> {@@}
Roots( W ) : GrpCox -> {@@}
Roots( G ) : GrpLie -> {@@}
Roots( RD ) : RootDtm -> {@@}
SimpleRoots( W ) : GrpCox -> Mtrx
SimpleRoots( RD ) : RootDtm -> Mtrx

coroots

Roots, coroots and weights (ROOT DATA FOR LIE THEORY)

CorootSpace

CorootSpace( W ) : GrpCox -> .
RootSpace( W ) : GrpCox -> .
RootSpace( RD ) : RootDtm -> .

correcting

Combinatorial and Geometrical Structures (OVERVIEW)
LINEAR CODES OVER FINITE FIELDS
LINEAR CODES OVER FINITE RINGS

Correlation

AutoCorrelation(S, t) : SeqEnum, RngIntElt -> RngIntElt
CorrelationGroup(D) : IncGeom -> GrpPerm
CrossCorrelation(S1, S2, t) : SeqEnum, SeqEnum, RngIntElt -> RngIntElt

correlation

Correlation Functions (PSEUDO-RANDOM BIT SEQUENCES)

CorrelationGroup

CorrelationGroup(D) : IncGeom -> GrpPerm

Cos

Cos(c) : FldComElt -> FldComElt
Cos(f) : RngSerElt -> RngSerElt
Cos(f) : RngSerElt -> RngSerElt

Cosec

Cosec(c) : FldComElt -> FldComElt
Cosec(f) : RngSerElt -> RngSerElt

Cosech

Cosech(s) : FldPrElt -> FldPrElt

Coset

coset

Action on a Coset Space (GROUPS)
Action on a Coset Space (MATRIX GROUPS)
Action on a Coset Space (PERMUTATION GROUPS)
Construction of a Coset Geometry (INCIDENCE GEOMETRY)
Coset Leaders (LINEAR CODES OVER FINITE FIELDS)
Coset Spaces (ABELIAN GROUPS)
Coset Spaces (POLYCYCLIC GROUPS)
Coset Spaces and Tables (FINITELY PRESENTED GROUPS)
Coset Spaces: Construction (FINITELY PRESENTED GROUPS)
Coset Tables (FINITELY PRESENTED GROUPS)
Coset Tables and Transversals (FINITE SOLUBLE GROUPS)
Coset Tables and Transversals (MATRIX GROUPS)
Interactive Coset Enumeration (FP GROUPS - ADVANCED FEATURES)

coset-action

Action on a Coset Space (PERMUTATION GROUPS)

coset-enumeration

Interactive Coset Enumeration (FP GROUPS - ADVANCED FEATURES)

coset-leader

Coset Leaders (LINEAR CODES OVER FINITE FIELDS)

coset-space

RightTransversal(G, H) : GrpAb, GrpAb -> {@ GrpAbElt @}, Map
Coset Spaces (ABELIAN GROUPS)
Coset Spaces (POLYCYCLIC GROUPS)
Coset Spaces: Construction (FINITELY PRESENTED GROUPS)

coset-space-action

Action on a Coset Space (GROUPS)

coset-space-table

Coset Spaces and Tables (FINITELY PRESENTED GROUPS)

coset-table

Coset Tables (FINITELY PRESENTED GROUPS)

coset-table-transversal

RightTransversal(G, H) : GrpMat, GrpMat -> {@ GrpMatElt @}, Map
Coset Tables and Transversals (MATRIX GROUPS)

coset-table-transversals

Coset Tables and Transversals (FINITE SOLUBLE GROUPS)

CosetAction

CosetDistanceDistribution

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

CosetEnumerationProcess

CosetEnumerationProcess(G, H: parameters) : GrpFP, GrpFP -> GrpFPCosetEnumProc

CosetGeometry

CosetGeometry(G, S) : GrpPerm, Set -> CosetGeom
CosetGeometry(G, S, I) : GrpPerm, Set, Set -> CosetGeom
CosetGeometry(D) : IncGeom -> BoolElt, CosetGeom

CosetImage

CosetImage(G, H) : GrpGPC, GrpGPC -> GrpPerm
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) : Grp, Grp -> GrpPerm
CosetImage(V) : GrpFPCos, Grp -> GrpPerm
CosetImage(P) : GrpFPCosetEnumProc -> GrpPerm
CosetImage(G, H) : GrpMat, GrpMat -> GrpPerm

CosetKernel

CosetKernel(G, H) : GrpFP, GrpFP -> GrpFP
CosetKernel(G, H) : Grp, Grp -> Grp
CosetKernel(G, H) : Grp, Grp -> Grp
CosetKernel(G, H) : Grp, Grp -> Grp
CosetKernel(G, H) : Grp, Grp -> Grp
CosetKernel(V) : GrpFPCos -> GrpFP
CosetKernel(P) : GrpFPCosetEnumProc -> GrpFP
CosetKernel(G, H) : GrpGPC, GrpGPC -> GrpGPC
CosetKernel(G, H) : GrpMat, GrpMat -> GrpMat

CosetLeaders

CosetLeaders(C) : Code -> {@ ModTupFldElt @}, Map
CodeFld_CosetLeaders (Example H97E13)

CosetRepresentatives

CosetRepresentatives(G) : GrpPSL2 -> SeqEnum
CosetRepresentatives(FS) : SymFry -> SeqEnum

Cosets

CosetSatisfying(P : parameters) : GrpFPCosetEnumProc -> { GrpFPElt }
CosetsSatisfying(P : parameters) : GrpFPCosetEnumProc -> { GrpFPElt }
CosetsSatisfying(T, S: parameters) : Map, { GrpFPElt }: -> { GrpFPCosElt }
DoubleCosets(G, H, K) : GrpFP, GrpFP, GrpFP -> { GrpFPDcosElt }
MaximalNumberOfCosets(P) : GrpFPCosetEnumProc -> RngIntElt
TotalNumberOfCosets(P) : GrpFPCosetEnumProc -> RngIntElt

cosets

Action on a Coset Space (FINITE SOLUBLE GROUPS)
Cosets (FINITE SOLUBLE GROUPS)
Cosets (PERMUTATION GROUPS)
Cosets and Transversals (PERMUTATION GROUPS)
Double Coset Spaces: Construction (FINITELY PRESENTED GROUPS)

cosets-action

Action on a Coset Space (FINITE SOLUBLE GROUPS)

cosets-transversals

Cosets and Transversals (PERMUTATION GROUPS)

CosetSatisfying

CosetSpace

CosetSpace(P) : GrpFPCosetEnumProc -> GrpFPCos
CosetSpace(G, H: parameters) : GrpFP, GrpFP: -> GrpFPCos
GrpFP_1_CosetSpace (Example H22E47)

cosetspaces

Coset Spaces and Transversals (FP GROUPS - ADVANCED FEATURES)

CosetsSatisfying

CosetTable

CosetTable(G, H) : GrpGPC, GrpGPC -> Map
CosetTable(P) : GrpFPCosetEnumProc -> Map
CosetTable(G, H) : Grp, Grp -> Hom(Grp)
CosetTable(G, H) : Grp, Grp -> Map
[Future release] CosetTable(G, f) : Grp, Hom(Grp) -> Hom(Grp)
CosetTable(G, H) : GrpFin, GrpFin -> Map
[Future release] CosetTable(G, f) : GrpFin, Hom(GrpFin) -> Hom(GrpFin)
CosetTable(G, H) : GrpPC, GrpPC -> Map
CosetTable(G, H: parameters) : GrpFP, GrpFP -> Map
GrpGPC_CosetTable (Example H24E7)

CosetTable1

GrpFP_1_CosetTable1 (Example H22E45)

CosetTable2

GrpFP_1_CosetTable2 (Example H22E46)

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
Cosh(f) : RngSerElt -> RngSerElt

cossey_hawkes

GrpPC_cossey_hawkes (Example H25E7)

Cot

Cot(c) : FldComElt -> FldComElt
Cot(f) : RngSerElt -> RngSerElt

Coth

Coth(s) : FldPrElt -> FldPrElt

Count

NFSCycleCount(n, F, tuple) : RngIntElt, RngMPolElt, Tup -> RngIntElt

counting_jacobian

Counting Points on the Jacobian (HYPERELLIPTIC CURVES)

Covalence

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

Cover

ProjectiveCover(M) : ModAlg -> ModAlg, ModMatFldElt, SeqEnum[ModMatFldElt], SeqEnum[ModMatFldElt], SeqEnum[RngIntElt]

Covering

CoveringRadius(C) : Code -> RngIntElt
CoveringRadius(L) : Lat -> FldRatElt
CoveringStructure(S, T) : Str, Str -> Str
ExistsCoveringStructure(S, T) : Str, Str -> BoolElt, Str

CoveringRadius

CoveringRadius(C) : Code -> RngIntElt
CoveringRadius(L) : Lat -> FldRatElt
CodeFld_CoveringRadius (Example H97E24)

CoveringStructure

CoveringStructure(S, T) : Str, Str -> Str

Covers

PartitionCovers(P1, P2) : SeqEnum, SeqEnum -> BoolElt

covers

Projective Covers (BASIC ALGEBRAS)

Coweight

CoweightLattice( G ) : RootDtm -> Lat
WeightLattice( G ) : RootDtm -> Lat
WeightLattice( RD ) : RootDtm -> Lat
WeightLattice( W ) : RootDtm -> Lat

CoweightLattice

CoweightLattice( G ) : RootDtm -> Lat
WeightLattice( G ) : RootDtm -> Lat
WeightLattice( RD ) : RootDtm -> Lat
WeightLattice( W ) : RootDtm -> Lat

Coweights

FundamentalCoweights( W ) : GrpCox -> SeqEnum
FundamentalWeights( W ) : GrpCox -> SeqEnum
FundamentalWeights( G ) : GrpLie -> SeqEnum
FundamentalWeights( RD ) : RootDtm -> Mtrx

Coxeter

Implicit Invocation of the Todd-Coxeter Algorithm (FINITELY PRESENTED GROUPS)
Index of a Subgroup: The Todd-Coxeter Algorithm (FINITELY PRESENTED GROUPS)
CoxeterElement( G ) : GrpCox -> GrpPermElt
CoxeterElement( W ) : GrpCox -> GrpPermElt
CoxeterElement( F ) : GrpFP -> SeqEnum
CoxeterForm( RD ) : RootDtm -> AlgMatElt
CoxeterGroup( GrpFP, W ) : Cat, GrpCox -> GrpFP, Map
CoxeterGroup( GrpFP, t ) : Cat, MonStgElt -> GrpFP
CoxeterGroup(GrpFP, t) : Cat, MonStgElt -> GrpFP
CoxeterGroup(GrpFP, W) : Cat, GrpCox -> GrpFP, Map
CoxeterGroup( F ) : GrpFP -> GrpCox, Map
CoxeterGroup( t ) : MonStgElt -> GrpCox
CoxeterGroup( RD ) : RootDtm -> GrpCox
CoxeterGroup( RD ) : RootDtm -> RngIntElt
CoxeterNumber( G ) : GrpCox -> GrpPermElt
CoxeterNumber( W ) : GrpCox -> GrpPermElt
Length( W, w ) : GrpCox, GrpPermElt -> RngIntElt
LocalCoxeterGroup( H ) : GrpCox -> GrpCox, Map
ToddCoxeter(G, H: parameters) : GrpFP, GrpFP -> RngIntElt, Map, RngIntElt, RngIntElt
ToddCoxeterSchreier(G: parameters) : GrpMat : ->
ToddCoxeterSchreier(G: parameters) : GrpPerm : ->
GrpFP_1_Coxeter (Example H22E10)

coxeter

Construction of the Standard Presentation for a Coxeter Group (FINITELY PRESENTED GROUPS)
COXETER GROUPS

coxeter-groups

COXETER GROUPS

CoxeterElement

CoxeterElement( G ) : GrpCox -> GrpPermElt
CoxeterElement( W ) : GrpCox -> GrpPermElt
CoxeterElement( F ) : GrpFP -> SeqEnum

CoxeterForm

DualCoxeterForm( RD ) : RootDtm -> AlgMatElt
CoxeterForm( RD ) : RootDtm -> AlgMatElt

CoxeterGroup

CoxeterGroup( GrpFP, W ) : Cat, GrpCox -> GrpFP, Map
CoxeterGroup( GrpFP, t ) : Cat, MonStgElt -> GrpFP
CoxeterGroup(GrpFP, t) : Cat, MonStgElt -> GrpFP
CoxeterGroup(GrpFP, W) : Cat, GrpCox -> GrpFP, Map
CoxeterGroup( F ) : GrpFP -> GrpCox, Map
CoxeterGroup( t ) : MonStgElt -> GrpCox
CoxeterGroup( RD ) : RootDtm -> GrpCox
CoxeterGroup( RD ) : RootDtm -> RngIntElt

CoxeterLength

CoxeterLength( W, w ) : GrpCox, GrpPermElt -> RngIntElt
Length( W, w ) : GrpCox, GrpPermElt -> RngIntElt

CoxeterNumber

CoxeterNumber( G ) : GrpCox -> GrpPermElt
CoxeterNumber( W ) : GrpCox -> GrpPermElt

CPU

Timing (OVERVIEW)

Cputime

Timing (OVERVIEW)
Cputime() : -> FldReElt
Cputime(t) : FldReElt -> FldReElt

Create

FldAC_Create (Example H56E1)
GrpCox_Create (Example H36E1)
GrpLie_Create (Example H37E1)
GrpMat_Create (Example H21E1)
Mat_Create (Example H62E1)
ModRng_Create (Example H64E5)
PMod_Create (Example H52E1)
RngGal_Create (Example H48E1)
RngGal_Create (Example H48E2)

create

Creating Lattices (MODULES OVER A MATRIX ALGEBRA)
Creating Names (INPUT AND OUTPUT)
Creating new root data from old (ROOT DATA FOR LIE THEORY)
Creating root data (ROOT DATA FOR LIE THEORY)
Creation (COXETER GROUPS)
Creation of Elements (ALGEBRAIC FUNCTION FIELDS)
Creation of G-Lattices (LATTICES)
Creation of p-adic Rings and Fields (p-ADIC RINGS AND FIELDS)
Creation of Structures (ALGEBRAIC FUNCTION FIELDS)
Subspaces (ALGEBRAIC FUNCTION FIELDS)
ModOrd_create (Example H65E1)

create-elts

Creation of Elements (ALGEBRAIC FUNCTION FIELDS)

create-ex

Newton_create-ex (Example H58E1)

create-name

Creating Names (INPUT AND OUTPUT)

create-new-root-datum

Creating new root data from old (ROOT DATA FOR LIE THEORY)

create-root-datum

Creating root data (ROOT DATA FOR LIE THEORY)

create-struct

Creation of Structures (ALGEBRAIC FUNCTION FIELDS)

create-subspaces

Subspaces (ALGEBRAIC FUNCTION FIELDS)

CreateA4wrC3

ModAlg_CreateA4wrC3 (Example H76E5)

CreateA7

ModAlg_CreateA7 (Example H76E7)

CreateComplexField

FldRe_CreateComplexField (Example H43E3)

CreateElements

FldRe_CreateElements (Example H43E4)

CreateHom

ModRng_CreateHom (Example H64E6)
ModRng_CreateHom (Example H64E7)

CreateHomGHom

ModAlg_CreateHomGHom (Example H76E22)

CreateK35

ModFld_CreateK35 (Example H63E2)

CreateK6

ModAlg_CreateK6 (Example H76E1)

CreateL27

ModAlg_CreateL27 (Example H76E2)

CreateLattice

ModAlg_CreateLattice (Example H76E19)

CreateM11

ModAlg_CreateM11 (Example H76E4)

CreateM12

ModAlg_CreateM12 (Example H76E6)

CreateMatrices

ModAlg_CreateMatrices (Example H76E3)

CreatePolyAction

ModAlg_CreatePolyAction (Example H76E8)

CreateQ6

ModFld_CreateQ6 (Example H63E1)

CreateSubgroupPoset

Grp_CreateSubgroupPoset (Example H19E16)

CreateZ6

ModRng_CreateZ6 (Example H64E1)

CreatingRootData

RootDtm_CreatingRootData (Example H35E3)

Creation

creation

öm_(R)(M, N) for matrix modules (FREE MODULES)
öm_(R)(M, N) for R-modules (FREE MODULES)
Alternative Models (ELLIPTIC CURVES)
Ambient Spaces (MODULAR FORMS)
Ambient Spaces (MODULAR SYMBOLS)
Cartesian Product Constructor and Functions (TUPLES AND CARTESIAN PRODUCTS)
Changing the Base Ring (ELLIPTIC CURVES)
Constructing Schemes (SCHEMES)
Constructing the Automorphism Group (INCIDENCE STRUCTURES AND DESIGNS)
Construction of a Base and Strong Generating Set (MATRIX GROUPS)
Construction of a Codeword (LINEAR CODES OVER FINITE FIELDS)
Construction of a Codeword (LINEAR CODES OVER FINITE RINGS)
Construction of a Conic (RATIONAL CURVES AND CONICS)
Construction of a Coset Geometry (INCIDENCE GEOMETRY)
Construction of a Free Abelian Group and its Elements (ABELIAN GROUPS)
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 Matrix Group (MATRIX GROUPS)
Construction of a General Permutation Group (PERMUTATION GROUPS)
Construction of a Generic Abelian Group (GENERIC ABELIAN GROUPS)
Construction of a Matrix (FREE MODULES)
Construction of a Plane (FINITE PLANES)
Construction of a Rewrite Monoid (MONOIDS GIVEN BY REWRITE SYSTEMS)
Construction of a Vector (VECTOR SPACES)
Construction of a Vector Space (VECTOR SPACES)
Construction of a Vector Space with Inner Product Matrix (VECTOR SPACES)
Construction of an Incidence Geometry (INCIDENCE GEOMETRY)
Construction of an SLP-Group and its Elements (GROUPS WHOSE ELEMENTS ARE STRAIGHT-LINE PROGRAMS)
Construction of Associative Algebras (ASSOCIATIVE ALGEBRAS)
Construction of Codes (LINEAR CODES OVER FINITE FIELDS)
Construction of Codes (LINEAR CODES OVER FINITE RINGS)
Construction of Elements (FREE MODULES)
Construction of Elements (GROUPS)
Construction of General Algebras and their Elements (ALGEBRAS)
Construction of Group Algebras and their Elements (GROUP ALGEBRAS)
Construction of Incidence and Coset Geometries (INCIDENCE GEOMETRY)
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 (MODULES OVER A MATRIX ALGEBRA)
Construction of New Ideals (IDEAL THEORY AND GRÖBNER BASES)
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 Database (DATABASES OF GROUPS)
Creating the Database (DATABASES OF GROUPS)
Creating the Database (LATTICES)
Creating the Poset of Subgroup Classes (GROUPS)
Creation (BASIC ALGEBRAS)
Creation (BASIC ALGEBRAS)
Creation (BASIC ALGEBRAS)
Creation (BASIC ALGEBRAS)
Creation (CHAIN COMPLEXES)
Creation (PLANE ALGEBRAIC CURVES)
Creation (RING OF INTEGERS)
Creation (SUBGROUPS OF PSL_2(R))
Creation (SUBGROUPS OF PSL_2(R))
Creation and Access Functions (QUATERNION ALGEBRAS)
Creation by Hand (RESOLUTION GRAPHS AND SPLICE DIAGRAMS)
Creation from Curve Singularities (RESOLUTION GRAPHS AND SPLICE DIAGRAMS)
Creation from Pencils (RESOLUTION GRAPHS AND SPLICE DIAGRAMS)
Creation Functions (BINARY QUADRATIC FORMS)
Creation Functions (CHARACTERS OF FINITE GROUPS)
Creation Functions (COPRODUCTS)
Creation Functions (CYCLOTOMIC FIELDS)
Creation Functions (ELLIPTIC CURVES)
Creation Functions (FINITE FIELDS)
Creation Functions (GALOIS RINGS)
Creation Functions (HYPERELLIPTIC CURVES)
Creation Functions (MAPPINGS)
Creation Functions (MODULAR CURVES)
Creation Functions (MODULAR FORMS)
Creation Functions (MODULAR SYMBOLS)
Creation Functions (ORDERS AND ALGEBRAIC FIELDS)
Creation Functions (POWER, LAURENT AND PUISEUX SERIES)
Creation Functions (RATIONAL FIELD)
Creation Functions (RATIONAL FUNCTION FIELDS)
Creation Functions (REAL AND COMPLEX FIELDS)
Creation Functions (RING OF INTEGERS)
Creation Functions (RING OF INTEGERS)
Creation Functions (UNIVARIATE POLYNOMIAL RINGS)
Creation Functions (VALUATION RINGS)
Creation of a Hyperelliptic Curve (HYPERELLIPTIC CURVES)
Creation of a Kummer Surface (HYPERELLIPTIC CURVES)
Creation of a Matrix Group (MATRIX GROUPS)
Creation of a Modular Curve (MODULAR CURVES)
Creation of a Permutation Group (PERMUTATION GROUPS)
Creation of Affine Algebras (AFFINE ALGEBRAS)
Creation of an Algebraic Geometric Code (LINEAR CODES OVER FINITE FIELDS)
Creation of an Elliptic Curve (ELLIPTIC CURVES)
Creation of Automatic Groups and Arithmetic with Words (AUTOMATIC GROUPS)
Creation of Automorphism Groups (AUTOMORPHISM GROUPS OF GROUPS)
Creation of Booleans (STATEMENTS AND EXPRESSIONS)
Creation of Cyclotomic Fields (CYCLOTOMIC FIELDS)
Creation of Divisors (PLANE ALGEBRAIC CURVES)
Creation of Elements (ALGEBRAIC FUNCTION FIELDS)
Creation of Elements (ALGEBRAIC FUNCTION FIELDS)
Creation of Elements (ALGEBRAIC FUNCTION FIELDS)
Creation of Elements (ALGEBRAIC FUNCTION FIELDS)
Creation of Elements (ALGEBRAICALLY CLOSED FIELDS)
Creation of Elements (FINITE FIELDS)
Creation of Elements (GALOIS RINGS)
Creation of Elements (INTRODUCTION [BASIC RINGS])
Creation of Elements (MODULAR SYMBOLS)
Creation of Elements (MODULES OVER ORDERS)
Creation of Elements (POWER, LAURENT AND PUISEUX SERIES)
Creation of Forms (BINARY QUADRATIC FORMS)
Creation of Generic Free Modules (MODULES OVER AFFINE ALGEBRAS)
Creation of Graded Polynomial Rings (IDEAL THEORY AND GRÖBNER BASES)
Creation of Groups and Word Arithmetic (GROUPS DEFINED BY REWRITE SYSTEMS)
Creation of Ideals (ALGEBRAIC FUNCTION FIELDS)
Creation of Ideals and Quotients (UNIVARIATE POLYNOMIAL RINGS)
Creation of Ideals in Orders (ORDERS AND ALGEBRAIC FIELDS)
Creation of Isomorphisms (HYPERELLIPTIC CURVES)
Creation of Lattice Elements (LATTICES)
Creation of Lattices (LATTICES)
Creation of Linear Systems (SCHEMES)
Creation of Local Rings and Fields (LOCAL RINGS AND FIELDS)
Creation of LP objects (LINEAR PROGRAMMING)
Creation of Maps (SCHEMES)
Creation of Matrices (MATRICES)
Creation of Modules (MODULES OVER ORDERS)
Creation of New Lists (LISTS)
Creation of Newton Polygons (NEWTON POLYGONS)
Creation of Point Sets (ELLIPTIC CURVES)
Creation of Points (ELLIPTIC CURVES)
Creation of Points (MODULAR CURVES)
Creation of Polynomial Rings (MULTIVARIATE POLYNOMIAL RINGS)
Creation of Polynomial Rings and Ideals (IDEAL THEORY AND GRÖBNER BASES)
Creation of Quaternion Algebras (QUATERNION ALGEBRAS)
Creation of Quaternion Orders (QUATERNION ALGEBRAS)
Creation of Splice Diagrams (RESOLUTION GRAPHS AND SPLICE DIAGRAMS)
Creation of Strings (INPUT AND OUTPUT)
Creation of Structures (ALGEBRAIC FUNCTION FIELDS)
Creation of Structures (ALGEBRAIC FUNCTION FIELDS)
Creation of Structures (ALGEBRAIC FUNCTION FIELDS)
Creation of Structures (ALGEBRAIC FUNCTION FIELDS)
Creation of Structures (QUADRATIC FIELDS)
Creation of Subgroup Schemes (ELLIPTIC CURVES)
Creation of Subgroups of PSL_2(R) (SUBGROUPS OF PSL_2(R))
Creation of Vector Spaces and Arithmetic with Vectors (VECTOR SPACES)
Creation Predicates (ELLIPTIC CURVES)
Creation Predicates (HYPERELLIPTIC CURVES)
Defining Ideals and Quotient Rings (INTRODUCTION [BASIC RINGS])
Definition of a Module (FREE MODULES)
Elementary Creation of Lattices (LATTICES)
Elements (MODULAR FORMS)
Explicit Creation (SCHEMES)
Free Groups and Words (FINITELY PRESENTED GROUPS)
General Function Field Places (ALGEBRAIC FUNCTION FIELDS)
Global Function Field Places (ALGEBRAIC FUNCTION FIELDS)
Labels (MODULAR FORMS)
Labels (MODULAR SYMBOLS)
New Rings from Old Ones (INTRODUCTION [BASIC RINGS])
Operations on Structure Constant Algebras and their Elements (STRUCTURE CONSTANT ALGEBRAS)
Other Ring Constructions (INTRODUCTION [BASIC RINGS])
Predicates on Curve Models (ELLIPTIC CURVES)
Predicates on Curve Models (HYPERELLIPTIC CURVES)
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 p-Quotient (FINITELY PRESENTED GROUPS)
The Construction of a Permutation Group (PERMUTATION GROUPS)
The Construction of a Rewrite Group (GROUPS DEFINED BY REWRITE SYSTEMS)
The Construction of a Rewrite Monoid (MONOIDS GIVEN BY REWRITE SYSTEMS)
The Construction of a Vector Space (VECTOR SPACES)
The Construction of an Automatic Group (AUTOMATIC GROUPS)
The Construction of Direct Sums and Tensor Products (MATRIX ALGEBRAS)
The Construction of Finitely Presented Groups (FINITELY PRESENTED GROUPS)
The Construction of Free Semigroups and their Elements (FINITELY PRESENTED SEMIGROUPS)
The Construction of Related Structures (INCIDENCE STRUCTURES AND DESIGNS)
The Database Itself (THE K3 DATABASE)
The Record Format Constructor (RECORDS)
The Subcode Constructor (LINEAR CODES OVER FINITE FIELDS)
The Subcode Constructor (LINEAR CODES OVER FINITE RINGS)
Twisting Elliptic Curves (ELLIPTIC CURVES)
AlgGrp_creation (Example H73E1)
FldQuad_creation (Example H54E1)

creation-access

Creation and Access Functions (QUATERNION ALGEBRAS)

Creation-Ambient

ModSym_Creation-Ambient (Example H88E2)

creation-ambient

Ambient Spaces (MODULAR FORMS)
Ambient Spaces (MODULAR SYMBOLS)

creation-arithmetic

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

creation-by-hand

Creation by Hand (RESOLUTION GRAPHS AND SPLICE DIAGRAMS)

creation-by-subspace

Scheme_creation-by-subspace (Example H81E34)

creation-change_ring

Changing the Base Ring (ELLIPTIC CURVES)

creation-class-function-ring

CharacterRing(G) : Grp -> AlgChtr
Structure Creation (CHARACTERS OF FINITE GROUPS)

Creation-CongruenceSubgroups

GrpPSL2_Creation-CongruenceSubgroups (Example H33E5)

creation-coset-geometry

Construction of a Coset Geometry (INCIDENCE GEOMETRY)

creation-curve

Creation of a Modular Curve (MODULAR CURVES)
Creation of an Elliptic Curve (ELLIPTIC CURVES)

creation-digraph

Construction of a General Digraph (GRAPHS)

creation-element

Construction of a Matrix (FREE MODULES)
Construction of a Vector (VECTOR SPACES)
Creation of Elements (ALGEBRAIC FUNCTION FIELDS)
Creation of Elements (ALGEBRAIC FUNCTION FIELDS)
Creation of Elements (ALGEBRAIC FUNCTION FIELDS)
Creation of Elements (ALGEBRAIC FUNCTION FIELDS)
Creation of Elements (INTRODUCTION [BASIC RINGS])
Creation of Elements (POWER, LAURENT AND PUISEUX SERIES)

creation-element-general

General Function Field Places (ALGEBRAIC FUNCTION FIELDS)

creation-element-global

Global Function Field Places (ALGEBRAIC FUNCTION FIELDS)

creation-elements

Creation of Elements (MODULAR SYMBOLS)
Elements (MODULAR FORMS)

Creation-Elements-1

ModSym_Creation-Elements-1 (Example H88E4)

Creation-Elements-2

ModSym_Creation-Elements-2 (Example H88E6)

creation-ex

RngLoc_creation-ex (Example H59E3)

creation-format

The Record Format Constructor (RECORDS)

creation-from-curve

Creation from Curve Singularities (RESOLUTION GRAPHS AND SPLICE DIAGRAMS)

creation-from-pencil

Creation from Pencils (RESOLUTION GRAPHS AND SPLICE DIAGRAMS)

creation-general

Construction of a General Group (GROUPS)
Construction of a General Permutation Group (PERMUTATION GROUPS)

creation-general-linear-group

Creation of a Matrix Group (MATRIX GROUPS)

creation-general-matrix-group

Construction of a General Matrix Group (MATRIX GROUPS)

creation-graph

Construction of a General Graph (GRAPHS)

creation-GrpPsl2

Creation of Subgroups of PSL_2(R) (SUBGROUPS OF PSL_2(R))

creation-GrpPsl2Elt

Creation (SUBGROUPS OF PSL_2(R))

creation-hom

öm_(R)(M, N) for matrix modules (FREE MODULES)

creation-hypcurve

Creation of a Hyperelliptic Curve (HYPERELLIPTIC CURVES)

creation-ideal

Construction of New Ideals (IDEAL THEORY AND GRÖBNER BASES)
Creation of Ideals (ALGEBRAIC FUNCTION FIELDS)

creation-incidence-geometry

Construction of an Incidence Geometry (INCIDENCE GEOMETRY)

creation-inner-product

KSpace(K, n, F) : Fld, RngIntElt, Mtrx -> ModTupFld
Construction of a Vector Space with Inner Product Matrix (VECTOR SPACES)

creation-kummer

Creation of a Kummer Surface (HYPERELLIPTIC CURVES)

creation-labels

Labels (MODULAR FORMS)

creation-magma

Construction of a Vector Space (VECTOR SPACES)

creation-model-predicates

Predicates on Curve Models (ELLIPTIC CURVES)
Predicates on Curve Models (HYPERELLIPTIC CURVES)

creation-models

Alternative Models (ELLIPTIC CURVES)

creation-module

Definition of a Module (FREE MODULES)

creation-other

Other Ring Constructions (INTRODUCTION [BASIC RINGS])

creation-predicates

Creation Predicates (ELLIPTIC CURVES)

creation-predicates-hypcurve

Creation Predicates (HYPERELLIPTIC CURVES)

creation-record

Creating a Record (RECORDS)

creation-related

The Construction of Related Structures (INCIDENCE STRUCTURES AND DESIGNS)

Creation-Space

ModForm_Creation-Space (Example H90E3)

Creation-Spaces

ModSym_Creation-Spaces (Example H88E3)

creation-spaces

Labels (MODULAR SYMBOLS)

creation-spchyp

Creation (SUBGROUPS OF PSL_2(R))

creation-structure

Creation of Structures (ALGEBRAIC FUNCTION FIELDS)
Creation of Structures (ALGEBRAIC FUNCTION FIELDS)
Creation of Structures (ALGEBRAIC FUNCTION FIELDS)
Creation of Structures (ALGEBRAIC FUNCTION FIELDS)

creation-symmetric

Construction of Elements (GROUPS)
Creation of a Permutation Group (PERMUTATION GROUPS)

creation-twists

Twisting Elliptic Curves (ELLIPTIC CURVES)

creation_predicates

Creation Predicates (ELLIPTIC CURVES)

CreationElements

ModForm_CreationElements (Example H90E5)

Cremona

EllipticCurveDatabase(: parameters) : -> DB
CremonaDatabase(: parameters) : -> DB
CremonaReference(D, E) : CrvEll -> MonStgElt

cremona-factorisation

Scheme_cremona-factorisation (Example H81E28)

CremonaDatabase

EllipticCurveDatabase(: parameters) : -> DB
CremonaDatabase(: parameters) : -> DB

CremonaReference

CremonaReference(D, E) : CrvEll -> MonStgElt

Cross

CrossCorrelation(S1, S2, t) : SeqEnum, SeqEnum, RngIntElt -> RngIntElt

CrossCorrelation

CrossCorrelation(S1, S2, t) : SeqEnum, SeqEnum, RngIntElt -> RngIntElt

CRT

ChineseRemainderTheorem(I1, L1, e1, L2) : RngOrdIdl, [RngIntElt], RngOrdElt, [RngIntElt] -> RngOrdElt
ClassRepresentative(I) : RngOrdFracIdl -> RngOrdFracIdl
CRT(I1, L1, e1, L2) : RngOrdIdl, [RngIntElt], RngOrdElt, [RngIntElt] -> RngOrdElt
ClassRepresentative(I) : RngOrdFracIdl -> RngOrdFracIdl
ChineseRemainderTheorem(I1, I2, e1, e2) : RngOrdIdl, RngOrdIdl, RngOrdElt, RngOrdElt -> RngOrdElt
ChineseRemainderTheorem(X, N) : [RngIntElt], [RngIntElt] -> RngIntElt

CrvHyp

Combinatorial and Geometrical Structures (OVERVIEW)

CrvMod

Combinatorial and Geometrical Structures (OVERVIEW)

CrvMod:class-polys

CrvMod_CrvMod:class-polys (Example H87E5)

CrvMod:modular-base-curve

CrvMod_CrvMod:modular-base-curve (Example H87E4)

CrvMod:modular-equations

CrvMod_CrvMod:modular-equations (Example H87E2)

CrvMod:moduli-points

CrvMod_CrvMod:moduli-points (Example H87E1)

CrvMod:subgroup-scheme

CrvMod_CrvMod:subgroup-scheme (Example H87E3)

crvpl

Maps and Curves (PLANE ALGEBRAIC CURVES)
Projective Closure and Affine Patches (PLANE ALGEBRAIC CURVES)

Crystallographic

IsCrystallographic( C ) : AlgMatElt -> BoolElt
IsCrystallographic( W ) : GrpCox -> BoolElt
IsCrystallographic( RD ) : RootDtm -> BoolElt

Cunningham

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

curly

Sets (OVERVIEW)

curly-bracket

Sets (OVERVIEW)

Current

Current(p) : Process -> Grp
Current(p) : Process -> GrpMat
Current(p) : Process -> GrpPerm, MonStgElt
CurrentLabel(p) : Process -> RngIntElt, RngIntElt
CurrentLabel(p) : Process -> RngIntElt, RngIntElt
CurrentLabel(p) : Process -> RngIntElt, RngIntElt, RngIntElt
GetCurrentDirectory() : ->
GetCurrentDirectory() : ->

CurrentLabel

CurrentLabel(p) : Process -> RngIntElt, RngIntElt
CurrentLabel(p) : Process -> RngIntElt, RngIntElt
CurrentLabel(p) : Process -> RngIntElt, RngIntElt, RngIntElt

Curve

CurveDivisor(D) : DivFunElt -> DivCrvElt
Div ! D : DivCrv, DivFunElt -> DivCrvElt
S ! P : PlcCrv, PlcFunElt -> PlcCrvElt
BaseCurve(X) : CrvMod -> CrvMod, MapSch
CremonaDatabase(: parameters) : -> DB
Curve(C) : Code -> Crv
Curve(Div) : DivCrv -> Crv
Curve(D) : DivCrvElt -> Crv
Curve(F) : FldFun -> Crv
Curve(F) : FldFun -> Crv
Curve(F) : FldFun -> Crv
Curve(J) : JacHyp -> CrvHyp
Curve(P) : PlcCrv -> Crv
Curve(P) : PlcCrvElt -> Crv
Curve(p) : Pt -> Crv
Curve(p) : Pt -> Crv
Curve(C) : Sch -> Crv
Curve(X) : Sch -> Crv
Curve(A,I) : Sch, RngMPol -> Crv
Curve(A,f) : Sch, RngMPolElt -> Crv
Curve(G) : SchGrpEll -> CrvEll
Curve(P) : SetPt -> Crv
Curve(P) : SetPt -> Crv
Curve(H) : SetPtEll -> CrvEll
EllipticCurve(C) : Crv -> CrvEll, Map, Map
EllipticCurve(C, P) : Crv, Pt -> CrvEll, Map, Map
EllipticCurve(C,p) : Crv, Pt -> CrvEll, Map, Map
EllipticCurve(C) : CrvHyp -> CrvEll, Map, Map
EllipticCurve(D, S): DB, RngIntElt, MonStgElt -> CrvEll
EllipticCurve(D, N, I, J): DB, RngIntElt, RngIntElt, RngIntElt -> CrvEll
EllipticCurve(f) : ModFrmElt -> CrvEll
EllipticCurve(j) : RngElt -> CrvEll
EllipticCurve([a,b]) : [ RngElt ] -> CrvEll
ExistsModularCurveDatabase(t) : MonStgElt -> BoolElt
HyperellipticCurve(h, f) : RngUPolElt, RngUPolElt -> CrvHyp
HyperellipticCurve(E) : SchEll -> CrvHyp, Map
HyperellipticCurveFromIgusa(S) : SeqEnum -> CrvHyp
HyperellipticCurveOfGenus(g, h, f) : RngIntElt, RngUPolElt, RngUPolElt -> CrvHyp
IsCurve(X) : Sch -> BoolElt,Crv
IsEllipticCurve(C) : CrvHyp -> BoolElt, CrvEll, Map
IsEllipticCurve(C) : CrvHyp -> BoolElt, CrvEll, Map, Map
IsEllipticCurve([a,b]) : [ RngElt ] -> BoolElt, CrvEll
IsHyperellipticCurve([h, g]) : [ RngUPolElt ] -> BoolElt, CrvHyp
IsHyperellipticCurveOfGenus(g, [h, f]) : RngIntElt, [RngUPolElt] -> BoolElt, CrvHyp
IsRationalCurve(X) : Sch -> BoolElt,CrvRat
IsRationalCurve(X) : Sch -> BoolElt,CrvRat
ModularCurve(D, N) : DB, RngIntElt -> CrvMod
ModularCurve(X,t,N) : Sch, MonStgElt, RngIntElt -> CrvMod
ModularCurveDatabase(t) : MonStgElt -> DB
ProjectiveCurve(F) : FldFun -> Crv
RationalCurve(X,f) : Sch,RngMPolElt -> CrvRat
ReduceCurve(C) : CrvHyp -> CrvHyp
Scheme(P) : SetPtEll -> CrvEll
SupersingularEllipticCurve(K) : FldFin -> CrvEll

curve

Combinatorial and Geometrical Structures (OVERVIEW)
Creation from Curve Singularities (RESOLUTION GRAPHS AND SPLICE DIAGRAMS)
Creation of a Modular Curve (MODULAR CURVES)
Creation of an Elliptic Curve (ELLIPTIC CURVES)
Curves (PLANE ALGEBRAIC CURVES)
ELLIPTIC CURVES
HYPERELLIPTIC CURVES
Local Geometry (PLANE ALGEBRAIC CURVES)
PLANE ALGEBRAIC CURVES

curve-base-change

Crv_curve-base-change (Example H82E2)

curve-differentials

Crv_curve-differentials (Example H82E12)

curve-hessian

Crv_curve-hessian (Example H82E3)

curve-iscusp

Crv_curve-iscusp (Example H82E4)

curve_from_invariants

Creating a Hyperelliptic Curve from Invariants (HYPERELLIPTIC CURVES)

CurveDivisor

CurveDivisor(D) : DivFunElt -> DivCrvElt
Div ! D : DivCrv, DivFunElt -> DivCrvElt

CurveFromIgusa

CrvHyp_CurveFromIgusa (Example H86E5)

curvepl

Genus and Singularities (PLANE ALGEBRAIC CURVES)
Global Geometry (PLANE ALGEBRAIC CURVES)

CurvePlace

CurvePlace(P) : PlcFunElt -> PlcCrvElt
S ! P : PlcCrv, PlcFunElt -> PlcCrvElt

Curves

NumberOfCurves(D) : DB -> RngIntElt
# D : DB -> RngIntElt
EllipticCurves(D) : DB -> [ CrvEll ]
EllipticCurves(D, S) : DB, MonStgElt -> [ CrvEll ]
EllipticCurves(D, N) : DB, RngIntElt -> [ CrvEll ]
EllipticCurves(D, N, I) : DB, RngIntElt, RngIntElt -> [ CrvEll ]
NumberOfCurves(D, N) : DB, RngIntElt -> RngIntElt
NumberOfCurves(D, N, i) : DB, RngIntElt, RngIntElt -> RngIntElt

curves

Base Change (PLANE ALGEBRAIC CURVES)
Basic Attributes (PLANE ALGEBRAIC CURVES)
Basic Invariants (PLANE ALGEBRAIC CURVES)
Creation (PLANE ALGEBRAIC CURVES)
Elliptic Curves (MODULAR SYMBOLS)
MODULAR CURVES
Plane Curves (PLANE ALGEBRAIC CURVES)

curves-attributes

Basic Attributes (PLANE ALGEBRAIC CURVES)

curves-base-change

Base Change (PLANE ALGEBRAIC CURVES)

curves-creation

Creation (PLANE ALGEBRAIC CURVES)

curves-in-space

Scheme_curves-in-space (Example H81E36)

curves-invariants

Basic Invariants (PLANE ALGEBRAIC CURVES)

Cusp

CuspWidth(G,x) : GrpPSL2, SetCspElt -> RngIntElt
DimensionCuspForms(eps, k) : GrpDrchElt, RngIntElt -> RngIntElt
DimensionCuspFormsGamma0(N, k) : RngIntElt, RngIntElt -> RngIntElt
DimensionCuspFormsGamma1(N, k) : RngIntElt, RngIntElt -> RngIntElt
DimensionNewCuspFormsGamma0(N, k) : RngIntElt, RngIntElt -> RngIntElt
DimensionNewCuspFormsGamma1(N, k) : RngIntElt, RngIntElt -> RngIntElt
IsCusp(p) : Crv,Pt -> BoolElt
IsCusp(z) : SpcHypElt -> BoolElt

cusp-example

GrpPSL2_cusp-example (Example H33E4)

Cuspidal

CuspidalSubspace(M) : ModBrdt -> ModBrdt
CuspidalSubspace(M) : ModFrm -> ModFrm
CuspidalSubspace(M) : ModSym -> ModSym
IsCuspidal(M) : ModBrdt -> BoolElt
IsCuspidal(M) : ModFrm -> BoolElt
IsCuspidal(M) : ModSym -> BoolElt

CuspidalSubgroup

ModSym_CuspidalSubgroup (Example H88E20)

CuspidalSubgroupTable

ModSym_CuspidalSubgroupTable (Example H88E21)

CuspidalSubspace

CuspidalSubspace(M) : ModBrdt -> ModBrdt
CuspidalSubspace(M) : ModFrm -> ModFrm
CuspidalSubspace(M) : ModSym -> ModSym

Cusps

Cusps(G) : GrpPSL2 -> SeqEnum
Cusps(FS) : SymFry -> SeqEnum
UpperHalfPlaneWithCusps() : -> SpcHyp

cusps

Cusps and elliptic points of congruence subgroups (SUBGROUPS OF PSL_2(R))

cusps-and-elliptic-points

Cusps and elliptic points of congruence subgroups (SUBGROUPS OF PSL_2(R))

CuspWidth

CuspWidth(G,x) : GrpPSL2, SetCspElt -> RngIntElt

Cut

CutVertices(G) : Grph -> { GrphVert }

CutVertices

CutVertices(G) : Grph -> { GrphVert }

Cycle

Cycle(e, x) : GrpPermElt, Elt -> SetIndx
CycleStructure(g) : GrpPermElt -> [ <RngIntElt, RngIntElt> ]
GirthCycle(G) : GrphUnd -> [GrphVert]

CycleStructure

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

Cyclic

CyclicSubgroups(G) : GrpPC -> SeqEnum
ElementaryAbelianSubgroups(G) : GrpPC -> SeqEnum
NilpotentSubgroups(G) : GrpPC -> SeqEnum
AbelianSubgroups(G) : GrpPC -> SeqEnum
ClassGroupCyclicFactorGenerators(O) : RngOrd -> ModHomElt
CyclicCode(u) : ModTupRngElt -> Code
CyclicCode(u) : ModTupRngElt -> Code
CyclicCode(n, g) : RngIntElt, RngUPolElt -> Code
CyclicCode(n, g) : RngIntElt, RngUPolElt -> Code
CyclicCode(n, T, K) : RngIntElt, [ FldFinElt ], FldFin -> Code
CyclicGroup(C, n) : Cat, RngIntElt -> GrpFin
CyclicGroup(GrpFP, n) : Cat, RngIntElt -> GrpFP
CyclicGroup(GrpGPC, n) : Cat, RngIntElt -> GrpGPC
CyclicGroup(GrpPC, n) : Cat, RngIntElt -> GrpPC
CyclicGroup(GrpPerm, n) : Cat, RngIntElt -> GrpPerm
CyclicSubgroups(G: parameters) : GrpFin -> [ rec< Grp, RngIntElt, RngIntElt, GrpFP> ]
CyclicSubgroups(G: parameters) : GrpPerm -> [ rec< GrpPerm, RngIntElt, RngIntElt, GrpFP> ]
IsCyclic(C) : Code -> BoolElt
IsCyclic(C) : Code -> BoolElt
IsCyclic(G) : GrpAb -> BoolElt
IsCyclic(G) : GrpFin -> BoolElt
IsCyclic(G) : GrpGPC -> BoolElt
IsCyclic(G) : GrpMat -> BoolElt
IsCyclic(G) : GrpPC -> BoolElt
IsCyclic(G) : GrpPerm -> BoolElt
QuasiCyclicCode(n,Gen,h) : RngIntElt, SeqEnum, RngIntElt -> Code
QuasiCyclicCode(n, Gen) : RngIntElt, [ RngUPolElt ] -> Code

cyclic

Construction of General Cyclic Codes (LINEAR CODES OVER FINITE RINGS)
Cyclic and Quasicyclic Codes (LINEAR CODES OVER FINITE FIELDS)

Cyclic6

FldAC_Cyclic6 (Example H56E5)
GB_Cyclic6 (Example H50E2)

CyclicCode

CyclicCode(u) : ModTupRngElt -> Code
CyclicCode(u) : ModTupRngElt -> Code
CyclicCode(n, g) : RngIntElt, RngUPolElt -> Code
CyclicCode(n, g) : RngIntElt, RngUPolElt -> Code
CyclicCode(n, T, K) : RngIntElt, [ FldFinElt ], FldFin -> Code
CodeFld_CyclicCode (Example H97E5)
CodeRng_CyclicCode (Example H98E4)

CyclicGroup

CyclicGroup(C, n) : Cat, RngIntElt -> GrpFin
CyclicGroup(GrpFP, n) : Cat, RngIntElt -> GrpFP
CyclicGroup(GrpGPC, n) : Cat, RngIntElt -> GrpGPC
CyclicGroup(GrpPC, n) : Cat, RngIntElt -> GrpPC
CyclicGroup(GrpPerm, n) : Cat, RngIntElt -> GrpPerm

CyclicSubgroups

CyclicSubgroups(G) : GrpPC -> SeqEnum
ElementaryAbelianSubgroups(G) : GrpPC -> SeqEnum
NilpotentSubgroups(G) : GrpPC -> SeqEnum
AbelianSubgroups(G) : GrpPC -> SeqEnum
CyclicSubgroups(G: parameters) : GrpFin -> [ rec< Grp, RngIntElt, RngIntElt, GrpFP> ]
CyclicSubgroups(G: parameters) : GrpPerm -> [ rec< GrpPerm, RngIntElt, RngIntElt, GrpFP> ]

Cyclotomic

CyclotomicField(m) : RngIntElt -> FldCyc
CyclotomicOrder(K) : FldCyc -> RngIntElt
CyclotomicPolynomial(m) : RngIntElt -> RngUPolElt
Z4CyclotomicFactors(n) : RngIntElt -> [RngUPolElt]

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

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