[____] [____] [_____] [____] [__] [Index] [Root]
Index C
Control-C key (OVERVIEW)
C
c range
CalculateCanonicalClass(~g) : GrphRes ->
CalculateMultiplicities(~g) : GrphRes ->
CalculateTransverseIntersections(~g) : GrphRes ->
CalculateCanonicalClass(~g) : GrphRes ->
CalculateMultiplicities(~g) : GrphRes ->
CalculateTransverseIntersections(~g) : GrphRes ->
Call by Value Evaluation (MAGMA SEMANTICS)
Expression (OVERVIEW)
Functions (OVERVIEW)
Functions, Procedures, and Mappings (OVERVIEW)
Expression (OVERVIEW)
Call by Value Evaluation (MAGMA SEMANTICS)
Expression (OVERVIEW)
Memory Usage (INPUT AND OUTPUT)
System Calls (INPUT AND OUTPUT)
CambridgeMatrix(t, K, n, Q) : RngIntElt, FldFint, RngIntElt, [ ] -> AlgMatElt
AlgMat_Cambridge (Example H73E2)
CambridgeMatrix(t, K, n, Q) : RngIntElt, FldFint, RngIntElt, [ ] -> AlgMatElt
CanChangeUniverse(S, V) : SeqEnum, Str -> Bool, SeqEnum
CanChangeUniverse(S, V) : SetEnum, Str -> Bool, SeqEnum
CanContinueEnumeration(P) : GrpFPCosetEnumProc -> BoolElt
CanRedoEnumeration(P) : GrpFPCosetEnumProc -> BoolElt
CanChangeUniverse(S, V) : SeqEnum, Str -> Bool, SeqEnum
CanChangeUniverse(S, V) : SetEnum, Str -> Bool, SeqEnum
CanContinueEnumeration(P) : GrpFPCosetEnumProc -> BoolElt
CanonicalDivisor(C) : Crv -> DivCrvElt
D ! 0 : DivCrv,RngIntElt -> DivCrvElt
CalculateCanonicalClass(~g) : GrphRes ->
CanonicalClass(g) : GrphRes -> SeqEnum
CanonicalDivisor(F) : FldFun -> DivFunElt
CanonicalGraph(G) : Grph -> Grph
CanonicalInvolution(X) : CrvMod -> MapSch
CanonicalMap(C) : Crv -> MapSch
CanonicalModularPolynomial(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 Forms (MATRICES)
Canonical Forms (MATRIX ALGEBRAS)
Canonical Forms over Euclidean Domains (MATRICES)
Canonical Forms over Fields (MATRICES)
Canonical Forms over General Rings (MATRICES)
Canonical Forms over Euclidean Domains (MATRICES)
Canonical Forms over Fields (MATRICES)
Canonical Forms (MATRIX ALGEBRAS)
Crv_canonical-map (Example H84E20)
Crv_canonical_divisor (Example H84E18)
CanonicalClass(g) : GrphRes -> SeqEnum
CanonicalDivisor(C) : Crv -> DivCrvElt
D ! 0 : DivCrv,RngIntElt -> DivCrvElt
CanonicalDivisor(F) : FldFun -> DivFunElt
AlgMat_CanonicalForms (Example H73E8)
Mat_CanonicalForms (Example H59E9)
CanonicalGraph(G) : Grph -> Grph
CanonicalHeight(P: parameters) : PtEll -> FldPrElt
Height(P: parameters) : PtEll -> FldPrElt
Height(P: Precision) : JacHypPt -> FldPrElt
AtkinLehnerInvolution(X,N) : CrvMod, RngIntElt -> MapSch
CanonicalInvolution(X) : CrvMod -> MapSch
CanonicalMap(C) : Crv -> MapSch
CanonicalModularPolynomial(N) : RngIntElt -> RngMPolElt
CanRedoEnumeration(P) : GrpFPCosetEnumProc -> BoolElt
car< R_1, ..., R_k > : Str, ..., Str -> SetCart
CodeFld_Card-Best-Comparison (Example H101E39)
Bounds on the Cardinality of a Largest Code (LINEAR CODES OVER FINITE FIELDS)
Groups (OVERVIEW)
Rings, Fields, and Algebras (OVERVIEW)
Sets (OVERVIEW)
CarmichaelLambda(n) : RngIntElt -> RngIntElt
FactoredCarmichaelLambda(n) : RngIntElt -> RngIntEltFact
CarmichaelLambda(n) : RngIntElt -> RngIntElt
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 Matrices (ROOT DATA FOR LIE THEORY)
Cartan Subalgebra (LIE ALGEBRAS)
Cartan Matrices (ROOT DATA FOR LIE THEORY)
LieConstant_A( RD, r, s) : RootDtm, RngIntElt, RngIntElt -> RngIntElt
CartanInteger( RD, r, s) : RootDtm, RngIntElt, RngIntElt -> RngIntElt
RootDtm_CartanMatrices (Example H33E1)
CartanMatrix( W ) : GrpCox -> AlgMatElt
CartanMatrix(g) : GrphRes -> Mtrx
CartanMatrix( G ) : GrpLie -> AlgMatElt
CartanMatrix( t ) : MonStgElt -> AlgMatElt
CartanMatrix( RD ) : RootDtm -> AlgMatElt
RootDtm_CartanMatrixFunctions (Example H33E2)
CartanName( C ) : AlgMatElt -> List
CartanName( G ) : GrpLie -> MonStgElt
CartanSubalgebra(L) : AlgLie -> AlgLie
AlgLie_CartanSubalgebra (Example H76E6)
The Cartesian Product Constructors (SETS)
CartesianPower(R, k) : Str, RngIntElt -> SetCart
CartesianProduct(G, H) : GrphDir, GrphDir -> GrphDir
CartesianProduct(R, S) : Str, ..., Str -> SetCart
TUPLES AND CARTESIAN PRODUCTS
The Cartesian Product Constructors (SETS)
CartesianPower(R, k) : Str, RngIntElt -> SetCart
CartesianProduct(G, H) : GrphDir, GrphDir -> GrphDir
CartesianProduct(R, S) : Str, ..., Str -> SetCart
Tup_CartesianProduct (Example H9E1)
Cartier(a) : DiffFunElt -> DiffFunElt
Cartier(b) : DiffFunElt -> DiffFunElt
CartierRepresentation(F) : FldFunG -> AlgMatElt, SeqEnum[DiffFunElt]
CartierRepresentation(F) : FldFunG -> AlgMatElt, SeqEnum[DiffFunElt]
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)
The Case Expression (STATEMENTS AND EXPRESSIONS)
The Case Statement (STATEMENTS AND EXPRESSIONS)
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
S cat:= T : List, List ->
s cat:= t : MonStgElt, MonStgElt -> MonStgElt
Catalan(R) : FldRe -> FldReElt
Categories and Parent (BRANDT MODULES)
ListCategories() : ->
Categories (MODULAR FORMS)
Categories (MODULAR SYMBOLS)
Categories ({THE MODULE OF}{SUPERSINGULAR POINTS})
Type(E) : CrvEll -> Cat
Category(E) : CrvEll -> Cat
Category(L) : Lat -> Cat
Category(S) : Obj -> Cat
Category(P) : PtEll -> Cat
Category(R) : Rng -> Cat
Category(r) : RngElt -> Cat
Category(G) : SchGrpEll -> Cat
Category(H) : SetPtEll -> Cat
Type(x) : Elt -> Cat
Associated Structures (ELLIPTIC CURVES)
Associated Structures (ELLIPTIC CURVES)
Associated Structures (ELLIPTIC CURVES)
Associated Structures (ELLIPTIC CURVES)
Category (OVERVIEW)
Magmas (or Structures) (OVERVIEW)
Module Categories (FREE MODULES)
Parent and Category (ALGEBRAIC FUNCTION FIELDS)
Parent and Category (ALGEBRAIC FUNCTION FIELDS)
Parent and Category (ALGEBRAIC FUNCTION FIELDS)
Parent and Category (ALGEBRAIC FUNCTION FIELDS)
Parent and Category (ALGEBRAIC FUNCTION FIELDS)
Parent and Category (ALGEBRAIC FUNCTION FIELDS)
Parent and Category (MULTIVARIATE POLYNOMIAL RINGS)
Parent and Category (ORDERS AND ALGEBRAIC FIELDS)
Parent and Category (POWER, LAURENT AND PUISEUX SERIES)
Parent and Category (UNIVARIATE POLYNOMIAL RINGS)
Parent and Category (VALUATION RINGS)
The Categories of Algebras (ALGEBRAS)
The Categories of Finite Groups (GROUPS)
The Category of Automatic Groups (AUTOMATIC GROUPS)
The Category of Matrix Groups (MATRIX GROUPS)
The Category of Permutation Groups (PERMUTATION GROUPS)
The Category of Rewrite Groups (GROUPS DEFINED BY REWRITE SYSTEMS)
The Category of Rewrite Monoids (MONOIDS GIVEN BY REWRITE SYSTEMS)
Transfer Functions Between Group Categories (GROUPS)
Vector Space Categories (VECTOR SPACES)
Transfer Functions Between Group Categories (GROUPS)
UnlabelledCayleyGraph(A) : Grp -> GrphDir
CayleyGraph(A) : Grp -> GrphDir
AlgCon_cayley (Example H70E2)
UnlabelledCayleyGraph(A) : Grp -> GrphDir
CayleyGraph(A) : Grp -> GrphDir
Graph_CayleyGraph (Example H97E9)
Ceiling(q) : FldRatElt -> RngIntElt
Ceiling(r) : FldReElt -> RngIntElt
Ceiling(n) : RngIntElt -> RngIntElt
VoronoiCell(L) : Lat -> [ ModTupFldElt ], SetEnum , [ ModTupFldElt ]
Plane_cent-coll (Example H99E15)
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(L) : Lat -> FldReElt
CentreDensity(L) : Lat -> FldReElt
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
CentralEndomorphisms(G, n) : GrpMat, RngIntElt -> [ AlgMatElt ]
CentralExtension(G, U, A) : GrpPC, GrpPC, AlgMatElt -> GrpPC
CentralExtensionProcess(G, U) : GrpPC, GrpPC -> Proc
CentralExtensions(G, U, Q) : GrpPC, GrpPC, [AlgMatElt] -> [GrpPC]
IsCentral(A) : FldAb -> BoolElt
IsCentral(G, H) : GrpAb, GrpAb -> BoolElt
IsCentral(G, H) : GrpFin -> BoolElt
IsCentral(G, H) : GrpGPC, GrpGPC -> BoolElt
IsCentral(G, H) : GrpMat -> BoolElt
IsCentral(G, H) : GrpPC, GrpPC -> BoolElt
IsCentral(G, H) : GrpPerm -> BoolElt
IsCentralCollineation(P, g) : Plane, GrpPermElt -> BoolElt, PlanePt, PlaneLn
LowerCentralSeries(L) : AlgLie -> [ AlgLie ]
LowerCentralSeries(G) : GrpFin -> [ GrpFin ]
LowerCentralSeries(G) : GrpGPC -> [GrpGPC]
LowerCentralSeries(G) : GrpMat -> [ GrpMat ]
LowerCentralSeries(G) : GrpPC -> [GrpPC]
LowerCentralSeries(G) : GrpPerm -> [ GrpPerm ]
UpperCentralSeries(L) : AlgLie -> [ AlgLie ]
UpperCentralSeries(G) : GrpAb -> [GrpAb]
UpperCentralSeries(G) : GrpFin -> [ GrpFin ]
UpperCentralSeries(G) : GrpGPC -> [GrpGPC]
UpperCentralSeries(G) : GrpMat -> [ GrpMat ]
UpperCentralSeries(G) : GrpPC -> [GrpPC]
UpperCentralSeries(G) : GrpPerm -> [ GrpPerm ]
Central Collineations (FINITE PLANES)
Central Extensions (FINITE SOLUBLE GROUPS)
Central Extensions (FINITE SOLUBLE GROUPS)
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
CentralEndomorphisms(G, n) : GrpMat, RngIntElt -> [ AlgMatElt ]
CentralExtension(G, U, A) : GrpPC, GrpPC, AlgMatElt -> GrpPC
GrpPC_CentralExtension (Example H24E28)
CentralExtensionProcess(G, U) : GrpPC, GrpPC -> Proc
CentralExtensions(G, U, Q) : GrpPC, GrpPC, [AlgMatElt] -> [GrpPC]
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
CentralisingMatrix(G) : GrpMat -> AlgMatElt
CentralisingMatrix(G) : GrpMat -> AlgMatElt
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(G, H) : GrpPerm, GrpPerm -> GrpPerm
GHomOverCentralizingField(M, N) : ModGrp, ModGrp -> ModMatGrp
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
CentredAffinePatch(S, p) : Sch, Pt -> Sch, MapSch
CentredAffinePatch(S, p) : Sch, Pt -> Sch, MapSch
CenterDensity(L) : Lat -> FldReElt
CentreDensity(L) : Lat -> FldReElt
CentreOfEndomorphismRing(G) : GrpMat -> AlgMat
Centres(X) : VSrfK3 -> SeqEnum
Centres(~X,DB) : VSrfK3,SeqEnum ->
HasSolubilityCertificate(C) : CrvCon -> BoolElt, SeqEnum
HasSolubilityCertificate(S) : SeqEnum[RngIntElt] -> BoolElt, SeqEnum
SolubilityCertificate(C) : CrvCon -> SeqEnum
Chabauty(P, p: Precision) : JacHypPt, RngIntElt -> SetIndx
Chabauty's Method (HYPERELLIPTIC CURVES)
Chabauty's Method (HYPERELLIPTIC CURVES)
Chabauty0(J) : JacHyp -> SetIndx
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
CodeFld_ChainCyclic (Example H101E25)
ChainMap(Q, C, D, n) : SeqEnum, ModCpx, ModCpx, RngIntElt -> ModMatCpxElt
ModCpx_Chainmaps (Example H82E2)
Chain Maps (CHAIN COMPLEXES)
ProjectionChains(X,DB) : VSrfK3,SeqEnum -> SeqEnum
UnprojectionChains(X,DB) : VSrfK3,SeqEnum -> SeqEnum
ChangGraphs() : -> [GrpUnd, GrpUnd, GrpUnd]
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) : ModRng, Rng -> ModRng, Map
ChangeRing(M, S, f) : ModRng, Rng, Map -> 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(A, R) : MtrxSprs, Ring -> MtrxSprs
ChangeRing(I, S) : RngMPol, Rng -> RngMPol
ChangeRing(P, S) : RngMPol, Rng -> RngMPol
ChangeRing(L, C) : RngPowLaz, Rng -> RngPowLaz, Map
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 ->
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 Ring (SPARSE MATRICES)
Changing Rings (ALGEBRAS)
Changing Rings (MATRIX ALGEBRAS)
Changing Rings (MATRIX GROUPS)
Changing Rings (UNIVARIATE POLYNOMIAL RINGS)
Changing Monomial Order (IDEAL THEORY AND GRÖBNER BASES)
Changing Coefficient Ring (IDEAL THEORY AND GRÖBNER BASES)
Changing Coefficient Ring (MULTIVARIATE POLYNOMIAL RINGS)
Changing Ring (MATRICES)
Changing Ring (SPARSE MATRICES)
Changing Rings (ALGEBRAS)
Changing Rings (MATRIX ALGEBRAS)
Changing Rings (MATRIX GROUPS)
Changing Rings (UNIVARIATE POLYNOMIAL RINGS)
Changing the Base Ring (ELLIPTIC CURVES)
ChangeBase(~G, Q) : GrpPerm, [Elt] ->
ChangeDirectory(s) : MonStgElt ->
ChangeOrder(I, order) : RngMPol, ..., -> RngMPol, Map
ChangeOrder(I, Q) : RngMPol, RngMPol -> RngMPol, Map
GB_ChangeOrder (Example H66E16)
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
ChangeRing(M, S) : ModRng, Rng -> ModRng, 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(M, S, f) : ModRng, Rng, Map -> ModRng, Map
ChangeRing(A, R) : Mtrx, Ring -> Mtrx
ChangeRing(A, R) : MtrxSprs, Ring -> MtrxSprs
ChangeRing(I, S) : RngMPol, Rng -> RngMPol
ChangeRing(P, S) : RngMPol, Rng -> RngMPol
ChangeRing(L, C) : RngPowLaz, Rng -> RngPowLaz, Map
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 H66E15)
RngPol_ChangeRing (Example H42E3)
ChangeSupport(~G, S) : Grph, SetIndx ->
ChangeSupport(G, S) : Grph, SetIndx -> Grph, GrphVertSet, GrphEdgeSet
ChangeUniverse(S, V) : SeqEnum, Str ->
ChangeUniverse(~S, V) : SetEnum, Str ->
ChangGraphs() : -> [GrpUnd, GrpUnd, GrpUnd]
Changing Basis (K[G]-MODULES AND GROUP REPRESENTATIONS)
Changing Basis (MODULES OVER A MATRIX ALGEBRA)
Changing the Coefficient Ring (K[G]-MODULES AND GROUP REPRESENTATIONS)
Changing the Coefficient Ring (MODULES OVER A MATRIX ALGEBRA)
Degeneracy Maps (MODULAR SYMBOLS)
Writing a Module over a Smaller Field (K[G]-MODULES AND GROUP REPRESENTATIONS)
Changing Basis (K[G]-MODULES AND GROUP REPRESENTATIONS)
Changing Basis (MODULES OVER A MATRIX ALGEBRA)
Degeneracy Maps (MODULAR SYMBOLS)
Changing the Coefficient Ring (K[G]-MODULES AND GROUP REPRESENTATIONS)
Changing the Coefficient Ring (MODULES OVER A MATRIX ALGEBRA)
Writing a Module over a Smaller Field (K[G]-MODULES AND GROUP REPRESENTATIONS)
PARTITIONS, WORDS AND YOUNG TABLEAUX
EulerFactorModChar(J) : JacHyp -> RngUPolElt
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
DominantCharacter(D, w) : RootDtm, [ ] -> [ ModTupRngElt ], [ RngIntElt ]
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 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)
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(G) : GrpFin -> [ RngIntElt ]
CharacterDegrees(G) : GrpFin -> [ RngIntElt ]
AbsoluteCharacteristicPolynomial(a) : FldAlgElt -> RngUPolElt
BerlekampMassey(S) : SeqEnum -> RngUPolElt, RngIntElt
Characteristic(F) : FldFun -> RngIntElt
Characteristic(R) : Rng -> 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 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 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 (FINITE SOLUBLE GROUPS)
ConnectionPolynomial(S) : SeqEnum -> RngUPolElt, RngIntElt
CharacteristicPolynomial(S) : SeqEnum -> RngUPolElt, RngIntElt
BerlekampMassey(S) : SeqEnum -> RngUPolElt, 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
GrpAuto_characteristicsubgps (Example H26E2)
CharacteristicVector(M, S) : ModRng, { RngIntElt } -> ModRngElt
CharacteristicVector(V, S) : ModTupFld, { RngElt } -> ModTupFldElt
CharacterRing(G) : Grp -> AlgChtr
ClassFunctionSpace(G) : Grp -> AlgChtr
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 ]
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
ChebyshevT(n) : RngIntElt -> RngUPolElt
ChebyshevFirst(n) : RngIntElt -> RngUPolElt
ChebyshevSecond(n) : RngIntElt -> RngUPolElt
ChebyshevT(n) : RngIntElt -> RngUPolElt
ChebyshevFirst(n) : RngIntElt -> RngUPolElt
ChebyshevU(n) : RngIntElt -> RngUPolElt
ChebyshevSecond(n) : RngIntElt -> RngUPolElt
ChebyshevT(n) : RngIntElt -> RngUPolElt
ChebyshevFirst(n) : RngIntElt -> RngUPolElt
ChebyshevU(n) : RngIntElt -> RngUPolElt
ChebyshevSecond(n) : RngIntElt -> RngUPolElt
CheckPolynomial(C) : Code -> RngUPolElt
ParityCheckMatrix(C) : Code -> ModMatFldElt
ParityCheckMatrix(C) : Code -> ModMatRngElt
Automorphism Group and Isomorphism Testing (HYPERELLIPTIC CURVES)
Checking of Maps (MAPPINGS)
Checking the soluble quotient (FP GROUPS - ADVANCED FEATURES)
Checking the soluble quotient (FP GROUPS - ADVANCED FEATURES)
CheckPolynomial(C) : Code -> RngUPolElt
ChevalleyBasis(L) : AlgLie -> [ AlgLieElt ], [ AlgLieElt ], [ AlgLieElt ]
ChevalleyGroup(s, n, K: parameters) : MonStgElt, RngIntElt, FldFin -> GrpMat
Chevalley Groups (MATRIX GROUPS)
ChevalleyBasis(L) : AlgLie -> [ AlgLieElt ], [ AlgLieElt ], [ AlgLieElt ]
AlgLie_ChevalleyBasis (Example H76E4)
ChevalleyGroup(s, n, K: parameters) : MonStgElt, RngIntElt, FldFin -> GrpMat
ChiefFactors(G) : GrpMat -> [ <RngIntElt, RngIntElt, RngIntElt, RngIntElt> ]
ChiefFactors(G) : GrpPerm -> [ <RngIntElt, RngIntElt, RngIntElt, RngIntElt> ]
ChiefSeries(G) : GrpAb -> [GrpAb]
ChiefSeries(G) : GrpMat -> [ GrpMat ], [ <RngIntElt, RngIntElt, RngIntElt, RngIntElt> ]
ChiefSeries(G) : GrpPC -> [GrpPC]
ChiefSeries(G) : GrpPerm -> [ GrpPerm ], [ <RngIntElt, RngIntElt, RngIntElt, RngIntElt> ]
ChiefFactors(G) : GrpMat -> [ <RngIntElt, RngIntElt, RngIntElt, RngIntElt> ]
ChiefFactors(G) : GrpPerm -> [ <RngIntElt, RngIntElt, RngIntElt, RngIntElt> ]
ChiefSeries(G) : GrpAb -> [GrpAb]
ChiefSeries(G) : GrpMat -> [ GrpMat ], [ <RngIntElt, RngIntElt, RngIntElt, RngIntElt> ]
ChiefSeries(G) : GrpPC -> [GrpPC]
ChiefSeries(G) : GrpPerm -> [ GrpPerm ], [ <RngIntElt, RngIntElt, RngIntElt, RngIntElt> ]
ChienChoyCode(P, G, n, S) : RngUPolElt, RngUPolElt, RngIntElt, FldFin -> Code
ChienChoyCode(P, G, n, S) : RngUPolElt, RngUPolElt, RngIntElt, FldFin -> Code
GetChild(SQP, i) : SQProc, RngIntElt -> List
DisownChildren(M) : ModSym ->
GetChildren(SQP) : SQProc -> List
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(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(L) : Lat -> AlgMatElt
Orthonormalize(L) : Lat -> AlgMatElt
Orthonormalize(M, K) : MtrxSpcElt, Fld -> AlgMatElt
ChienChoyCode(P, G, n, S) : RngUPolElt, RngUPolElt, RngIntElt, FldFin -> Code
ChromaticIndex(G) : GrphUnd -> RngIntElt
ChromaticNumber(G) : GrphUnd -> RngIntElt
ChromaticPolynomial(G) : GrphUnd -> RngUPolElt
ChromaticIndex(G) : GrphUnd -> RngIntElt
ChromaticNumber(G) : GrphUnd -> RngIntElt
Graph_ChromaticNumber (Example H97E13)
ChromaticPolynomial(G) : GrphUnd -> RngUPolElt
cInvariants(E) : CrvEll -> [ RngElt ]
[Future release] CircuitSpace(G) : GrphUnd -> ModTup
[Future release] EulerianCircuit(G) : GrphUnd -> [GrphVert]
Connectedness, Paths and Circuits (GRAPHS)
Paths and Circuits in a Graph (GRAPHS)
[Future release] CircuitSpace(G) : GrphUnd -> ModTup
BorderedDoublyCirculantQRCode(p,a,b) : RngIntElt, RngElt, RngElt -> Code
DoublyCirculantQRCode(p) : RngIntElt -> Code
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(C) : Crv -> GrpAb, Map, Map
ClassGroup(K) : FldQuad -> GrpAb, Map
ClassGroup(Q) : FldRat -> GrpAb, Map
ClassGroup(F : parameters) : FldFun -> GrpAb, Map, Map
ClassGroup(F : parameters) : FldFun -> GrpAb, Map, Map
ClassGroup(Q: parameters) : QuadBin -> GrpAb, Map
ClassGroup(O: parameters) : RngOrd -> GrpAb, Map
ClassGroup(O) : RngFunOrd -> GrpAb, Map, 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) : GrpMat -> Map
ClassMap(G) : GrpPC -> Map
ClassMap(G: parameters) : GrpFin -> 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 }
HilberClassField(K) : FldAlg -> FldAb
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) : GrpGPC -> RngIntElt
NilpotencyClass(G) : GrpMat -> RngIntElt
NilpotencyClass(G) : GrpPC -> RngIntElt
NilpotencyClass(G) : GrpPerm -> 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) ->
SteinitzClass(M) : ModDed -> RngOrdIdl
WeberClassPolynomial(D) : RngIntElt -> RngUPolElt
WeberClassPolynomial(D) : RngIntElt -> RngUPolElt
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 Groups (CLASS FIELD THEORY)
Residue Class Rings (RING OF INTEGERS)
Structure Creation (CHARACTERS OF FINITE GROUPS)
FldAb_class-field (Example H51E5)
Class Group (BINARY QUADRATIC FORMS)
Ideal Class Group (QUADRATIC FIELDS)
Linear Equivalence and Class Group (PLANE ALGEBRAIC CURVES)
Class Information from a Conjugacy Class Poset (GROUPS)
GrpPC_class_map (Example H24E12)
ClassAction(A) : GrpAuto -> Map, GrpPerm, SetIndx
PermutationRepresentation(A) : GrpAuto -> Map, GrpPerm, SetIndx
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 H16E14)
Conjugacy Classes of Subgroups (FINITE SOLUBLE GROUPS)
Conjugacy Classes of Subgroups (GROUPS)
Enumeration of Ideal Classes (QUATERNION ALGEBRAS)
CharacterRing(G) : Grp -> AlgChtr
ClassFunctionSpace(G) : Grp -> AlgChtr
ClassGroup(C) : Crv -> GrpAb, Map, Map
ClassGroup(K) : FldQuad -> GrpAb, Map
ClassGroup(Q) : FldRat -> GrpAb, Map
ClassGroup(F : parameters) : FldFun -> GrpAb, Map, Map
ClassGroup(F : parameters) : FldFun -> GrpAb, Map, Map
ClassGroup(Q: parameters) : QuadBin -> GrpAb, Map
ClassGroup(O: parameters) : RngOrd -> GrpAb, Map
ClassGroup(O) : RngFunOrd -> GrpAb, Map, Map
ClassGroup(Z) : RngInt -> GrpAb, Map
RngOrd_ClassGroup (Example H48E18)
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 ]
ClassicalForms(G): GrpMat -> BoolElt
ClassicalModularPolynomial(N) : RngIntElt -> RngMPolElt
ClassicalPeriod(M, j, prec) : ModSym, RngIntElt, RngIntElt -> FldPrElt
ClassicalType(G) : GrpMat -> MonStgElt
RecognizeClassical( G : parameters): GrpMat -> BoolElt
Classical Groups (MATRIX GROUPS)
ClassicalForms(G): GrpMat -> BoolElt
GrpMat_ClassicalForms (Example H21E29)
Classical forms (MATRIX GROUPS)
ClassicalModularPolynomial(N) : RngIntElt -> RngMPolElt
ClassicalPeriod(M, j, prec) : ModSym, RngIntElt, RngIntElt -> FldPrElt
ClassicalType(G) : GrpMat -> MonStgElt
Classification of Root Data (ROOT DATA FOR LIE THEORY)
Classification of Root Data (ROOT DATA FOR LIE THEORY)
ClassImage(A) : GrpAuto -> GrpPerm
ClassMap(G) : GrpAb -> Map
ClassMap(G) : GrpMat -> Map
ClassMap(G) : GrpPC -> Map
ClassMap(G: parameters) : GrpFin -> 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
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(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
GrpPGp_ClassTwo (Example H25E6)
ClassUnion(A) : GrpAuto -> SetIndx
ClearPrevious() : ->
ClearVerbose() : ->
Deleting an identifier (OVERVIEW)
ClearPrevious() : ->
ClearVerbose() : ->
ShrikhandeGraph() : -> GrphUnd
GewirtzGraph() : -> GrphUnd
ClebschGraph() : -> GrphUnd
ClebschInvariants(C) : CrvHyp -> SeqEnum
ClebschInvariants(f) : RngUPolElt -> SeqEnum
ClebschToIgusaClebsch(Q) : SeqEnum -> SeqEnum
HyperellipticCurveFromIgusaClebsch(S) : SeqEnum -> CrvHyp
IgusaClebschInvariants(C: parameters) : CrvHyp -> SeqEnum
IgusaClebschInvariants(f: parameters) : RngUPolElt -> SeqEnum
IgusaClebschInvariants(h, f) : RngUPolElt, RngUPolElt -> SeqEnum
IgusaClebschToIgusa(S) : SeqEnum -> SeqEnum
ShrikhandeGraph() : -> GrphUnd
GewirtzGraph() : -> GrphUnd
ClebschGraph() : -> GrphUnd
ClebschInvariants(C) : CrvHyp -> SeqEnum
ClebschInvariants(f) : RngUPolElt -> SeqEnum
ClebschToIgusaClebsch(Q) : SeqEnum -> SeqEnum
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 }
Cliques, Independent Sets (GRAPHS)
Cliques, Independent Sets (GRAPHS)
CliqueNumber(G: parameters) : GrphUnd -> RngIntElt
AllCliques(G) : GrphUnd -> SeqEnum
AllCliques(G, k) : GrphUnd, RngIntEl -> SeqEnum
AllCliques(G, k, m: parameters) : GrphUnd, RngIntElt, BoolElt -> SeqEnum
Graph_Cliques (Example H97E14)
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
Short and Close Vectors (LATTICES)
HasCompleteCosetTable(P) : GrpFPCosetEnumProc -> BoolElt
HasClosedCosetTable(P) : GrpFPCosetEnumProc -> BoolElt
ALGEBRAICALLY CLOSED FIELDS
ClosestVectors(L, w) : Lat, ModTupRngElt -> [ LatElt ], RngElt
ClosestVectorsMatrix(L, w) : Lat, ModTupRngElt -> ModMatRngElt, RngElt
Lat_Closest (Example H64E7)
Shortest and Closest Vectors (LATTICES)
ClosestVectors(L, w) : Lat, ModTupRngElt -> [ LatElt ], RngElt
ClosestVectorsMatrix(L, w) : Lat, ModTupRngElt -> ModMatRngElt, RngElt
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
AlgebraicClosure() : -> FldAC
ClosureGraph(P, G) : GrpPerm, GrphUnd -> GrphUnd
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
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)
Projective Closure and Affine Patches (PLANE ALGEBRAIC CURVES)
ClosureGraph(P, G) : GrpPerm, GrphUnd -> GrphUnd
IsCluster(X) : Sch -> BoolElt,Clstr
Scheme(p) : Pt -> Sch
Scheme(X,f) : Sch,RngMPolElt -> Sch
Scheme_cluster-degree5 (Example H83E7)
Zero-dimensional Schemes (SCHEMES)
x cmpeq y : Elt, Elt -> BoolElt
x cmpne y : Elt, Elt -> BoolElt
GrpFP_1_Co1 (Example H19E52)
Lifting a Quotient by Choosing an Individual Cocycle (FP GROUPS - ADVANCED FEATURES)
RepresentativeCocycles(G, U, Ext, Hom) : GrpPC, GrpPC, [AlgMatElt], [AlgMatElt]-> [AlgMatElt]
Combinatorial and Geometrical Structures (OVERVIEW)
AlgebraicGeometricCode(S, D) : [PlcCrvElt], DivCrvElt -> Code
AlternantCode(A, Y, r, S) : [ FldFinElt ], [ FldFinElt ], RngIntElt, FldFin -> Code
AugmentCode(C) : Code -> Code
BDLC(K, n, d) : FldFin,RngIntElt,RngIntElt -> Code
BKLC(K, n, k) : FldFin,RngIntElt,RngIntElt -> Code
BLLC(K, k, d) : FldFin,RngIntElt,RngIntElt -> Code, BoolElt
ChienChoyCode(P, G, n, S) : RngUPolElt, RngUPolElt, RngIntElt, FldFin -> Code
CodeComplement(C,C1) : Code, Code -> Code
CodeJuxtaposition(C1, C2) : Code,Code -> Code
CodeToString(n) : RngIntElt -> MonStgElt
ConcatenatedCode(O, I) : Code, Code -> Code
CordaroWagnerCode(n) : RngIntElt -> Code
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
EvenWeightCode(n) : RngIntElt -> Code
ExpurgateCode(C) : Code -> Code
ExpurgateCode(C, L) : Code,[ModTupFldElt] -> Code
ExpurgateWeightCode(C, w) : Code,RngIntElt -> Code
ExtendCode(C) : Code -> Code
ExtendCode(C) : Code -> Code
ExtendCode(C, n) : Code, RngIntElt -> Code
ExtendCode(C, n) : Code, RngIntElt -> Code
FireCode(h, s, n) : RngUPolElt, RngIntElt, RngIntElt -> Code
GabidulinCode(A, W, Z, t) : [ FldFinElt ], [ FldFinElt ], [ FldFinElt ], RngIntElt -> Code
GeneralizedSrivastavaCode(A, W, Z, t, S) : [ FldFinElt ], [ FldFinElt ], [ FldFinElt ], RngIntElt, FldFin -> Code
GolayCode(K, extend) : FldFin, BoolElt -> Code
GoppaCode(L, G) : [ FldFinElt ], RngUPolElt -> Code
HammingCode(K, r) : FldFin, RngIntElt -> Code
HermitianCode(q, r) : RngIntElt, RngIntElt -> Code
JustesenCode(N, K) : Code, FldFinElt, RngIntElt -> Code
KerdockCode(m): RngIntElt, RngUPolElt -> Code
KerdockCode(m, h): RngIntElt, RngUPolElt -> Code
LengthenCode(C) : Code -> Code
LinearCode(C, S) : Code, FldFin -> Code, Map
LinearCode<R, n | L> : FldFin, RngIntElt, List -> Code
LinearCode(D, K) : Inc, FldFin -> Code
LinearCode(A) : ModMatRngElt -> Code
LinearCode(A) : ModMatRngElt -> Code
LinearCode(U) : ModTupRng -> Code
LinearCode(U) : ModTupRng -> Code
LinearCode(P, K) : Plane, FldFin -> Code
LinearCode<R, n | L> : Rng, RngIntElt, List -> Code
NonPrimitiveAlternantCode(n,m,r) : RngIntElt,RngIntElt,RngIntElt->Code
PadCode(C, n) : Code, RngIntElt -> Code
PadCode(C, n) : Code, RngIntElt -> Code
PermutationCode(u, G) : ModTupRngElt, GrpPerm -> Code
PermutationCode(u, G) : ModTupRngElt, GrpPerm -> Code
PowerResidueCode(K,n,p) : FldFin, RngIntElt, RngIntElt -> Code
PreparataCode(m): RngIntElt, RngUPolElt -> Code
PreparataCode(m, h): RngIntElt, RngUPolElt -> Code
PunctureCode(C, i) : Code, RngIntElt -> Code
PunctureCode(C, i) : Code, RngIntElt -> Code
PunctureCode(C, S) : Code, { RngIntElt } -> Code
PunctureCode(C, S) : Code, { RngIntElt } -> Code
QuasiCyclicCode(n,Gen,h) : RngIntElt, SeqEnum, RngIntElt -> Code
QuasiCyclicCode(n, Gen) : RngIntElt, [ RngUPolElt ] -> Code
RandomLinearCode(K, n, k) : FldFin, RngIntElt, RngIntElt -> Code
ReedMullerCode(r, m) : RngIntElt, RngIntElt -> Code
ReedSolomonCode(K, d, b) : FldFin, RngIntElt, RngIntElt -> Code
ReedSolomonCode(n, d) : RngIntElt, RngIntElt -> Code
RepetitionCode(R, n) : FldFin, RngIntElt -> Code
RepetitionCode(R, n) : Rng, RngIntElt -> Code
ShortenCode(C, i) : Code, RngIntElt -> Code
ShortenCode(C, i) : Code, RngIntElt -> Code
ShortenCode(C, S) : Code, { RngIntElt } -> Code
ShortenCode(C, S) : Code, { RngIntElt } -> Code
SimplexCode(r) : RngIntElt -> Code
SrivastavaCode(A, W, mu, S) : [ FldFinElt ], [ FldFinElt ], RngIntElt, FldFin -> Code
StringToCode(s) : MonStgElt -> RngIntElt
SubcodeBetweenCode(C1, C2, k) : Code,Code,RngIntElt -> Code
SubfieldCode(C, S) : Code, FldFin -> Code
SubfieldRepresentationCode(C, S) : Code, FldFin -> Code
SubfieldRepresentationParityCode(C, K) : Code, FldFin -> Code
UniverseCode(R, n) : FldFin, RngIntElt -> Code
UniverseCode(R, n) : Rng, RngIntElt -> Code
UniverseCode(R, n) : Rng, RngIntElt -> Code
ZeroCode(R, n) : FldFin, RngIntElt -> Code
ZeroCode(R, n) : Rng, RngIntElt -> Code
ZeroSumCode(R, n) : FldFin, RngIntElt -> Code
ZeroSumCode(R, n) : Rng, RngIntElt -> Code
ZinovievCode(I, O) : [Code], [Code] -> Code
Lat_Code (Example H64E2)
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)
Graphs Constructed from Designs (GRAPHS)
The Code Space (LINEAR CODES OVER FINITE FIELDS)
CodeComplement(C,C1) : Code, Code -> Code
CodeFld_CodeFromMatrix (Example H101E2)
CodeRng_CodeFromMatrix (Example H102E2)
CodeJuxtaposition(C1, C2) : Code,Code -> Code
Algebraic Geometric Codes (LINEAR CODES OVER FINITE FIELDS)
Algebraic Geometric Codes (PLANE ALGEBRAIC CURVES)
Best Known Linear Codes (LINEAR CODES OVER FINITE FIELDS)
Combining Codes (LINEAR CODES OVER FINITE FIELDS)
Combining Codes (LINEAR CODES OVER FINITE RINGS)
Maximum Distance Separable Codes (LINEAR CODES OVER FINITE FIELDS)
Plane_codes (Example H99E18)
CodeToString(n) : RngIntElt -> MonStgElt
ApparentCodimension(X) : VSrfK3 -> RngIntElt
Codimension(X) : Sch -> RngIntElt
Codimension(X) : VSrfK3 -> RngIntElt
Codomain(f) : Map -> Grp
Codomain(f) : Map -> Grp
Codomain(f) : Map -> Grp
Codomain(f) : Map -> Grp
Codomain(f) : Map -> Struct
Codomain(f) : MapIsoSch -> CrvHyp
Codomain(f) : MapSch -> Sch
Codomain(a) : ModMatElt -> ModTupFld
Codomain(f) : ModMatFldElt -> ModAlg
Codomain(S) : ModMatRng -> ModTupRng
Codomain(a) : ModMatRngElt -> ModTupRng
Domain(P) : PowMap -> Str
Coefficient Arithmetic (PLANE ALGEBRAIC CURVES)
RngLaz_coeff_non_spiral (Example H57E8)
BaseRing(J) : JacHyp -> Rng
CoefficientRing(J) : JacHyp -> Rng
BaseField(J) : JacHyp -> Fld
BaseField(C) : Sch -> Fld
BaseField(K) : SrfKum -> Fld
BaseRing(B) : AlgBas -> Rng
BaseRing(R) : AlgMat -> Rng
BaseRing(E) : CrvEll -> Rng
BaseRing(F) : Fld -> Rng
CoefficientRing(F) : FldFun -> Rng
BaseRing(A) : FldAb -> Ring
BaseRing(F) : FldFunRat -> Rng
BaseRing(L) : Lat -> Rng
BaseRing(M) : ModDed -> Rng
BaseRing(A) : Mtrx -> Rng
BaseRing(A) : MtrxSprs -> Rng
BaseRing(O) : RngFunOrd -> Rng
BaseRing(P) : RngMPol -> Rng
BaseRing(O) : RngOrd -> Rng
BaseRing(R) : RngPowLaz -> Rng
BaseRing(R) : RngSer -> Rng
BaseRing(P) : RngUPol -> Rng
BaseRing(C) : Sch -> Rng
BaseRing(G) : SchGrpEll -> Rng
Coefficient(a, g) : AlgGrpElt, GrpElt -> RngElt
Coefficient(f, n) : ModFrmElt, RngIntElt -> RngElt
Coefficient(x, i) : RngLocElt, RngIntElt -> RngLocElt
Coefficient(x, i) : RngLocElt, RngIntElt -> RngLocElt
Coefficient(f, i, k) : RngMPolElt, RngIntElt, RngIntElt -> RngElt
Coefficient(s, i) : RngPowLazElt, RngIntElt -> RngElt
Coefficient(s, T) : RngPowLazElt, SeqEnum -> RngElt
Coefficient(f, i) : RngSerSerElt, RngElt -> RngElt
Coefficient(p, i) : RngUPolElt, RngIntElt -> RngElt
CoefficientField(x) : AlgChtrElt -> Rng
CoefficientField(V) : ModTupFld -> Fld
CoefficientMap(L) : LinSys -> ModTupFldElt
CoefficientRing(A) : Alg -> Rng
CoefficientRing(A) : AlgGen -> Rng
CoefficientRing(G) : GrpMat -> Rng
CoefficientRing(M) : ModMPol -> ModMPol
CoefficientRing(M) : ModTupRng -> Rng
CoefficientRing(M) : ModTupRng -> Rng
CoefficientRing(R) : RngInvar -> Grp
CoefficientRing(Q) : RngMPolRes -> Rng
CoefficientRing(X) : Sch -> Fld
CoefficientField(X) : Sch -> Fld
CoefficientSpace(L) : LinSys -> ModTupFld
GroundField(F) : FldAlg -> Fld
LSeriesLeadingCoefficient(M, j, prec) : ModSym, RngIntElt, RngIntElt -> FldPrElt, RngIntElt
LeadingCoefficient(u) : AlgFPElt -> RngElt
LeadingCoefficient(f) : RngMPolElt -> RngElt
LeadingCoefficient(f, i) : RngMPolElt, RngIntElt -> RngElt
LeadingCoefficient(s) : RngPowLazElt -> RngElt
LeadingCoefficient(f) : RngSerElt -> RngElt
LeadingCoefficient(f) : RngUPolElt -> RngElt
MonomialCoefficient(u, m) : AlgFPElt, MonElt -> RngElt
MonomialCoefficient(f, m) : RngMPolElt, RngMPolElt -> RngElt
MonomialCoefficient(p, m) : RngUPolElt, RngUPolElt -> RngElt
PolynomialCoefficient(s, i) : RngPowLazElt, RngIntElt -> RngPowLazElt
TrailingCoefficient(f) : RngMPolElt -> RngElt
TrailingCoefficient(f, i) : RngMPolElt, RngIntElt -> RngElt
TrailingCoefficient(p) : RngUPolElt -> RngElt
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)
Coefficients and Degree (POWER, LAURENT AND PUISEUX SERIES)
Coefficients, Monomials and Terms (MULTIVARIATE POLYNOMIAL RINGS)
Coefficients and Terms (UNIVARIATE POLYNOMIAL RINGS)
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(L) : LinSys -> ModTupFldElt
BaseRing(J) : JacHyp -> Rng
CoefficientRing(J) : JacHyp -> Rng
BaseField(J) : JacHyp -> Fld
BaseField(C) : Sch -> Fld
BaseField(K) : SrfKum -> Fld
BaseRing(B) : AlgBas -> Rng
BaseRing(R) : AlgMat -> Rng
BaseRing(E) : CrvEll -> Rng
BaseRing(F) : Fld -> Rng
BaseRing(A) : FldAb -> Ring
BaseRing(F) : FldFunRat -> Rng
BaseRing(L) : Lat -> Rng
BaseRing(M) : ModDed -> Rng
BaseRing(A) : Mtrx -> Rng
BaseRing(A) : MtrxSprs -> Rng
BaseRing(O) : RngFunOrd -> Rng
BaseRing(P) : RngMPol -> Rng
BaseRing(O) : RngOrd -> Rng
BaseRing(R) : RngPowLaz -> Rng
BaseRing(R) : RngSer -> Rng
BaseRing(P) : RngUPol -> Rng
BaseRing(C) : Sch -> Rng
BaseRing(G) : SchGrpEll -> Rng
CoefficientRing(A) : Alg -> Rng
CoefficientRing(A) : AlgGen -> Rng
CoefficientRing(G) : GrpMat -> Rng
CoefficientRing(M) : ModMPol -> ModMPol
CoefficientRing(M) : ModTupRng -> Rng
CoefficientRing(M) : ModTupRng -> Rng
CoefficientRing(R) : RngInvar -> Grp
CoefficientRing(Q) : RngMPolRes -> Rng
CoefficientRing(X) : Sch -> Fld
Coefficients(a) : AlgGrpElt -> SeqEnum
Coefficients(x) : RngLocElt -> [ RngLocElt ]
Coefficients(x) : RngLocElt -> [ RngLocElt ]
Coefficients(f) : RngMPolElt -> [ RngElt ]
Coefficients(f, i) : RngMPolElt, RngIntElt -> [ RngElt ]
Coefficients(s, n) : RngPowLazElt, RngIntElt -> [RngElt]
Coefficients(f) : RngSerElt -> [ RngElt ], RngIntElt, RngIntElt
Coefficients(p) : RngUPolElt -> [ RngElt ]
CoefficientsNonSpiral(s, n) : RngPowLazElt, [RngIntElt] -> SeqEnum
HilbertCoefficients(X,n) : VSrfK3,RngIntElt -> SeqEnum
aInvariants(E) : CrvEll -> [ RngElt ]
RngMPol_Coefficients (Example H43E4)
CoefficientsNonSpiral(s, n) : RngPowLazElt, [RngIntElt] -> SeqEnum
CoefficientSpace(L) : LinSys -> ModTupFld
BaseField(A) : FldAb -> Field
CoeffientField(A) : FldAb -> Field
BaseField(A) : FldAb -> Field
CoeffientField(A) : FldAb -> Field
Finding Coefficients of Lazy Series (LAZY POWER SERIES RINGS)
ModDed_coerce-quo (Example H63E7)
IsCoercible(X,Q) : Sch,SeqEnum -> BoolElt,Pt
IsCoercible(S, x) : Str, Elt -> Bool, Elt
Bang(D, C) : Struct, Struct -> Map
Coercion(D, C) : Struct, Struct -> Map
FldRat_Coercion (Example H39E1)
RngInt_Coercion (Example H38E5)
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 OF 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 H24E14)
ModSym_Coercion-spaces (Example H90E10)
Class Groups Coercions (BINARY QUADRATIC FORMS)
IsCohenMacaulay(R) : RngInvar -> BoolElt
CohomologicalDimension(G, M, i) : GrpFin, ModRng, RngIntElt -> RngIntElt
CohomologicalDimension(G, M, i) : GrpPerm, ModRng, RngIntElt -> RngIntElt
CohomologicalDimension(G, M, i) : GrpFin, ModRng, RngIntElt -> RngIntElt
CohomologicalDimension(G, M, i) : GrpPerm, ModRng, RngIntElt -> RngIntElt
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 H81E5)
GrpPerm_Cohomology (Example H20E30)
Cohomology (ABELIAN GROUPS)
Cohomology (BASIC ALGEBRAS)
Cohomology (GROUPS)
Cohomology (PERMUTATION GROUPS)
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
CoisogenyGroup( G ) : GrpLie -> RootDtm
CoisogenyGroup( RD ) : RootDtm -> GrpAb
CoisogenyGroup( G ) : GrpLie -> RootDtm
CoisogenyGroup( RD ) : RootDtm -> GrpAb
Cokernel(f) : ModMatCpxElt -> ModCpx, ModMatCpxElt
Cokernel(a) : ModMatElt -> ModTupFld
Cokernel(f) : ModMatFldElt -> ModAlg,ModMatFldElt
Cokernel(a) : ModMatRngElt -> ModTupRng
Collect(P, Q) : Process(pQuot), [ <RngIntElt, RngIntElt> ] -> [ RngIntElt ] ->
CollectRelations(~P) : Process(pQuot) ->
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) : SQProc ->
DeleteSplitCollector(SQP) : SQProc, RngIntElt ->
DeleteNonsplitCollector(SQP) : SQProc, RngIntElt ->
Symbolic Collector (FP GROUPS - ADVANCED FEATURES)
CollectRelations(~P) : Process(pQuot) ->
IsCollinear(P, S) : Plane, { PlanePt } -> BoolElt, PlaneLn
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 H99E13)
The Collineation Group of a Plane (FINITE PLANES)
The Collineation Group of a Plane (FINITE PLANES)
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(P, k) : Plane, RngIntElt -> GrpPerm, GSet, GSet, PowMap, Map
Plane_CollineationGSet (Example H99E12)
CollineationSubgroup(P) : Plane -> GrpPerm, GSet, GSet, PowMap, Map
IdealQuotient(I, J) : RngMPol, RngMPol -> RngMPol
ColonIdeal(I, J) : RngMPol, RngMPol -> RngMPol
ColonIdeal(I, f) : RngMPol, RngMPolElt -> RngMPol, RngIntElt
ColonIdeal(I, J) : RngOrdIdl, RngOrdIdl -> RngOrdIdl
IdealQuotient(I, J) : RngMPol, RngMPol -> RngMPol
ColonIdeal(I, J) : RngMPol, RngMPol -> RngMPol
ColonIdeal(I, f) : RngMPol, RngMPolElt -> RngMPol, RngIntElt
ColonIdeal(I, J) : RngOrdIdl, RngOrdIdl -> RngOrdIdl
OptimalEdgeColouring(G) : GrphUnd -> SeqEnum
OptimalVertexColouring(G) : GrphUnd -> SeqEnum
Colourings (GRAPHS)
AddColumn(~a, u, i, j) : AlgMatElt, RngElt, RngIntElt, RngIntElt ->
AddColumn(A, c, i, j) : Mtrx, RngElt, RngIntElt, RngIntElt -> Mtrx
Column(t, j) : Tbl, RngIntElt -> MonOrdElt
ColumnSkewLength(t, j) : Tbl,RngIntElt -> RngIntElt
ColumnSubmatrix(A, i) : Mtrx, RngIntElt -> Mtrx
ColumnSubmatrix(A, i, k) : Mtrx, RngIntElt, RngIntElt -> Mtrx
ColumnSubmatrixRange(A, i, j) : Mtrx, RngIntElt, RngIntElt -> Mtrx
ColumnWeight(A, j) : MtrxSprs, RngIntElt -> RngIntElt
ColumnWeights(A) : MtrxSprs -> [RngIntElt]
ColumnWeights(A) : MtrxSprs -> [RngIntElt]
ColumnWord(t) : Tbl -> SeqEnum
FirstIndexOfColumn(t, j) : Tbl,RngIntElt -> RngIntElt
HadamardColumnDesign(H, i) : AlgMatElt, RngIntElt -> Dsgn
LastIndexOfColumn(t, j) : Tbl,RngIntElt -> RngIntElt
MultiplyColumn(~a, u, i) : AlgMatElt, RngElt, RngIntElt ->
MultiplyColumn(A, c, i) : Mtrx, RngElt, RngIntElt -> Mtrx
Row and Column Operations (MATRICES)
Row and Column Operations (MATRIX ALGEBRAS)
ColumnLength(t, j): Tbl,RngIntElt -> RnfIntElt
LastIndexOfColumn(t, j) : Tbl,RngIntElt -> RngIntElt
Columns(t) : Tbl -> SeqEnum[MonOrdElt]
NFSCharacterColumns(n, F, tuple) : RngIntElt, RngMPolElt, Tup -> .
NumberOfColumns(a) : AlgMatElt -> RngIntElt
NumberOfColumns(u) : ModTupFldElt -> RngIntElt
NumberOfColumns(A) : Mtrx -> RngIntElt
NumberOfColumns(A) : MtrxSprs -> RngIntElt
SetAutoColumns(b) : BoolElt ->
SetColumns(n) : RngIntElt ->
SwapColumns(~a, i, j) : AlgMatElt, RngIntElt, RngIntElt ->
SwapColumns(A, i, j) : Mtrx, RngIntElt, RngIntElt -> Mtrx
ColumnSkewLength(t, j) : Tbl,RngIntElt -> RngIntElt
ColumnSubmatrix(A, i) : Mtrx, RngIntElt -> Mtrx
ColumnSubmatrix(A, i, k) : Mtrx, RngIntElt, RngIntElt -> Mtrx
ColumnSubmatrixRange(A, i, j) : Mtrx, RngIntElt, RngIntElt -> Mtrx
ColumnWeight(A, j) : MtrxSprs, RngIntElt -> RngIntElt
ColumnWeights(A) : MtrxSprs -> [RngIntElt]
ColumnWeights(A) : MtrxSprs -> [RngIntElt]
ColumnWord(t) : Tbl -> SeqEnum
ENUMERATIVE COMBINATORICS
Combinatorial and Geometrical Structures (OVERVIEW)
Combinatorial and Geometrical Structures (OVERVIEW)
Counting Tableaux (PARTITIONS, WORDS AND YOUNG TABLEAUX)
Combinatorial Functions (ENUMERATIVE COMBINATORICS)
Combinatorial Functions (RING OF INTEGERS)
Combining Codes (LINEAR CODES OVER FINITE FIELDS)
Combining Codes (LINEAR CODES OVER FINITE RINGS)
Combining Codes (LINEAR CODES OVER FINITE FIELDS)
Combining Codes (LINEAR CODES OVER FINITE RINGS)
Command Line Options (ENVIRONMENT AND OPTIONS)
Performing shell commands from Magma (OVERVIEW)
Command Line Options (ENVIRONMENT AND OPTIONS)
Comments (OVERVIEW)
Comments and Continuation (STATEMENTS AND EXPRESSIONS)
Comments and Continuation (STATEMENTS AND EXPRESSIONS)
CommonOverfield(K, L) : FldFin, FldFin -> FldFin
CommonZeros(L) : SeqEnum[ FldFunElt ] -> SeqEnum[ PlcFunElt ]
ExtendedGreatestCommonDivisor(m, n) : RngIntElt, RngIntElt -> RngIntElt, RngIntElt, RngIntElt
ExtendedGreatestCommonDivisor(f, g) : RngUPolElt, RngUPolElt -> RngUPolElt, RngUPolElt, RngUPolElt
ExtendedGreatestCommonDivisor(v, w) : RngValElt, RngValElt -> RngValElt, RngValElt, RngValElt
ExtendedGreatestCommonDivisor(s) : [RngIntElt] -> RngIntElt, [RngIntElt]
GCD(D1, D2) : DivFunElt, DivFunElt -> DivFunElt
Gcd(a, b) : RngQuadElt, RngQuadElt -> RngQuadElt
GreatestCommonDivisor(a, b) : RngIntResElt, RngIntResElt -> RngIntResElt
GreatestCommonDivisor(f, g) : RngMPolElt, RngMPolElt -> RngMPolElt
GreatestCommonDivisor(f, g) : RngUPolElt, RngUPolElt -> RngUPolElt
GreatestCommonDivisor(g, h) : RngUPolElt, RngUPolElt -> RngUPolElt
GreatestCommonDivisor(g, h) : RngUPolElt, RngUPolElt -> RngUPolElt
GreatestCommonDivisor(v, w) : RngValElt, RngValElt -> RngValElt
GreatestCommonDivisor(s) : [RngIntElt] -> RngIntElt
GreatestCommonDivisor(Q) : [RngIntResElt] -> RngIntResElt
LCM(D1, D2) : DivFunElt, DivFunElt -> DivFunElt
LCM(I, J) : RngOrdFracIdl, RngOrdFracIdl -> RngOrdFracIdl
Lcm(a, b) : RngQuadElt, RngQuadElt -> RngQuadElt
LeastCommonMultiple(m, n) : RngIntElt, RngIntElt -> RngIntElt
LeastCommonMultiple(a, b) : RngIntResElt, RngIntResElt -> RngIntResElt
LeastCommonMultiple(f, g) : RngMPolElt, RngMPolElt -> RngMPolElt
LeastCommonMultiple(f, g) : RngUPolElt, RngUPolElt -> RngUPolElt
LeastCommonMultiple(Q) : Seq(RngIntResElt) -> RngIntResElt
LeastCommonMultiple(s) : [RngIntElt] -> RngIntElt
ModulesOverCommonField(M, N) : ModGrp, ModGrp -> ModGrp, ModGrp
PuiseuxExponentsCommon(p, q) : RngSerElt, RngSerElt -> SeqEnum
Contpp(p) : RngUPolElt -> RngIntElt, RngUPolElt
Common Divisors and Common Multiples (UNIVARIATE POLYNOMIAL RINGS)
Greatest Common Divisors (MULTIVARIATE POLYNOMIAL RINGS)
Greatest Common Divisors (QUADRATIC FIELDS)
CommonOverfield(K, L) : FldFin, FldFin -> FldFin
CommonZeros(L) : SeqEnum[ FldFunElt ] -> SeqEnum[ PlcFunElt ]
IsCommutative(A) : AlgGen -> BoolElt
IsCommutative(R) : Rng -> BoolElt
Groups (OVERVIEW)
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
Groups (OVERVIEW)
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
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
CompactInjectiveResolution(M, n) : ModAlg, RngIntElt -> List, ModMatFldElt
CompactPresentation(G) : GrpPC -> [RngIntElt]
CompactProjectiveResolution(M, n) : ModAlg, RngIntElt -> Tup
SetAutoCompact(b) : BoolElt ->
CompactPresentation (FINITE SOLUBLE GROUPS)
CompactPresentation (FINITE SOLUBLE GROUPS)
CompactInjectiveResolution(M, n) : ModAlg, RngIntElt -> List, ModMatFldElt
CompactPresentation(G) : GrpPC -> [RngIntElt]
GrpPC_CompactPresentation (Example H24E25)
CompactProjectiveResolution(M, n) : ModAlg, RngIntElt -> Tup
CompanionMatrix(p) : RngPolElt -> AlgMatElt
CompanionMatrix(f) : RngUPolElt -> AlgMatElt
CompanionMatrix(p) : RngPolElt -> AlgMatElt
CompanionMatrix(f) : RngUPolElt -> AlgMatElt
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 and Membership Testing (ALGEBRAS)
GrpPerm_CompFactors (Example H20E25)
Tamagawa Numbers and Orders of Component Groups (MODULAR SYMBOLS)
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
OrthogonalComplement(M) : ModSS -> ModSS
Constructing Complements, Line Graphs; Contraction, Switching (GRAPHS)
Constructing Complements, Line Graphs; Contraction, Switching (GRAPHS)
ComplementaryDivisor(D,p) : DivCrvElt,Pt -> DivCrvElt
ComplementaryDivisor(D) : DivFunElt -> DivFunElt
ComplementaryErrorFunction(r) : FldReElt -> FldReElt
ComplementaryDivisor(D,p) : DivCrvElt,Pt -> DivCrvElt
ComplementaryDivisor(D) : DivFunElt -> DivFunElt
Erfc(r) : FldReElt -> FldReElt
ComplementaryErrorFunction(r) : FldReElt -> FldReElt
ComplementBasis(G) : GrpPC -> [GrpPC]
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 and Supplements (PERMUTATION GROUPS)
Decomposabilty and Complements (MODULES OVER A MATRIX ALGEBRA)
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
Construction of a Group Algebra (GROUP ALGEBRAS)
Construction of the Complete Matrix Algebra (MATRIX ALGEBRAS)
Construction of a Group Algebra (GROUP ALGEBRAS)
Construction of the Complete Matrix Algebra (MATRIX ALGEBRAS)
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
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 (INTRODUCTION [BASIC RINGS])
Completions (LOCAL RINGS AND FIELDS)
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
REAL AND COMPLEX FIELDS
Real and Complex Valued Functions (ORDERS AND ALGEBRAIC FIELDS)
Rings, Fields, and Algebras (OVERVIEW)
The Associated Complex Torus (MODULAR SYMBOLS)
The Associated Complex Torus (MODULAR SYMBOLS)
ComplexConjugate(a) : FldCycElt -> FldCycElt
ComplexConjugate(s) : FldPrElt -> FldPrElt
ComplexConjugate(a) : FldQuadElt -> FldQuadElt
ComplexConjugate(q) : FldRatElt -> FldRatElt
ComplexConjugate(n) : RngIntElt -> RngIntElt
ComplexEmbeddings(f) : ModFrmElt -> List
ModCpx_Complexes (Example H82E1)
CHAIN COMPLEXES
Complexes of Modules over Basic Algebras (CHAIN COMPLEXES)
ComplexField() : Null -> FldPr
ComplexField(p) : RngIntElt -> FldCom
ComplexToPolar(c) : FldComElt -> FldReElt, FldReElt
ComplexValue(x) : SpcHypElt) -> FldPrElt
BaseComponent(L) : LinSys -> SchProj
Component(v) : GrphResVert -> GrphRes
Component(u) : GrphVert -> Grph
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(M, p) : ModSym, RngIntElt -> RngIntElt
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
StronglyConnectedComponents(G) : GrphUnd -> [GrphDir]
SymmetricComponents(x, n) : AlgChtrElt, RngIntElt -> SetEnum
SymplecticComponents(x, n) : AlgChtrElt, RngIntElt -> SetEnum
ComposeQuotients(SQ1, SQ2, SQ3: parameter) : SQProc, SQProc, SQProc -> BoolElt, SQProc
ComposeQuotients(SQ1, SQ2, SQ3: parameter) : SQProc, SQProc, SQProc -> BoolElt, SQProc
Composite(I,J) : AlgQuatOrd, AlgQuatOrd -> AlgQuatOrd
I * J : AlgQuatOrd, AlgQuatOrd -> AlgQuatOrd
MergeFields(F, L) : FldAlg, FldAlg -> SeqEnum
CompositeFields(F, L) : FldAlg, FldAlg -> SeqEnum
MergeFields(F, L) : FldAlg, FldAlg -> SeqEnum
RngOrd_CompositeFields (Example H48E2)
Composition(f, g) : QuadBinElt, QuadBinElt -> QuadBinElt
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 (MAPPINGS)
Composition and Chief Factors (MATRIX GROUPS)
Composition and Chief Series (PERMUTATION GROUPS)
Composition and Decomposition (CHARACTERS OF FINITE GROUPS)
Composition and Reversion (POWER, LAURENT AND PUISEUX SERIES)
Composition Series (MODULES OVER A MATRIX ALGEBRA)
Composition and Decomposition (CHARACTERS OF FINITE GROUPS)
Composition and Chief Factors (MATRIX GROUPS)
Composition and Reversion (POWER, LAURENT AND PUISEUX SERIES)
Composition and Chief Series (PERMUTATION GROUPS)
Composition Series (MODULES OVER A MATRIX ALGEBRA)
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)
RngSer_CompositionReversion (Example H56E2)
CompositionSeries(A) : AlgGen -> [ AlgGen ], [ AlgGen ], AlgMatElt
CompositionSeries(G) : GrpPC -> [GrpPC]
CompositionSeries(G, i) : GrpPC, RngIntElt -> [GrpPC]
CompositionSeries(M) : ModRng, ModRng -> [ ModRng ], [ ModRng ], AlgMatElt
RngOrd_Compositum (Example H48E9)
ModAlg_CompSeries (Example H77E6)
HasComputableAbelianQuotient(G) : GrpFP -> BoolElt, GrpAb, Map
HasComputableLCS(G) : GrpGPC -> BoolElt
HasInfiniteComputableAbelianQuotient(G) : GrpFP -> BoolElt, GrpAb, Map
Structure Computation (GENERIC ABELIAN GROUPS)
ConcatenatedCode(O, I) : Code, Code -> Code
ConcatenatedCode(O, I) : Code, Code -> Code
CodeFld_ConcatenatedCode (Example H101E32)
Strings (OVERVIEW)
IsConcurrent(P, R) : Plane, { PlaneLn } -> BoolElt, PlanePt
The case expression (OVERVIEW)
The case statement (OVERVIEW)
The if statement (OVERVIEW)
The select expression (OVERVIEW)
ConditionalClassGroup(O) : RngOrd -> GrpAb, Map
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)
The Simple Conditional Expression (STATEMENTS AND EXPRESSIONS)
The Simple Conditional Statement (STATEMENTS AND EXPRESSIONS)
ConditionalClassGroup(O) : RngOrd -> GrpAb, Map
ConditionedGroup(G) : GrpPC -> GrpPC
IsConditioned(G) : GrpPC -> BoolElt
Conditioned Presentations (FINITE SOLUBLE GROUPS)
Conditioned Presentations (FINITE SOLUBLE GROUPS)
ConditionedGroup(G) : GrpPC -> GrpPC
Point conditions (SCHEMES)
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(D) : DB -> RngIntElt, RngIntElt
TangentCone(p) : Crv,Pt -> Crv
TangentCone(p) : Sch,Pt -> Sch
IsConfluent(G) : GrpAtc -> BoolElt
IsConfluent(G) : GrpRWS -> BoolElt
IsConfluent(M) : MonRWS -> BoolElt
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
Structure of congruence subgroups (SUBGROUPS OF PSL_2(R))
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
ModForm_Congruences (Example H93E18)
Congruences (MODULAR FORMS)
CongruenceSubgroup(N) : RngIntElt -> GrpPSL2
CongruenceSubgroup(i,N) : RngIntElt, RngIntElt -> GrpPSL2
CongruenceSubgroup([N,M,P]) : SeqEnum -> GrpPSL2
Combinatorial and Geometrical Structures (OVERVIEW)
Conic(C) : Crv -> MapSch
Conic(P, S) : Plane, { PlanePt } -> SetEnum
Conic(P,S) : Prj, Pt -> Crv
Conic(X,f) : Prj, RngMPolElt -> CrvCon
IsConic(C) : Sch -> BoolElt, CrvCon
IsConic(X) : Sch -> BoolElt,CrvCon
RATIONAL CURVES AND CONICS
CrvCon_ConicAccess (Example H86E5)
CrvCon_ConicAutomorphisms (Example H86E12)
CrvCon_ConicCreation (Example H86E1)
CrvCon_ConicCurve (Example H86E3)
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 H23E12)
Conjugacy (FINITE SOLUBLE GROUPS)
Groups (OVERVIEW)
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> ]
ComplexConjugate(a) : FldCycElt -> FldCycElt
ComplexConjugate(s) : FldPrElt -> FldPrElt
ComplexConjugate(a) : FldQuadElt -> FldQuadElt
ComplexConjugate(q) : FldRatElt -> FldRatElt
ComplexConjugate(n) : RngIntElt -> RngIntElt
Conjugate(x) : AlgQuatElt -> AlgQuatElt
Conjugate(I) : AlgQuatOrd -> AlgQuatOrd
Conjugate(a, k) : FldAlgElt, RngIntElt -> FldPrElt
Conjugate(a, r) : FldCycElt, FldCycElt -> FldCycElt
Conjugate(a, n) : FldCycElt, RngIntElt -> FldCycElt
Conjugate(a) : FldQuadElt -> FldQuadElt
Conjugate(q) : FldRatElt -> FldRatElt
Conjugate(n) : RngIntElt -> RngIntElt
Conjugate(I) : RngQuadFracIdl -> RngQuadFracIdl
Conjugate(t) : Tbl -> Tbl
ConjugatePartition(P) : SeqEnum -> SeqEnum
ExcludedConjugate(P) : GrpFPCosetEnumProc -> GrpFPElt
ExistsExcludedConjugate(P) : GrpFPCosetEnumProc -> BoolElt, GrpFPElt
GaloisConjugate(x, j) : AlgChtrElt, RngIntElt -> AlgChtrElt
IsConjugate(G, H, K) : GrpAb, GrpAb, GrpAb -> BoolElt, GrpAbElt
IsConjugate(G, H, K) : GrpAb, GrpAb, GrpAb -> BoolElt, GrpAbElt
IsConjugate(G, g, h) : GrpAb, GrpAbElt, GrpAbElt -> BoolElt, GrpAbElt
IsConjugate(G, H, K) : GrpFin, GrpFin, GrpFin -> BoolElt, GrpFinElt
IsConjugate(G, H, K) : GrpFin, GrpFin, GrpFin -> BoolElt, GrpFinElt
IsConjugate(G, g, h) : GrpFin, GrpFinElt, GrpFinElt -> BoolElt, GrpFinElt
IsConjugate(G, g, h) : GrpFin, GrpFinElt, GrpFinElt -> BoolElt, GrpFinElt
IsConjugate(G, H, K) : GrpFP, GrpFP, GrpFP -> BoolElt, GrpFPElt
IsConjugate(G, H, K) : GrpGPC, GrpGPC, GrpGPC -> BoolElt, GrpGPCElt
IsConjugate(G, H, K) : GrpGPC, GrpGPC, GrpGPC -> BoolElt, GrpGPCElt
IsConjugate(G, g, h) : GrpGPC, GrpGPCElt, GrpGPCElt -> BoolElt, GrpGPCElt
[Future release] IsConjugate(G, H, K) : GrpMat, GrpMat, GrpMat -> BoolElt, GrpMatElt | Unass
IsConjugate(G, g, h) : GrpMat, GrpMatElt, GrpMatElt -> BoolElt, GrpMatElt | Unass
IsConjugate(G, H, K) : GrpPC, GrpPC, GrpPC -> BoolElt, GrpPCElt
IsConjugate(G, g, h) : GrpPC, GrpPCElt, GrpPCElt -> BoolElt, GrpPCElt
IsConjugate(G, g, h) : GrpPC, GrpPCElt, GrpPCElt -> BoolElt, GrpPCElt
IsConjugate(G, H, K) : GrpPerm, GrpPerm, GrpPerm -> BoolElt, GrpPermElt
IsConjugate(G, g, h) : GrpPerm, GrpPermElt, GrpPermElt -> BoolElt, GrpPermElt
IsConjugate(G, Y, y, z) : GrpPerm, GSet, Elt, Elt -> BoolElt, GrpPermElt
LeftConjugate(u, v) : GrpBrdElt, GrpBrdElt -> GrpBrdElt
LeftConjugate(~u, v) : GrpBrdElt, GrpBrdElt -> GrpBrdElt
H ^ g : GrpAb, GrpAbElt -> GrpAb
H ^ g : GrpFin, GrpFinElt -> GrpFin
H ^ u : GrpFP, GrpFPElt -> GrpFP
H ^ g : GrpGPC, GrpGPCElt -> GrpGPC
H ^ g : GrpMat, GrpMatElt -> GrpMat
H ^ g : GrpPC, GrpPCElt -> GrpPC
H ^ g : GrpPerm, GrpPermElt -> GrpPerm
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) : QuadBinElt -> QuadBinElt
Conjugates, Norm and Trace (RATIONAL FIELD)
Conjugates, Norm and Trace (RING OF INTEGERS)
ConjugatePartition(P) : SeqEnum -> SeqEnum
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 (CYCLOTOMIC FIELDS)
Conjugates (QUADRATIC FIELDS)
Groups (OVERVIEW)
Connect(v,w) : GrphResVert,GrphResVert -> GrphRes
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
StronglyConnectedComponents(G) : GrphUnd -> [GrphDir]
Connectedness in a Graph (GRAPHS)
Connectedness, Paths and Circuits (GRAPHS)
Connectedness in a Graph (GRAPHS)
Connectedness, Paths and Circuits (GRAPHS)
ConnectingHomomorphism(f,g,n) : MapChn, MapChn, RngIntElt -> ModMatFldElt
ConnectingHomomorphism(f,g,n) : MapChn, MapChn, RngIntElt -> ModMatFldElt
ConnectionPolynomial(S) : SeqEnum -> RngUPolElt, RngIntElt
CharacteristicPolynomial(S) : SeqEnum -> RngUPolElt, RngIntElt
BerlekampMassey(S) : SeqEnum -> RngUPolElt, RngIntElt
ConnectionNumber(D, p, B) : Inc, IncPt, IncBlk -> RngIntElt
ConnectionNumber(D, p, B) : Inc, IncPt, IncBlk -> RngIntElt
ConnectionPolynomial(S) : SeqEnum -> RngUPolElt, RngIntElt
CharacteristicPolynomial(S) : SeqEnum -> RngUPolElt, RngIntElt
BerlekampMassey(S) : SeqEnum -> RngUPolElt, RngIntElt
Constructions (p-ADIC RINGS AND FIELDS)
Element Constructions and Conversions (LOCAL RINGS AND FIELDS)
Element Constructions and Conversions (LOCAL RINGS AND FIELDS)
RandomConsecutiveBits(n, a, b) : RngIntElt, RngIntElt -> RngIntElt
Consistency(~P: parameters) : Process(pQuot) ->
IsConsistent(G) : GrpGPC -> BoolElt
IsConsistent(G) : GrpPC -> 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
LieConstant_A( RD, r, s) : RootDtm, RngIntElt, RngIntElt -> RngIntElt
CartanInteger( RD, r, s) : RootDtm, RngIntElt, RngIntElt -> RngIntElt
ConstantField(F) : FldFun -> Rng
ConstantMap(X,Y,p) : Sch,Sch,Pt -> MapSch
ConstantWords(C, i) : Code, RngIntElt -> { ModTupFldElt }
DimensionOfExactConstantField(F) : FldFun -> RngIntElt
ExactConstantField(F) : FldFunG -> Rng, Map
HeightConstant(J: parameters) : JacHyp -> FldPrElt, FldPrElt
IsConstant(a) : FldFunElt -> BoolElt, RngElt
IsZero(I) : Map -> BoolElt
LeftStringLength( RD, r, s ) : RootDtm, RngIntElt, RngIntElt -> RngIntElt
LieConstant_epsilon( RD, r, s ) : RootDtm, RngIntElt, RngIntElt -> RngIntElt
LieConstant_eta( RD, r, s ) : RootDtm, RngIntElt, RngIntElt -> RngIntElt
LieConstant_N( RD, r, s ) : RootDtm, RngIntElt, RngIntElt -> RngIntElt
LieConstant_M( RD, r, s, i ) : RootDtm, RngIntElt, RngIntElt, RngIntElt -> RngIntElt
LieConstant_C( RD, i, j, r, s ) : RootDtm, RngIntElt, RngIntElt, RngIntElt, RngIntElt -> RngIntElt
NumberOfConstantWords(C, i) : Code, RngIntElt -> RngIntElt
RightStringLength( RD, r, s ) : RootDtm, RngIntElt, RngIntElt -> RngIntElt
StructureConstant(G, i, j, k) : Grp, RngIntElt, RngIntElt, RngIntElt -> RngIntElt
Constants (REAL AND COMPLEX FIELDS)
DefiningConstantField(F) : FldFun -> Rng
ConstantField(F) : FldFun -> Rng
map< X -> Y | Q > : Sch,Sch,SeqEnum -> MapSch
ConstantMap(X,Y,p) : Sch,Sch,Pt -> MapSch
StructureConstants( RD ) : RootDtm -> RngIntElt
Constants Associated with Crystallographic Root Data (ROOT DATA FOR LIE THEORY)
Constants Associated with Crystallographic Root Data (ROOT DATA FOR LIE THEORY)
ConstantWords(C, i) : Code, RngIntElt -> { ModTupFldElt }
Constituent(C, i) : Cop, RngIntElt -> Struct
AbsolutelyIrreducibleConstituents(M) : ModGrp -> [ ModGrp ]
Constituents(M) : ModRng -> [ ModRng ]
ConstituentsWithMultiplicities(M) : ModRng -> [ <ModRng, RngIntElt> ]
ConstituentsWithMultiplicities(M) : ModRng -> [ <ModRng, RngIntElt> ]
Miscellaneous Graph Constructions (GRAPHS)
Miscellaneous Graph Constructions (GRAPHS)
Constructions (LOCAL RINGS AND FIELDS)
Constraint(L, n) : LP, RngIntElt -> Mtrx, Mtrx, RngIntElt
RemoveConstraint(L, n) : LP, RngIntElt ->
AddConstraints(L, lhs, rhs) : LP, Mtrx, Mtrx ->
NumberOfConstraints(L) : LP -> RngIntElt
ConstructTable(A) : AlgGrp ->
Element Constructions and Conversions (p-ADIC RINGS AND FIELDS)
Element Constructions and Conversions (p-ADIC RINGS AND FIELDS)
GrpSLP_ConstructingHomomorphisms (Example H29E2)
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
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 Braid Groups and their Elements (BRAID GROUPS)
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 of a Base and Strong Generating Set (PERMUTATION GROUPS)
Construction Functions (FINITE SOLUBLE GROUPS)
Construction of Quotient Groups (FINITE SOLUBLE GROUPS)
Construction of Quotient Groups (MATRIX GROUPS)
Construction of Quotient Groups (PERMUTATION GROUPS)
Abelian and p-Quotients (FINITE SOLUBLE GROUPS)
Abelian, Nilpotent and Soluble Quotients (MATRIX GROUPS)
Abelian, Nilpotent and Soluble Quotients (PERMUTATION GROUPS)
Some Basic Families of Codes (LINEAR CODES OVER FINITE FIELDS)
Standard Subgroups (PERMUTATION GROUPS)
Construction of a Subgroup (PERMUTATION GROUPS)
Construction of Subgroups (MATRIX GROUPS)
GrpMat_Constructions (Example H21E10)
Constructions (CLASS FIELD THEORY)
General Constructions (MODULES OVER A MATRIX ALGEBRA)
Point computations (SCHEMES)
Standard Subgroup Constructions (FINITE SOLUBLE GROUPS)
Standard Subgroups (MATRIX GROUPS)
ConstructionX(C1, C2, C3) : Code, Code, Code -> Code
CodeFld_constructionX (Example H101E33)
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
GrpBrd_Constructor (Example H30E1)
GrpGPC_Constructor (Example H23E1)
GrpMat_Constructor (Example H21E3)
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)
Design_Constructors (Example H98E1)
Graph_Constructors (Example H97E1)
Graph_Constructors (Example H97E3)
Graph_Constructors (Example H97E4)
Graph_Constructors (Example H97E5)
GrpPerm_Constructors (Example H20E12)
IncidenceGeometry_Constructors (Example H100E1)
IncidenceGeometry_Constructors (Example H100E2)
IncidenceGeometry_Constructors (Example H100E3)
IncidenceGeometry_Constructors (Example H100E4)
IncidenceGeometry_Constructors (Example H100E5)
IncidenceGeometry_Constructors (Example H100E6)
IncidenceGeometry_Constructors (Example H100E7)
IncidenceGeometry_Constructors (Example H100E8)
Plane_Constructors (Example H99E1)
ConstructTable(A) : AlgGrp ->
RootDtm_consts (Example H33E17)
FacesContaining(N,p) : NwtnPgon,Tup -> SeqEnum
ContainsQuadrangle(P, S) : Plane, { PlanePt } -> BoolElt
ContainsQuadrangle(P, S) : Plane, { PlanePt } -> BoolElt
Content(L) : Lat -> RngElt
Content(w) : MonOrdElt -> SeqEnum[RngIntElt]
Content(u) : MonPlcElt -> SeqEnum[RngIntElt]
Content(f) : RngMPolElt -> RngIntElt
Content(I) : RngOrdFracIdl -> RngIntElt
Content(I) : RngQuadFracIdl -> RngQuadFracIdl
Content(p) : RngUPolElt -> RngIntElt
Content(t) : Tbl -> SeqEnum
ContentAndPrimitivePart(f) : RngMPolElt -> RngIntElt, RngMPolElt
ContentAndPrimitivePart(p) : RngUPolElt -> RngIntElt, RngUPolElt
TableauxOnShapeWithContent(S, C) : SeqEnum[RngIntElt], SeqEnum[RngIntElt] -> SetEnum
TableauxWithContent(C) : SeqEnum[RngIntElt] -> SetEnum
Contpp(f) : RngMPolElt -> RngIntElt, RngMPolElt
Content and Primitive Part (MULTIVARIATE POLYNOMIAL RINGS)
Content and Primitive Part (UNIVARIATE POLYNOMIAL RINGS)
Contpp(f) : RngMPolElt -> RngIntElt, RngMPolElt
Content and Primitive Part (MULTIVARIATE POLYNOMIAL RINGS)
Contpp(f) : RngMPolElt -> RngIntElt, RngMPolElt
ContentAndPrimitivePart(f) : RngMPolElt -> RngIntElt, RngMPolElt
ContentAndPrimitivePart(p) : RngUPolElt -> RngIntElt, RngUPolElt
The Initial Context (MAGMA SEMANTICS)
Comments and Continuation (STATEMENTS AND EXPRESSIONS)
CanContinueEnumeration(P) : GrpFPCosetEnumProc -> BoolElt
ContinueEnumeration(~P: parameters) : GrpFPCosetEnumProc ->
Early Exit from Iterative Statements (STATEMENTS AND EXPRESSIONS)
The continue statement (OVERVIEW)
Early Exit from Iterative Statements (STATEMENTS AND EXPRESSIONS)
ContinuedFraction(r) : FldPrElt -> [ RngIntElt ]
Continued Fractions (REAL AND COMPLEX FIELDS)
Continued Fractions (REAL AND COMPLEX FIELDS)
ContinuedFraction(r) : FldPrElt -> [ RngIntElt ]
ContinueEnumeration(~P: parameters) : GrpFPCosetEnumProc ->
Contpp(f) : RngMPolElt -> RngIntElt, RngMPolElt
ContentAndPrimitivePart(f) : RngMPolElt -> RngIntElt, RngMPolElt
ContentAndPrimitivePart(p) : RngUPolElt -> RngIntElt, RngUPolElt
Contract(e) : GrphEdge -> Grph
Contract(u, v) : GrphVert, GrphVert -> Grph
Contract(S) : { GrphVert } -> Grph
Contraction(D, b) : Inc, IncBlk -> Inc
Contraction(D, p) : Inc, IncPt -> Inc
Constructing Complements, Line Graphs; Contraction, Switching (GRAPHS)
Extension and Contraction of Ideals (IDEAL THEORY AND GRÖBNER BASES)
GenusContribution(g) : GrphRes -> RngIntElt
Control-C key (OVERVIEW)
Controlling Selection of a Base (MATRIX GROUPS)
Quitting (OVERVIEW)
<Ctrl>-\
<Ctrl>-\
<Ctrl>-_
<Ctrl>-A
<Ctrl>-B
Control-C key (OVERVIEW)
<Ctrl>-C
<Ctrl>-C
Quitting (OVERVIEW)
<Ctrl>-D
quit;
<Ctrl>-E
<Ctrl>-F
<Ctrl>-H
<Ctrl>-I
<Ctrl>-J
<Ctrl>-K
<Ctrl>-L
<Ctrl>-M
<Ctrl>-N
<Ctrl>-P
<Ctrl>- space
<Ctrl>-U
<Ctrl>-V<char>
<Ctrl>-W
<Ctrl>-X
<Ctrl>-Y
<Ctrl>-Z
GrpFP_1_ControlExtn (Example H19E15)
Design_conv (Example H98E10)
Convergents(s) : [ RngIntElt ] -> ModMatRngElt
GrpAtc_Conversion (Example H28E9)
GrpRWS_Conversion (Example H27E8)
MonRWS_Conversion (Example H15E8)
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 GEOMETRY)
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)
Conversion to and from Dense-representation Matrices (SPARSE MATRICES)
Conversion to number fields (CLASS FIELD THEORY)
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 Functions (INCIDENCE GEOMETRY)
Converting between Graphs and Digraphs (GRAPHS)
ConvertFromManinSymbol(M, x) : ModSym, Tup -> ModSymElt
Conversion (COXETER GROUPS)
ConvertFromManinSymbol(M, x) : ModSym, Tup -> ModSymElt
Convolution(f, g) : RngSerElt, RngSerElt -> RngSerElt
ConwayPolynomial(p, n) : RngIntElt, RngIntElt -> RngUPolElt
ExistsConwayPolynomial(p, n) : RngIntElt, RngIntElt -> BoolElt, RngUPolElt
IsConway(F) : FldFin -> BoolElt
Conway Polynomials (FINITE FIELDS)
ConwayPolynomial(p, n) : RngIntElt, RngIntElt -> RngUPolElt
Coordelt(L, C) : Lat, [ RngIntElt ] -> LatElt
CoordinatesToElement(L, C) : Lat, [ RngIntElt ] -> LatElt
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(L) : Lat -> Lat
CoordinateRing(L) : Lat -> RngInt
CoordinateRing(A) : Sch -> Rng
CoordinateRing(C) : Sch -> Rng
CoordinateRing(A) : Sch -> RngMPol
CoordinateRing(X) : Sch -> RngMPol
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 H101E12)
GB_Coordinates (Example H66E7)
CoordinateSpace(L) : Lat -> ModTupFld, Map
Coordelt(L, C) : Lat, [ RngIntElt ] -> LatElt
CoordinatesToElement(L, C) : Lat, [ RngIntElt ] -> LatElt
CoordinateVector(L, v) : LatElt -> LatElt
CoordinateVector(v) : LatElt -> LatElt
Choosing Coordinates (PLANE ALGEBRAIC CURVES)
Function Fields and Divisors (PLANE ALGEBRAIC CURVES)
Aggregate (OVERVIEW)
cop< S_1, S_2, ..., S_k > : Struct, Struct, ... -> Cop, [ Map ]
Coproduct_cop (Example H11E1)
Coppersmith(K) : FldFin ->
CoprimeBasis(S) : [ RngIntElt ] -> [ RngIntElt ]
CoprimeBasis(S) : [ RngIntElt ] -> [ RngIntElt ]
COPRODUCTS
CordaroWagnerCode(n) : RngIntElt -> Code
CordaroWagnerCode(n) : RngIntElt -> Code
Core(G, H) : GrpAb, GrpAb -> GrpAb
Core(G, H) : GrpFin, GrpFin -> GrpFin
Core(G, H) : GrpFP, GrpFP -> GrpFP
Core(G, H) : GrpGPC, GrpGPC -> GrpGPC
Core(G, H) : GrpMat, GrpMat -> GrpMat
Core(G, H) : GrpPC, GrpPC -> GrpPC
Core(G, H) : GrpPerm, GrpPerm -> GrpPerm
CoreflectionGroup( W ) : GrpCox -> GrpMat, Map
ReflectionGroup( W ) : GrpCox -> GrpMat, Map
ReflectionMatrices( RD ) : RootDtm -> []
ReflectionMatrix( RD, r ) : RootDtm, RngIntElt -> []
SimpleReflectionMatrices( RD ) : RootDtm -> []
CoreflectionGroup( W ) : GrpCox -> GrpMat, Map
ReflectionGroup( W ) : GrpCox -> GrpMat, Map
CoreflectionMatrices( RD ) : RootDtm -> []
ReflectionMatrices( RD ) : RootDtm -> []
CoreflectionMatrix( RD, r ) : RootDtm, RngIntElt -> []
ReflectionMatrix( RD, r ) : RootDtm, RngIntElt -> []
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, ., . -> .
Actions on Roots and Coroots (COXETER GROUPS)
Operations and Properties for (co)roots (ROOT DATA FOR LIE THEORY)
CorootAction( W ) : GrpCox -> Map
RootAction( W ) : GrpCox -> Map
RootAction( F ) : GrpFP -> Map
GrpCox_CorootAction (Example H34E10)
CorootGSet( W ) : GrpCox -> GSet
RootGSet( W ) : GrpCox -> GSet
CorootHeight( RD, r ) : RootDtm, RngIntElt -> RngIntElt
RootHeight( RD, r ) : RootDtm, RngIntElt -> RngIntElt
CorootNorm( RD, r ) : RootDtm, RngIntElt -> RngIntElt
RootNorm( RD, r ) : RootDtm, RngIntElt -> RngIntElt
CorootNorms( RD ) : RootDtm -> [RngIntElt]
RootNorms( RD ) : RootDtm -> [RngIntElt]
CorootPosition( W, v ) : GrpCox, . -> {@@}
RootPosition( W, v ) : GrpCox, . -> {@@}
RootPosition( G, v ) : GrpLie, . -> {@@}
RootPosition( RD, v ) : RootDtm, . -> {@@}
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
Roots, Coroots and Weights (ROOT DATA FOR LIE THEORY)
CorootSpace( W ) : GrpCox -> .
RootSpace( W ) : GrpCox -> .
RootSpace( RD ) : RootDtm -> .
Combinatorial and Geometrical Structures (OVERVIEW)
LINEAR CODES OVER FINITE FIELDS
LINEAR CODES OVER FINITE RINGS
AutoCorrelation(S, t) : SeqEnum, RngIntElt -> RngIntElt
CorrelationGroup(D) : IncGeom -> GrpPerm
CrossCorrelation(S1, S2, t) : SeqEnum, SeqEnum, RngIntElt -> RngIntElt
Correlation Functions (PSEUDO-RANDOM BIT SEQUENCES)
CorrelationGroup(D) : IncGeom -> GrpPerm
Cos(c) : FldComElt -> FldComElt
Cos(f) : RngSerElt -> RngSerElt
Cos(f) : RngSerElt -> RngSerElt
Cosec(c) : FldComElt -> FldComElt
Cosec(f) : RngSerElt -> RngSerElt
Cosech(s) : FldPrElt -> FldPrElt
CosetAction(G, H) : Grp, Grp -> Hom(Grp), Grp, Grp
CosetAction(G, H) : Grp, Grp -> Hom(Grp), GrpPerm, Grp
CosetAction(G, H) : Grp, Grp -> Hom(Grp), GrpPerm, Grp
CosetAction(G, H) : Grp, Grp -> Hom(Grp), GrpPerm, GrpPC
CosetAction(V) : GrpFPCos, Grp -> Hom(Grp), GrpPerm
CosetAction(P) : GrpFPCosetEnumProc -> Map, GrpPerm, GrpFP
CosetAction(G, H) : GrpGPC, GrpGPC -> Map, GrpPerm, GrpGPC
CosetAction(G, H) : GrpMat, GrpMat -> Hom(Grp), GrpPerm, GrpMat
CosetAction(G, H: parameters) : Grp, Grp -> Hom(Grp), GrpPerm, GrpPerm
CosetDistanceDistribution(C) : Code -> [ <RngIntElt, RngIntElt> ]
CosetEnumerationProcess(G, H: parameters) : GrpFP, GrpFP -> GrpFPCosetEnumProc
CosetGeometry(G, S) : GrpPerm, Set -> CosetGeom
CosetGeometry(G, S, I) : GrpPerm, Set, Set -> CosetGeom
CosetGeometry(D) : IncGeom -> BoolElt, CosetGeom
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) : GrpGPC, GrpGPC -> GrpPerm
CosetImage(G, H) : GrpMat, GrpMat -> GrpPerm
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(G, H) : GrpFP, GrpFP -> GrpFP
CosetKernel(V) : GrpFPCos -> GrpFP
CosetKernel(P) : GrpFPCosetEnumProc -> GrpFP
CosetKernel(G, H) : GrpGPC, GrpGPC -> GrpGPC
CosetKernel(G, H) : GrpMat, GrpMat -> GrpMat
CosetLeaders(C) : Code -> {@ ModTupFldElt @}, Map
CosetRepresentatives(G) : GrpPSL2 -> SeqEnum
CosetRepresentatives(FS) : SymFry -> SeqEnum
CosetSpace(P) : GrpFPCosetEnumProc -> GrpFPCos
CosetSpace(G, H: parameters) : GrpFP, GrpFP: -> GrpFPCos
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(P) : GrpFPCosetEnumProc -> Map
CosetTable(G, H) : GrpGPC, GrpGPC -> Map
CosetTable(G, H) : GrpPC, GrpPC -> Map
CosetTable(G, H: parameters) : GrpFP, GrpFP -> Map
CosetTableToPermutationGroup(G, T) : GrpFP, Map -> GrpPerm
CosetTableToRepresentation(G, T): GrpFP, Map -> Map, GrpPerm, Grp
CosetsSatisfying(P : parameters) : GrpFPCosetEnumProc -> { GrpFPElt }
CosetsSatisfying(T, S: parameters) : Map, { GrpFPElt }: -> { GrpFPCosElt }
DoubleCoset(G, H, g, K ) : GrpFP, GrpFP, GrpFPElt, GrpFP -> GrpFPDcosElt
DoubleCoset(G, H, g, K ) : GrpPerm, GrpPerm, GrpPermElt, GrpPerm -> GrpPermDcosElt
ExistsCosetSatisfying(P : parameters) : GrpFPCosetEnumProc -> BoolElt, GrpFPElt
ExistsNormalisingCoset(P) : GrpFPCosetEnumProc -> BoolElt, GrpFPElt
ExplicitCoset(V, i) : GrpFPCos, RngIntElt -> GrpFPCosElt
HasClosedCosetTable(P) : GrpFPCosetEnumProc -> BoolElt
HasValidCosetTable(P) : GrpFPCosetEnumProc -> BoolElt
IndexedCoset(V, C) : GrpFPCos, GrpFPCosElt -> GrpFPCosElt
IndexedCoset(V, w) : GrpFPCos, GrpFPElt -> GrpFPCosElt
RightCosetSpace(P) : GrpFPCosetEnumProc -> GrpFPCos
RightCosetSpace(G, H: parameters) : GrpFP, GrpFP -> GrpFPCos
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)
Action on a Coset Space (PERMUTATION GROUPS)
Interactive Coset Enumeration (FP GROUPS - ADVANCED FEATURES)
Coset Leaders (LINEAR CODES OVER FINITE FIELDS)
RightTransversal(G, H) : GrpAb, GrpAb -> {@ GrpAbElt @}, Map
Coset Spaces (ABELIAN GROUPS)
Coset Spaces (POLYCYCLIC GROUPS)
Coset Spaces: Construction (FINITELY PRESENTED GROUPS)
Action on a Coset Space (GROUPS)
Coset Spaces and Tables (FINITELY PRESENTED GROUPS)
Coset Tables (FINITELY PRESENTED GROUPS)
RightTransversal(G, H) : GrpMat, GrpMat -> {@ GrpMatElt @}, Map
Coset Tables and Transversals (MATRIX GROUPS)
Coset Tables and Transversals (FINITE SOLUBLE GROUPS)
CosetAction(G, H) : Grp, Grp -> Hom(Grp), Grp, Grp
CosetAction(G, H) : Grp, Grp -> Hom(Grp), GrpPerm, Grp
CosetAction(G, H) : Grp, Grp -> Hom(Grp), GrpPerm, Grp
CosetAction(G, H) : Grp, Grp -> Hom(Grp), GrpPerm, GrpPC
CosetAction(V) : GrpFPCos, Grp -> Hom(Grp), GrpPerm
CosetAction(P) : GrpFPCosetEnumProc -> Map, GrpPerm, GrpFP
CosetAction(G, H) : GrpGPC, GrpGPC -> Map, GrpPerm, GrpGPC
CosetAction(G, H) : GrpMat, GrpMat -> Hom(Grp), GrpPerm, GrpMat
CosetAction(G, H: parameters) : Grp, Grp -> Hom(Grp), GrpPerm, GrpPerm
GrpGPC_CosetAction (Example H23E8)
GrpMat_CosetAction (Example H21E25)
Grp_CosetAction (Example H16E9)
CosetDistanceDistribution(C) : Code -> [ <RngIntElt, RngIntElt> ]
CosetEnumerationProcess(G, H: parameters) : GrpFP, GrpFP -> GrpFPCosetEnumProc
CosetGeometry(G, S) : GrpPerm, Set -> CosetGeom
CosetGeometry(G, S, I) : GrpPerm, Set, Set -> CosetGeom
CosetGeometry(D) : IncGeom -> BoolElt, CosetGeom
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) : GrpGPC, GrpGPC -> GrpPerm
CosetImage(G, H) : GrpMat, GrpMat -> GrpPerm
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(G, H) : GrpFP, GrpFP -> GrpFP
CosetKernel(V) : GrpFPCos -> GrpFP
CosetKernel(P) : GrpFPCosetEnumProc -> GrpFP
CosetKernel(G, H) : GrpGPC, GrpGPC -> GrpGPC
CosetKernel(G, H) : GrpMat, GrpMat -> GrpMat
CosetLeaders(C) : Code -> {@ ModTupFldElt @}, Map
CodeFld_CosetLeaders (Example H101E13)
CosetRepresentatives(G) : GrpPSL2 -> SeqEnum
CosetRepresentatives(FS) : SymFry -> SeqEnum
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
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)
Action on a Coset Space (FINITE SOLUBLE GROUPS)
Cosets and Transversals (PERMUTATION GROUPS)
CosetSatisfying(P : parameters) : GrpFPCosetEnumProc -> { GrpFPElt }
CosetsSatisfying(P : parameters) : GrpFPCosetEnumProc -> { GrpFPElt }
CosetsSatisfying(T, S: parameters) : Map, { GrpFPElt }: -> { GrpFPCosElt }
GrpFP_1_CosetSatisfying (Example H19E51)
CosetSpace(P) : GrpFPCosetEnumProc -> GrpFPCos
CosetSpace(G, H: parameters) : GrpFP, GrpFP: -> GrpFPCos
GrpFP_1_CosetSpace (Example H19E47)
Coset Spaces and Transversals (FP GROUPS - ADVANCED FEATURES)
CosetSatisfying(P : parameters) : GrpFPCosetEnumProc -> { GrpFPElt }
CosetsSatisfying(P : parameters) : GrpFPCosetEnumProc -> { GrpFPElt }
CosetsSatisfying(T, S: parameters) : Map, { GrpFPElt }: -> { GrpFPCosElt }
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(P) : GrpFPCosetEnumProc -> Map
CosetTable(G, H) : GrpGPC, GrpGPC -> Map
CosetTable(G, H) : GrpPC, GrpPC -> Map
CosetTable(G, H: parameters) : GrpFP, GrpFP -> Map
GrpGPC_CosetTable (Example H23E7)
GrpFP_1_CosetTable1 (Example H19E45)
GrpFP_1_CosetTable2 (Example H19E46)
CosetTableToPermutationGroup(G, T) : GrpFP, Map -> GrpPerm
CosetTableToRepresentation(G, T): GrpFP, Map -> Map, GrpPerm, Grp
Cosh(s) : FldPrElt -> FldPrElt
Cosh(f) : RngSerElt -> RngSerElt
Cosh(f) : RngSerElt -> RngSerElt
GrpPC_cossey_hawkes (Example H24E7)
Cot(c) : FldComElt -> FldComElt
Cot(f) : RngSerElt -> RngSerElt
Coth(s) : FldPrElt -> FldPrElt
NFSCycleCount(n, F, tuple) : RngIntElt, RngMPolElt, Tup -> RngIntElt
Counting Points on the Jacobian (HYPERELLIPTIC CURVES)
Tableau_CountStandardTab (Example H96E25)
Tableau_CountTabAlph-Binomial (Example H96E26)
Covalence(D, s) : Dsgn, RngIntElt -> RngIntElt
Covalence(D, S) : Inc, { IncPt } -> RngIntElt
ProjectiveCover(M) : ModAlg -> ModAlg, ModMatFldElt, SeqEnum[ModMatFldElt], SeqEnum[ModMatFldElt], SeqEnum[RngIntElt]
CoveringRadius(C) : Code -> RngIntElt
CoveringRadius(L) : Lat -> FldRatElt
CoveringStructure(S, T) : Str, Str -> Str
ExistsCoveringStructure(S, T) : Str, Str -> BoolElt, Str
CoveringRadius(C) : Code -> RngIntElt
CoveringRadius(L) : Lat -> FldRatElt
CodeFld_CoveringRadius (Example H101E24)
CoveringStructure(S, T) : Str, Str -> Str
PartitionCovers(P1, P2) : SeqEnum, SeqEnum -> BoolElt
Projective Covers (BASIC ALGEBRAS)
CoweightLattice( G ) : RootDtm -> Lat
WeightLattice( G ) : RootDtm -> Lat
WeightLattice( RD ) : RootDtm -> Lat
WeightLattice( W ) : RootDtm -> Lat
CoweightLattice( G ) : RootDtm -> Lat
WeightLattice( G ) : RootDtm -> Lat
WeightLattice( RD ) : RootDtm -> Lat
WeightLattice( W ) : RootDtm -> Lat
FundamentalCoweights( W ) : GrpCox -> SeqEnum
FundamentalWeights( W ) : GrpCox -> SeqEnum
FundamentalWeights( G ) : GrpLie -> SeqEnum
FundamentalWeights( RD ) : RootDtm -> Mtrx
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, W) : Cat, GrpCox -> GrpFP, Map
CoxeterGroup( GrpFP, t ) : Cat, MonStgElt -> GrpFP
CoxeterGroup(GrpFP, t) : Cat, MonStgElt -> GrpFP
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) : GrpMat : ->
ToddCoxeterSchreier(G: parameters) : GrpPerm : ->
GrpFP_1_Coxeter (Example H19E10)
Construction of the Standard Presentation for a Coxeter Group (FINITELY PRESENTED GROUPS)
COXETER GROUPS
COXETER GROUPS
CoxeterElement( G ) : GrpCox -> GrpPermElt
CoxeterElement( W ) : GrpCox -> GrpPermElt
CoxeterElement( F ) : GrpFP -> SeqEnum
DualCoxeterForm( RD ) : RootDtm -> AlgMatElt
CoxeterForm( RD ) : RootDtm -> AlgMatElt
CoxeterGroup( GrpFP, W ) : Cat, GrpCox -> GrpFP, Map
CoxeterGroup(GrpFP, W) : Cat, GrpCox -> GrpFP, Map
CoxeterGroup( GrpFP, t ) : Cat, MonStgElt -> GrpFP
CoxeterGroup(GrpFP, t) : Cat, MonStgElt -> GrpFP
CoxeterGroup( F ) : GrpFP -> GrpCox, Map
CoxeterGroup( t ) : MonStgElt -> GrpCox
CoxeterGroup( RD ) : RootDtm -> GrpCox
CoxeterGroup( RD ) : RootDtm -> RngIntElt
CoxeterLength( W, w ) : GrpCox, GrpPermElt -> RngIntElt
Length( W, w ) : GrpCox, GrpPermElt -> RngIntElt
CoxeterNumber( G ) : GrpCox -> GrpPermElt
CoxeterNumber( W ) : GrpCox -> GrpPermElt
Timing (OVERVIEW)
Timing (OVERVIEW)
Cputime() : -> FldReElt
Cputime(t) : FldReElt -> FldReElt
FldAC_Create (Example H52E1)
GrpCox_Create (Example H34E1)
GrpLie_Create (Example H35E1)
GrpMat_Create (Example H21E1)
Mat_Create (Example H59E1)
ModRng_Create (Example H62E5)
PMod_Create (Example H68E1)
RngGal_Create (Example H46E1)
RngGal_Create (Example H46E2)
SMat_Create (Example H60E1)
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 elements (ORDERS AND ALGEBRAIC FIELDS)
Creation of G-Lattices (LATTICES)
Creation of p-adic Rings and Fields (p-ADIC RINGS AND FIELDS)
Creation of Structures (ALGEBRAIC FUNCTION FIELDS)
Creation of structures (ORDERS AND ALGEBRAIC FIELDS)
Creation of Tableaux (PARTITIONS, WORDS AND YOUNG TABLEAUX)
Subspaces (ALGEBRAIC FUNCTION FIELDS)
ModDed_create (Example H63E1)
Creation of Elements (ALGEBRAIC FUNCTION FIELDS)
Newton_create-ex (Example H54E1)
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 of Structures (ALGEBRAIC FUNCTION FIELDS)
Subspaces (ALGEBRAIC FUNCTION FIELDS)
ModGrp_CreateA4wrC3 (Example H78E4)
ModGrp_CreateA7 (Example H78E6)
FldRe_CreateComplexField (Example H41E3)
FldRe_CreateElements (Example H41E4)
ModRng_CreateHom (Example H62E6)
ModRng_CreateHom (Example H62E7)
ModAlg_CreateHomGHom (Example H77E12)
ModFld_CreateK35 (Example H61E2)
ModAlg_CreateK6 (Example H77E1)
ModGrp_CreateL27 (Example H78E1)
ModAlg_CreateLattice (Example H77E9)
ModGrp_CreateM11 (Example H78E3)
ModGrp_CreateM12 (Example H78E5)
ModGrp_CreateMatrices (Example H78E2)
ModGrp_CreatePolyAction (Example H78E7)
ModFld_CreateQ6 (Example H61E1)
Grp_CreateSubgroupPoset (Example H16E16)
ModRng_CreateZ6 (Example H62E1)
RootDtm_CreatingRootData (Example H33E3)
Creation (CHAIN COMPLEXES)
Creation of Elements (BRANDT MODULES)
Operations on Elements (BRANDT MODULES)
AlgAff_Creation (Example H67E1)
AlgMat_Creation (Example H73E1)
CrvEll_Creation (Example H87E1)
CrvHyp_Creation (Example H88E1)
FldFunG_Creation (Example H53E1)
GrpAbGen_Creation (Example H17E1)
GrpPSL2_Creation (Example H31E2)
ModSym_Creation (Example H90E1)
RngOrd_Creation (Example H48E1)
RngPol_Creation (Example H42E1)
RngSer_Creation (Example H56E1)
Alternative Models (ELLIPTIC CURVES)
Ambient Spaces (MODULAR FORMS)
Ambient Spaces (MODULAR SYMBOLS)
Ambient Spaces ({THE MODULE OF}{SUPERSINGULAR POINTS})
Cartesian Product Constructor and Functions (TUPLES AND CARTESIAN PRODUCTS)
Changing the Base Ring (ELLIPTIC CURVES)
Constructing Automorphism Groups (INCIDENCE STRUCTURES AND DESIGNS)
Constructing Schemes (SCHEMES)
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 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 OF 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 (CLASS FIELD THEORY)
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 Functions ({THE MODULE OF}{SUPERSINGULAR POINTS})
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 Algebraic Function Fields (ALGEBRAIC FUNCTION FIELDS)
Creation of Algebraic Function Fields and their Orders (ALGEBRAIC FUNCTION FIELDS)
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 (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 DEDEKIND DOMAINS)
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 Lazy Series Rings (LAZY POWER SERIES RINGS)
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 DEDEKIND DOMAINS)
Creation of New Lists (LISTS)
Creation of Newton Polygons (NEWTON POLYGONS)
Creation of Orders of Algebraic Function Fields (ALGEBRAIC FUNCTION FIELDS)
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 Sparse Matrices (SPARSE MATRICES)
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 (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)
Elements ({THE MODULE OF}{SUPERSINGULAR POINTS})
Explicit Creation (SCHEMES)
Free Groups and Words (FINITELY PRESENTED GROUPS)
General Function Field Places (ALGEBRAIC FUNCTION FIELDS)
Global Function Field Places (ALGEBRAIC FUNCTION FIELDS)
Hom_(R)(M, N) for matrix modules (FREE MODULES)
Hom_(R)(M, N) for R-modules (FREE MODULES)
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)
Subspaces ({THE MODULE OF}{SUPERSINGULAR POINTS})
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)
AlgGrp_creation (Example H74E1)
FldCyc_creation (Example H50E1)
FldQuad_creation (Example H49E1)
ModSS_Creation of elements (Example H92E2)
ModSS_Creation of spaces (Example H92E1)
ModSS_Creation of subspaces (Example H92E3)
Creation and Access Functions (QUATERNION ALGEBRAS)
ModSym_Creation-Ambient (Example H90E2)
Ambient Spaces (MODULAR FORMS)
Ambient Spaces (MODULAR SYMBOLS)
Ambient Spaces ({THE MODULE OF}{SUPERSINGULAR POINTS})
Creation of Vector Spaces and Arithmetic with Vectors (VECTOR SPACES)
Creation by Hand (RESOLUTION GRAPHS AND SPLICE DIAGRAMS)
Scheme_creation-by-subspace (Example H83E34)
Changing the Base Ring (ELLIPTIC CURVES)
CharacterRing(G) : Grp -> AlgChtr
Structure Creation (CHARACTERS OF FINITE GROUPS)
GrpPSL2_Creation-CongruenceSubgroups (Example H31E5)
Construction of a Coset Geometry (INCIDENCE GEOMETRY)
Creation of a Modular Curve (MODULAR CURVES)
Creation of an Elliptic Curve (ELLIPTIC CURVES)
Construction of a General Digraph (GRAPHS)
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 (INTRODUCTION [BASIC RINGS])
Creation of Elements (POWER, LAURENT AND PUISEUX SERIES)
General Function Field Places (ALGEBRAIC FUNCTION FIELDS)
Global Function Field Places (ALGEBRAIC FUNCTION FIELDS)
Creation of Elements (MODULAR SYMBOLS)
Elements (MODULAR FORMS)
Elements ({THE MODULE OF}{SUPERSINGULAR POINTS})
ModSym_Creation-Elements-1 (Example H90E4)
ModSym_Creation-Elements-2 (Example H90E6)
RngLoc_creation-ex (Example H55E3)
Creation of Algebraic Function Fields (ALGEBRAIC FUNCTION FIELDS)
The Record Format Constructor (RECORDS)
Creation from Curve Singularities (RESOLUTION GRAPHS AND SPLICE DIAGRAMS)
Creation from Pencils (RESOLUTION GRAPHS AND SPLICE DIAGRAMS)
Construction of a General Group (GROUPS)
Construction of a General Permutation Group (PERMUTATION GROUPS)
Creation of a Matrix Group (MATRIX GROUPS)
Construction of a General Matrix Group (MATRIX GROUPS)
Construction of a General Graph (GRAPHS)
Creation of Subgroups of PSL_2(R) (SUBGROUPS OF PSL_2(R))
Creation (SUBGROUPS OF PSL_2(R))
Hom_(R)(M, N) for matrix modules (FREE MODULES)
Creation of a Hyperelliptic Curve (HYPERELLIPTIC CURVES)
Construction of New Ideals (IDEAL THEORY AND GRÖBNER BASES)
Construction of an Incidence Geometry (INCIDENCE GEOMETRY)
KSpace(K, n, F) : Fld, RngIntElt, Mtrx -> ModTupFld
Construction of a Vector Space with Inner Product Matrix (VECTOR SPACES)
Creation of a Kummer Surface (HYPERELLIPTIC CURVES)
Labels (MODULAR FORMS)
Construction of a Vector Space (VECTOR SPACES)
Predicates on Curve Models (ELLIPTIC CURVES)
Predicates on Curve Models (HYPERELLIPTIC CURVES)
Alternative Models (ELLIPTIC CURVES)
Definition of a Module (FREE MODULES)
Other Ring Constructions (INTRODUCTION [BASIC RINGS])
Creation Predicates (ELLIPTIC CURVES)
Creation Predicates (HYPERELLIPTIC CURVES)
Creating a Record (RECORDS)
FldFunG_creation-rel (Example H53E2)
The Construction of Related Structures (INCIDENCE STRUCTURES AND DESIGNS)
Creation of Orders of Algebraic Function Fields (ALGEBRAIC FUNCTION FIELDS)
ModForm_Creation-Space (Example H93E3)
ModSym_Creation-Spaces (Example H90E3)
Labels (MODULAR SYMBOLS)
Creation (SUBGROUPS OF PSL_2(R))
Creation of Structures (ALGEBRAIC FUNCTION FIELDS)
Creation of Structures (ALGEBRAIC FUNCTION FIELDS)
Subspaces ({THE MODULE OF}{SUPERSINGULAR POINTS})
Construction of Elements (GROUPS)
Creation of a Permutation Group (PERMUTATION GROUPS)
FldFunG_creation_herm (Example H53E3)
Creation Predicates (ELLIPTIC CURVES)
ModForm_CreationElements (Example H93E5)
EllipticCurveDatabase(: parameters) : -> DB
CremonaDatabase(: parameters) : -> DB
CremonaReference(D, E) : CrvEll -> MonStgElt
Scheme_cremona-factorisation (Example H83E28)
EllipticCurveDatabase(: parameters) : -> DB
CremonaDatabase(: parameters) : -> DB
CremonaReference(D, E) : CrvEll -> MonStgElt
CrossCorrelation(S1, S2, t) : SeqEnum, SeqEnum, RngIntElt -> RngIntElt
CrossCorrelation(S1, S2, t) : SeqEnum, SeqEnum, RngIntElt -> RngIntElt
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
Automorphisms of Conics (RATIONAL CURVES AND CONICS)
Conics (RATIONAL CURVES AND CONICS)
Isomorphisms of Conics (RATIONAL CURVES AND CONICS)
Rational Points on Conics (RATIONAL CURVES AND CONICS)
Conics (RATIONAL CURVES AND CONICS)
Rational Points on Conics (RATIONAL CURVES AND CONICS)
Automorphisms of Conics (RATIONAL CURVES AND CONICS)
Isomorphisms of Conics (RATIONAL CURVES AND CONICS)
Access Functions (RATIONAL CURVES AND CONICS)
Automorphisms (RATIONAL CURVES AND CONICS)
Introduction (RATIONAL CURVES AND CONICS)
Isomorphisms (RATIONAL CURVES AND CONICS)
Isomorphisms with Standard Models (RATIONAL CURVES AND CONICS)
Rational Curve and Conic Creation (RATIONAL CURVES AND CONICS)
Rational Curves and Conics (RATIONAL CURVES AND CONICS)
Automorphisms (RATIONAL CURVES AND CONICS)
Introduction (RATIONAL CURVES AND CONICS)
Isomorphisms (RATIONAL CURVES AND CONICS)
Rational Curves and Conics (RATIONAL CURVES AND CONICS)
Access Functions (RATIONAL CURVES AND CONICS)
Rational Curve and Conic Creation (RATIONAL CURVES AND CONICS)
Isomorphisms with Standard Models (RATIONAL CURVES AND CONICS)
Combinatorial and Geometrical Structures (OVERVIEW)
Combinatorial and Geometrical Structures (OVERVIEW)
Maps and Curves (PLANE ALGEBRAIC CURVES)
Projective Closure and Affine Patches (PLANE ALGEBRAIC CURVES)
Automorphisms of Rational Curves (RATIONAL CURVES AND CONICS)
Isomorphisms of Rational Curves (RATIONAL CURVES AND CONICS)
Automorphisms of Rational Curves (RATIONAL CURVES AND CONICS)
Isomorphisms of Rational Curves (RATIONAL CURVES AND CONICS)
IsCrystallographic( C ) : AlgMatElt -> BoolElt
IsCrystallographic( W ) : GrpCox -> BoolElt
IsCrystallographic( RD ) : RootDtm -> BoolElt
Cunningham(b, k, c) : RngIntElt, RngIntElt, RngIntElt -> SeqEnum
Sets (OVERVIEW)
Sets (OVERVIEW)
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(p) : Process -> RngIntElt, RngIntElt
CurrentLabel(p) : Process -> RngIntElt, RngIntElt
CurrentLabel(p) : Process -> RngIntElt, RngIntElt, RngIntElt
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(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, MapIsoSch, MapIsoSch
EllipticCurve(C, P) : Crv, Pt -> CrvEll, Map, Map
EllipticCurve(C,p) : Crv, Pt -> CrvEll, Map, Map
EllipticCurve(C) : CrvHyp -> CrvEll, MapIsoSch, MapIsoSch
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
HasCurve(F) : FldFun -> BoolElt
HyperellipticCurve(E) : CrvEll -> CrvHyp, Map
HyperellipticCurve(h, f) : RngUPolElt, RngUPolElt -> CrvHyp
HyperellipticCurveFromIgusaClebsch(S) : SeqEnum -> CrvHyp
HyperellipticCurveOfGenus(g, h, f) : RngIntElt, RngUPolElt, RngUPolElt -> CrvHyp
IsCurve(X) : Sch -> BoolElt,Crv
IsEllipticCurve(C) : CrvHyp -> BoolElt, CrvEll, MapIsoSch, MapIsoSch
IsEllipticCurve(C) : CrvHyp -> BoolElt, CrvEll, MapIsoSch, MapIsoSch
IsEllipticCurve([a,b]) : [ RngElt ] -> BoolElt, CrvEll
IsHyperellipticCurve([h, g]) : [ RngUPolElt ] -> BoolElt, CrvHyp
IsHyperellipticCurveOfGenus(g, [h, f]) : RngIntElt, [RngUPolElt] -> BoolElt, CrvHyp
IsRationalCurve(C) : 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) : Prj, RngMPolElt -> CrvRat
ReduceCurve(C) : CrvHyp -> CrvHyp
Scheme(P) : SetPtEll -> CrvEll
SupersingularEllipticCurve(K) : FldFin -> CrvEll
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
Crv_curve-base-change (Example H84E2)
Crv_curve-differentials (Example H84E12)
Crv_curve-hessian (Example H84E3)
Crv_curve-iscusp (Example H84E4)
Creating a Hyperelliptic Curve from Invariants (HYPERELLIPTIC CURVES)
CurveDivisor(D) : DivFunElt -> DivCrvElt
Div ! D : DivCrv, DivFunElt -> DivCrvElt
CrvHyp_CurveFromIgusa (Example H88E5)
Genus and Singularities (PLANE ALGEBRAIC CURVES)
Global Geometry (PLANE ALGEBRAIC CURVES)
CurvePlace(P) : PlcFunElt -> PlcCrvElt
S ! P : PlcCrv, PlcFunElt -> PlcCrvElt
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
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)
Basic Attributes (PLANE ALGEBRAIC CURVES)
Base Change (PLANE ALGEBRAIC CURVES)
Creation (PLANE ALGEBRAIC CURVES)
Scheme_curves-in-space (Example H83E36)
Basic Invariants (PLANE ALGEBRAIC CURVES)
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
GrpPSL2_cusp-example (Example H31E4)
CuspidalSubspace(M) : ModBrdt -> ModBrdt
CuspidalSubspace(M) : ModFrm -> ModFrm
CuspidalSubspace(M) : ModSS -> ModSS
CuspidalSubspace(M) : ModSym -> ModSym
IsCuspidal(M) : ModBrdt -> BoolElt
IsCuspidal(M) : ModFrm -> BoolElt
IsCuspidal(M) : ModSym -> BoolElt
ModSym_CuspidalSubgroup (Example H90E21)
ModSym_CuspidalSubgroupTable (Example H90E22)
CuspidalSubspace(M) : ModBrdt -> ModBrdt
CuspidalSubspace(M) : ModFrm -> ModFrm
CuspidalSubspace(M) : ModSS -> ModSS
CuspidalSubspace(M) : ModSym -> ModSym
Cusps(G) : GrpPSL2 -> SeqEnum
Cusps(FS) : SymFry -> SeqEnum
UpperHalfPlaneWithCusps() : -> SpcHyp
Cusps and elliptic points of congruence subgroups (SUBGROUPS OF PSL_2(R))
Cusps and elliptic points of congruence subgroups (SUBGROUPS OF PSL_2(R))
CuspWidth(G,x) : GrpPSL2, SetCspElt -> RngIntElt
CutVertices(G) : Grph -> { GrphVert }
CutVertices(G) : Grph -> { GrphVert }
Cycle(e, x) : GrpPermElt, Elt -> SetIndx
CycleStructure(g) : GrpPermElt -> [ <RngIntElt, RngIntElt> ]
GirthCycle(G) : GrphUnd -> [GrphVert]
CycleStructure(g) : GrpPermElt -> [ <RngIntElt, RngIntElt> ]
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
Construction of General Cyclic Codes (LINEAR CODES OVER FINITE RINGS)
Cyclic and Quasicyclic Codes (LINEAR CODES OVER FINITE FIELDS)
FldAC_Cyclic6 (Example H52E5)
GB_Cyclic6 (Example H66E2)
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 H101E5)
CodeRng_CyclicCode (Example H102E4)
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) : 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> ]
CyclotomicField(m) : RngIntElt -> FldCyc
CyclotomicOrder(K) : FldCyc -> RngIntElt
CyclotomicPolynomial(m) : RngIntElt -> RngUPolElt
Z4CyclotomicFactors(n) : RngIntElt -> [RngUPolElt]
CYCLOTOMIC FIELDS
Functions Returning a Scalar (CHARACTERS OF FINITE GROUPS)
Rings, Fields, and Algebras (OVERVIEW)
FldAb_cyclotomic-extension (Example H51E8)
CyclotomicField(m) : RngIntElt -> FldCyc
CyclotomicOrder(K) : FldCyc -> RngIntElt
CyclotomicPolynomial(m) : RngIntElt -> RngUPolElt
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