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

Index B


B-key

B

b-key

b

Bach

BachBound(K) : FldNum -> RngIntElt

BachBound

BachBound(K) : FldNum -> RngIntElt

backspace-key

<Delete>
<Backspace>

Bad

BadPrimes(E) : CrvEll -> [ RngIntElt ]
BadPrimes(C) : CrvHyp -> SeqEnum
BadPrimes(J) : JacHyp -> SeqEnum

BadPrimes

BadPrimes(E) : CrvEll -> [ RngIntElt ]
BadPrimes(C) : CrvHyp -> SeqEnum
BadPrimes(J) : JacHyp -> SeqEnum

Baer

BaerDerivation(q2) : RngIntElt -> PlaneAff, PlanePtSet, PlaneLnSet
BaerSubplane(P) : PlaneProj -> PlaneProj, PlanePtSet, PlaneLnSet

baer

Plane_baer (Example H95E14)

BaerDerivation

BaerDerivation(q2) : RngIntElt -> PlaneAff, PlanePtSet, PlaneLnSet

BaerSubplane

BaerSubplane(P) : PlaneProj -> PlaneProj, PlanePtSet, PlaneLnSet

Balanced

IsBalanced(D, t: parameters) : Inc, RngIntElt -> BoolElt, RngIntElt

Ball

Ball(u, n) : GrphVert, RngIntElt -> { GrphVert }
Ball(u, n) : Vert, RngIntElt -> { GrphVert }

Bang

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

Base

Base(G) : GrpMat -> [Elt]
Base(G) : GrpPerm -> [Elt]
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
BaseComponent(L) : LinSys -> SchProj
BaseCurve(X) : CrvMod -> CrvMod, MapSch
BaseExtend(G, R) : GrpDrch, Rng -> GrpDrch
BaseExtend(G, R, z) : GrpDrch, Rng, RngElt -> GrpDrch
BaseExtend(M,R) : ModBrdt, Rng -> ModBrdt
BaseExtend(M, phi) : ModFrm, Map -> ModFrm, Map
BaseExtend(M, R) : ModFrm, Rng -> ModFrm, Map
BaseField(A) : AlgQuat -> Fld
BaseField(Q) : FldRat -> FldRat
BaseField(J) : JacHyp -> Fld
CoefficientRing(J) : JacHyp -> Rng
BaseField(C) : Sch -> Fld
CoefficientRing(C) : Sch -> Fld
BaseField(K) : SrfKum -> Fld
CoefficientRing(K) : SrfKum -> Rng
BaseImage(x) : GrpPermElt -> [Elt]
BaseMPolynomial(n, m, d) : RngIntElt, RngIntElt, RngIntElt -> RngMPolElt
BaseModule(R, S) : AlgMat, Rng -> ModTup
BasePoint(G, i) : GrpMat, RngIntElt -> Elt
BasePoint(G, i) : GrpPerm, RngIntElt -> Elt
BasePoints(L) : LinSys -> SeqEnum
BasePoints(f) : MapSch -> SetEnum
BaseRing(B) : AlgBas -> Rng
BaseRing(R) : AlgMat -> Rng
BaseRing(S) : AlgQuatOrd -> Rng
BaseRing(E) : CrvEll -> Rng
BaseRing(F) : Fld -> Rng
CoefficientRing(F) : FldFun -> Rng
BaseRing(F) : FldFunRat -> Rng
BaseRing( G ) : GrpLie -> Rng
BaseRing(G) : GrpPSL2 -> Rng
BaseRing(L) : Lat -> Rng
BaseRing(M) : ModBrdt -> Rng
BaseRing(M) : ModOrd -> Rng
BaseRing(A) : Mtrx -> Rng
BaseRing(F) : RngFunOrd -> Rng
BaseRing(P) : RngMPol -> Rng
BaseRing(O) : RngOrd -> Rng
BaseRing(R) : RngSer -> Rng
BaseRing(P) : RngUPol -> Rng
BaseRing(C) : Sch -> Rng
BaseField(C) : Sch -> Fld
BaseRing(X) : Sch -> Rng
BaseRing(G) : SchGrpEll -> Rng
BaseScheme(L) : LinSys -> SchProj
BaseScheme(f) : MapSch -> Sch
ChangeBase(~G, Q) : GrpPerm, [Elt] ->
ChangeRing(L, S) : Lat, Rng -> Lat, Map
BaseExtend(L, S) : Lat, Rng -> Lat, Map
CoefficientField(V) : ModTupFld -> Fld
CoefficientRing(A) : AlgGen -> Rng
CoefficientRing(G) : GrpMat -> Rng
CoefficientRing(M) : ModMPol -> ModMPol
CoefficientRing(M) : ModTupRng -> Rng
CoefficientRing(M) : ModTupRng -> Rng
CoefficientRing(X) : Sch -> Fld
GoodBasePoints(G: parameters) : GrpMat -> []
GroundField(F) : FldAlg -> Fld
IsBasePointFree(L) : LinSys -> BoolElt

base

Base and Strong Generating Set (MATRIX GROUPS)
Base and Strong Generating Set (PERMUTATION GROUPS)
Base Change (PLANE ALGEBRAIC CURVES)
Base Change for Schemes (SCHEMES)
Base Extension (MODULAR FORMS)
Base Ring and Base Change (LATTICES)
Construction of a Base and Strong Generating Set (PERMUTATION GROUPS)

base-change-schemes

Scheme_base-change-schemes (Example H81E9)

base-extend

Base Extension (MODULAR FORMS)

base-ring

BaseChange(L, S) : Lat, Rng -> Lat, Map
BaseExtend(L, S) : Lat, Rng -> Lat, Map
Base Ring and Base Change (LATTICES)

base_change_curve

Changing the Base Ring (HYPERELLIPTIC CURVES)

base_change_jacobian

BaseExtend(J, n) : JacHyp, RngIntElt -> JacHyp
Changing the Base Ring (HYPERELLIPTIC CURVES)

base_field_kummer

BaseExtend(K, n): SrfKum, RngIntElt -> SrfKum
Changing the Base Ring (HYPERELLIPTIC CURVES)

base_ring_curve

BaseRing(C) : Sch -> Fld
CoefficientRing(C) : Sch -> Fld
Base Ring (HYPERELLIPTIC CURVES)

base_ring_jacobian

BaseRing(J) : JacHyp -> Rng
CoefficientRing(J) : JacHyp -> Rng
Base Ring (HYPERELLIPTIC CURVES)

base_ring_kummer

BaseRing(K) : SrfKum -> Rng
CoefficientRing(K) : SrfKum -> Rng
Base Ring (HYPERELLIPTIC CURVES)

BaseChange

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

BaseChangeMatrix

BaseChangeMatrix(A) : AlgBas -> ModAlg

BaseComponent

BaseComponent(L) : LinSys -> SchProj

BaseCurve

BaseCurve(X) : CrvMod -> CrvMod, MapSch

BaseExtend

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(X, n) : Sch, RngIntElt -> Sch
BaseChange(A,K) : Sch,Rng -> 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
BaseExtend(G, R) : GrpDrch, Rng -> GrpDrch
BaseExtend(G, R, z) : GrpDrch, Rng, RngElt -> GrpDrch
BaseExtend(M,R) : ModBrdt, Rng -> ModBrdt
BaseExtend(M, phi) : ModFrm, Map -> ModFrm, Map
BaseExtend(M, R) : ModFrm, Rng -> ModFrm, Map
ChangeRing(L, S) : Lat, Rng -> Lat, Map
CrvEll_BaseExtend (Example H85E2)
ModForm_BaseExtend (Example H90E4)

BaseExtension

CrvHyp_BaseExtension (Example H86E2)

BaseField

BaseRing(A) : AlgQuat -> Fld
BaseField(A) : AlgQuat -> Fld
BaseField(Q) : FldRat -> FldRat
BaseField(J) : JacHyp -> Fld
BaseField(C) : Sch -> Fld
BaseField(K) : SrfKum -> Fld
BaseRing(F) : Fld -> Rng
BaseRing(C) : Sch -> Rng
CoefficientField(V) : ModTupFld -> Fld
CoefficientRing(X) : Sch -> Fld
GroundField(F) : FldAlg -> Fld

BaseImage

BaseImage(x) : GrpPermElt -> [Elt]

BaseModule

BaseModule(R, S) : AlgMat, Rng -> ModTup

BaseMPolynomial

BaseMPolynomial(n, m, d) : RngIntElt, RngIntElt, RngIntElt -> RngMPolElt

BasePoint

BasePoint(G, i) : GrpMat, RngIntElt -> Elt
BasePoint(G, i) : GrpPerm, RngIntElt -> Elt

BasePoints

BasePoints(L) : LinSys -> SeqEnum
BasePoints(f) : MapSch -> SetEnum

BaseRing

BaseRing(A) : AlgQuat -> Fld
BaseField(A) : AlgQuat -> Fld
BaseField(J) : JacHyp -> Fld
BaseField(C) : Sch -> Fld
BaseField(K) : SrfKum -> Fld
BaseRing(B) : AlgBas -> Rng
BaseRing(R) : AlgMat -> Rng
BaseRing(S) : AlgQuatOrd -> Rng
BaseRing(E) : CrvEll -> Rng
BaseRing(F) : Fld -> Rng
BaseRing(F) : FldFunRat -> Rng
BaseRing( G ) : GrpLie -> Rng
BaseRing(G) : GrpPSL2 -> Rng
BaseRing(L) : Lat -> Rng
BaseRing(M) : ModBrdt -> Rng
BaseRing(M) : ModOrd -> Rng
BaseRing(A) : Mtrx -> Rng
BaseRing(F) : RngFunOrd -> Rng
BaseRing(P) : RngMPol -> Rng
BaseRing(O) : RngOrd -> Rng
BaseRing(R) : RngSer -> Rng
BaseRing(P) : RngUPol -> Rng
BaseRing(C) : Sch -> Rng
BaseRing(X) : Sch -> Rng
BaseRing(G) : SchGrpEll -> Rng
CoefficientRing(A) : AlgGen -> Rng
CoefficientRing(G) : GrpMat -> Rng
CoefficientRing(M) : ModMPol -> ModMPol
CoefficientRing(M) : ModTupRng -> Rng
CoefficientRing(M) : ModTupRng -> Rng

Bases

Bases (MODULAR FORMS)
ModForm_Bases (Example H90E6)
RngOrd_Bases (Example H53E14)

bases

Bases (ALGEBRAS)
Bases (MATRIX ALGEBRAS)
Bases (MODULAR SYMBOLS)

BaseScheme

BaseScheme(L) : LinSys -> SchProj
BaseScheme(f) : MapSch -> Sch

Basic

BasicAlgebra(FA, N, LR, R) : AlgFP, RngIntElt, SeqEnum, SeqEnum -> AlgBas
BasicAlgebra(G, k) : GrpPerm, FldFin -> AlgBas
BasicAlgebra(Q) : SeqEnum[Tup] -> AlgBas
BasicDegrees( W ) : GrpCox -> RngIntElt
BasicOrbit(G, i) : GrpMat, RngIntElt -> SetIndx
BasicOrbit(G, i) : GrpPerm, RngIntElt -> SetIndx
BasicOrbitLength(G, i) : GrpMat, RngIntElt -> RngIntElt
BasicOrbitLength(G, i) : GrpPerm, RngIntElt -> RngIntElt
BasicOrbitLengths(G) : GrpMat -> [RngIntElt]
BasicOrbitLengths(G) : GrpPerm -> [RngIntElt]
BasicOrbits(G) : GrpPerm -> [SetIndx]
BasicStabilizer(G, i) : GrpMat, RngIntElt -> GrpMat
BasicStabilizer(G, i) : GrpPerm, RngIntElt -> GrpPerm
BasicStabilizerChain(G) : GrpMat -> [GrpMat]
BasicStabilizerChain(G) : GrpPerm -> [GrpPerm]
IsMemberBasicOrbit(G, i, a) : GrpPerm, RngIntElt, Elt -> BoolElt

basic

BASIC ALGEBRAS
Basic Attributes of Schemes (SCHEMES)
Basic Functions (DATABASES OF GROUPS)
Basic Small Group Functions (DATABASES OF GROUPS)
Functions of the Ambient Space (SCHEMES)

basic-example

GrpPSL2_basic-example (Example H33E1)

basic-isolgps

Basic Functions (DATABASES OF GROUPS)

basic-trngps

Basic Small Group Functions (DATABASES OF GROUPS)

BasicAccess

GrpAtc_BasicAccess (Example H31E4)
GrpPerm_BasicAccess (Example H20E4)
GrpRWS_BasicAccess (Example H30E4)
MonRWS_BasicAccess (Example H18E4)

BasicAlgebra

BasicAlgebra(FA, N, LR, R) : AlgFP, RngIntElt, SeqEnum, SeqEnum -> AlgBas
BasicAlgebra(G, k) : GrpPerm, FldFin -> AlgBas
BasicAlgebra(Q) : SeqEnum[Tup] -> AlgBas

BasicAlgebras

AlgBas_BasicAlgebras (Example H79E1)

BasicDegrees

BasicDegrees( W ) : GrpCox -> RngIntElt
GrpCox_BasicDegrees (Example H36E8)

BasicOperations

RootDtm_BasicOperations (Example H35E6)

BasicOrbit

BasicOrbit(G, i) : GrpMat, RngIntElt -> SetIndx
BasicOrbit(G, i) : GrpPerm, RngIntElt -> SetIndx

BasicOrbitLength

BasicOrbitLength(G, i) : GrpMat, RngIntElt -> RngIntElt
BasicOrbitLength(G, i) : GrpPerm, RngIntElt -> RngIntElt

BasicOrbitLengths

BasicOrbitLengths(G) : GrpMat -> [RngIntElt]
BasicOrbitLengths(G) : GrpPerm -> [RngIntElt]

BasicOrbits

BasicOrbits(G) : GrpPerm -> [SetIndx]

BasicProperties

GrpPerm_BasicProperties (Example H20E5)

Basics

ModForm_Basics (Example H90E1)

BasicStabiliser

BasicStabiliser(G, i) : GrpMat, RngIntElt -> GrpMat
BasicStabilizer(G, i) : GrpMat, RngIntElt -> GrpMat
BasicStabilizer(G, i) : GrpPerm, RngIntElt -> GrpPerm

BasicStabiliserChain

BasicStabiliserChain(G) : GrpMat -> [GrpMat]
BasicStabilizerChain(G) : GrpMat -> [GrpMat]
BasicStabilizerChain(G) : GrpPerm -> [GrpPerm]

BasicStabilizer

BasicStabiliser(G, i) : GrpMat, RngIntElt -> GrpMat
BasicStabilizer(G, i) : GrpMat, RngIntElt -> GrpMat
BasicStabilizer(G, i) : GrpPerm, RngIntElt -> GrpPerm

BasicStabilizerChain

BasicStabiliserChain(G) : GrpMat -> [GrpMat]
BasicStabilizerChain(G) : GrpMat -> [GrpMat]
BasicStabilizerChain(G) : GrpPerm -> [GrpPerm]

Basis

AbelianBasis(G) : GrpFin -> [ GrpFinElt ], [ RngIntElt ]
AbelianBasis(G) : GrpPC -> [ GrpPCElt ], [ RngIntElt ]
AbsoluteBasis(K) : FldAlg -> [FldAlgElt]
Basis(B) : AlgBas -> SeqEnum
Basis(A) : AlgGen -> [ AlgGenElt ]
Basis(R) : AlgMat -> [ AlgMatElt ]
Basis(A) : AlgQuat -> SeqEnum
Basis(S) : AlgQuatOrd -> SeqEnum
Basis(C) : Code -> [ ModTupRngElt ]
Basis(C) : Code -> [ ModTupRngElt ]
Basis(D) : DivCrvElt -> SeqEnum
Basis(F) : FldFun -> SeqEnum[FldFunElt]
Basis(Q) : FldRat -> [FldRatElt]
Basis(L) : Lat -> [ FldReElt ]
Basis(M) : ModBrdt -> SeqEnum
Basis(M) : ModFrm -> SeqEnum
Basis(M) : ModMPol -> RngMPolElt
Basis(M) : ModOrd -> SeqEnum
Basis(M) : ModSym -> SeqEnum
Basis(V) : ModTupFld -> [ModTupFldElt]
Basis(M) : ModTupRng -> [ModTupRngElt]
Basis(D : parameters) : DivFunElt -> [ FldFunElt ]
Basis(O) : RngFunOrd -> SeqEnum[FldFunElt]
Basis(I) : RngFunOrdIdl -> [FldFunElt]
Basis(I) : RngMPol -> RngMPolElt
Basis(O) : RngOrd -> [ FldOrdElt ]
Basis(I) : RngOrdIdl -> [RngOrdElt]
BasisElement(A, i) : AlgGen, RngIntElt -> AlgGenElt
BasisElement(R, i) : AlgMat, RngIntElt -> AlgMatElt
BasisElement(M, i) : ModMPol, RngIntElt -> RngMPolElt
BasisElement(V, i) : ModTupFld, RngIntElt -> ModTupFldElt
BasisElement(I, i) : RngMPol, RngIntElt -> RngMPolElt
BasisMatrix(S) : AlgGrpSub -> ModMatRngElt
BasisMatrix(L) : Lat -> ModMatRngElt
BasisMatrix(M) : ModMPol -> ModMatRngElt
BasisMatrix(V) : ModTupFld -> ModMatElt
BasisMatrix(I) : RngFunOrdIdl -> AlgMatElt
BasisMatrix(O) : RngOrd -> AlgMatElt
BasisMatrix(I) : RngOrdFracIdl -> MtrxSpcElt
BasisOfDifferentialsFirstKind(F) : FldFunG -> SeqEnum[DiffFunElt]
BasisProduct(A, i, j) : AlgGen, RngIntElt, RngIntElt -> AlgGenElt
BasisProducts(A) : AlgGen -> [[ AlgGenElt ]]
CharacterTable(G) : Grp -> SeqEnum
ComplementBasis(G) : GrpPC -> [GrpPC]
CoprimeBasis(S) : [ RngIntElt ] -> [ RngIntElt ]
DifferentialBasis(D) : DivCrvElt -> SeqEnum
DifferentialBasis(D) : DivFunElt -> [DiffFunElt]
DifferentialBasis(D) : DivFunElt -> [DiffFunElt]
DualBasisLattice(L) : Lat -> Lat
ExtendBasis(S, A) : AlgGen, AlgGen -> [ AlgElt ]
ExtendBasis(U, V) : ModTupFld, ModTupFld -> [ModTupFldElt]
ExtendBasis(Q, U) : [ModTupFldElt], ModTupFld -> [ModTupFldElt]
FactorBasis(K, B) : FldNum, RngIntElt -> [ RngOrdIdl ]
FactorBasis(O) : RngOrd -> [ RngOrdIdl ], Integer
GeneratorMatrix(C) : Code -> ModMatFldElt
GroebnerBasis(I: parameters) : RngMPol -> RngMPolElt
GroebnerBasis(S, d : parameters) : [ RngMPol ], RngInt -> RngMPolElt
GroebnerBasis(S, d: parameters) : [ RngMPol ], RngInt -> RngMPolElt
GroebnerBasis(S: parameters) : [ RngMPolElt ] -> [ RngMPolElt ]
GroebnerBasis(X) : Sch -> SeqEnum
GroebnerBasisUnreduced(S: parameters) : [ RngMPolElt ] -> [ RngMPolElt ]
HasGroebnerBasis(I) : RngMPol -> BoolElt
HilbertGroebnerBasis(S, H) : [ RngMPolElt ], FldFunRatUElt -> BoolElt, [ RngMPolElt ]
HomogeneousModuleTestBasis(P, S, L) : [ RngMPol ], [ RngMPol ], [ RngMPol ] -> [ BoolElt ], [ [ RngMPol ] ]
ImageWithBasis(X, M) : ModMatRngElt, ModRng -> ModRng
IntegralBasis(F) : FldAlg -> [ FldAlgElt ]
IntegralBasis(Q) : FldRat -> [ FldRatElt ]
IntegralBasis(M) : ModSym -> Lat
KMatrixSpaceWithBasis(Q) : [ ModMatRngElt ] -> ModMatRng
LatticeWithBasis(G, B) : GrpMat, ModMatRngElt -> Lat
LatticeWithBasis(G, B, M) : GrpMat, ModMatRngElt, AlgMatElt -> Lat
LatticeWithBasis(B) : ModMatRngElt -> Lat
LatticeWithBasis(B, M) : ModMatRngElt, AlgMatElt -> Lat
MinimalBasis(M) : ModMPol -> [ ModMPolElt ]
MinimalBasis(X) : Sch -> [ RngMPolElt ]
MinimalBasis(S) : [ ModMPolElt ] -> [ ModMPolElt ]
PrimeBasis(n) : RngIntElt -> [RngIntElt]
PrimeBasis(n) : RngIntElt -> [RngIntElt]
PseudoBasis(M) : ModOrd -> SeqEnum
RMatrixSpaceWithBasis(Q) : [ ModMatRngElt ] -> ModMatRng
RMatrixSpaceWithBasis(Q) : [ModTupRngElt] -> ModMatRng
RModuleWithBasis(Q) : [ModRngElt] -> ModTupRng
ReduceGroebnerBasis(S) : [ RngMPolElt ] -> [ RngMPolElt ]
ReducedBasis(S) : AlgQuatOrd -> SeqEnum
ReducedBasis(S: Precision) : [JacHypPt] -> SeqEnum, AlgMatElt
ShortBasis(D : parameters) : DivFunElt -> [RngElt], [RngIntElt]
SylowBasis(G) : GrpPC -> [GrpPC]
TensorBasis(G) : GrpMat -> GrpMatElt
TensorInducedBasis(G) : GrpMat -> GrpMatElt
VectorSpaceWithBasis(B) : [ModTupFldElt] -> ModTupFld
KModuleWithBasis(B) : [ModTupFldElt] -> ModTupFld
qExpansionBasis(M, prec) : ModBrdt, RngIntElt -> SeqEnum
qExpansionBasis(M, prec : parameters) : ModSym, RngIntElt -> SeqEnum
qIntegralBasis(M, prec : parameters: Al) : ModSym, RngIntElt -> SeqEnum
ModFld_Basis (Example H63E13)

basis

Bases (FREE MODULES)
Bases (VECTOR SPACES)
Basis of a Module (MODULES OVER ORDERS)
Basis Representation (ORDERS AND ALGEBRAIC FIELDS)
Basis Representation (ORDERS AND ALGEBRAIC FIELDS)
Changing Basis (MODULES OVER A MATRIX ALGEBRA)
Construction of a Module with Specified Basis (FREE MODULES)
Construction of Gröbner Bases (IDEAL THEORY AND GRÖBNER BASES)
Module Bases (MODULES OVER AFFINE ALGEBRAS)
Modules öm_(R)(M, N) with Given Basis (FREE MODULES)

basis-ring

RngOrd_basis-ring (Example H53E13)

Basis_Reduction

AlgQuat_Basis_Reduction (Example H71E11)

BasisElement

A . i : AlgGen, RngIntElt -> AlgGenElt
BasisElement(A, i) : AlgGen, RngIntElt -> AlgGenElt
BasisElement(R, i) : AlgMat, RngIntElt -> AlgMatElt
BasisElement(M, i) : ModMPol, RngIntElt -> RngMPolElt
BasisElement(V, i) : ModTupFld, RngIntElt -> ModTupFldElt
BasisElement(I, i) : RngMPol, RngIntElt -> RngMPolElt

BasisMatrix

BasisMatrix(S) : AlgGrpSub -> ModMatRngElt
BasisMatrix(L) : Lat -> ModMatRngElt
BasisMatrix(M) : ModMPol -> ModMatRngElt
BasisMatrix(V) : ModTupFld -> ModMatElt
BasisMatrix(I) : RngFunOrdIdl -> AlgMatElt
BasisMatrix(O) : RngOrd -> AlgMatElt
BasisMatrix(I) : RngOrdFracIdl -> MtrxSpcElt
GeneratorMatrix(C) : Code -> ModMatFldElt

BasisOfDifferentialsFirstKind

BasisOfHolomorphicDifferentials(F) : FldFunG -> SeqEnum[DiffFunElt]
BasisOfDifferentialsFirstKind(F) : FldFunG -> SeqEnum[DiffFunElt]

BasisOfHolomorphicDifferentials

BasisOfHolomorphicDifferentials(F) : FldFunG -> SeqEnum[DiffFunElt]
BasisOfDifferentialsFirstKind(F) : FldFunG -> SeqEnum[DiffFunElt]

BasisProduct

BasisProduct(A, i, j) : AlgGen, RngIntElt, RngIntElt -> AlgGenElt

BasisProducts

BasisProducts(A) : AlgGen -> [[ AlgGenElt ]]

Basket

Basket(X) : VSrfK3 -> SeqEnum
K3SurfacesFromBasket(DB,B) : SeqEnum,SeqEnum -> SeqEnum

Baskets

Baskets(n) : RngIntElt -> SeqEnum,SeqEnum,SeqEnum,SeqEnum

BBSModulus

BlumBlumShubModulus(b) : RngIntElt -> RngIntElt
BBSModulus(b) : RngIntElt -> RngIntElt

BCH

BCH Codes and their Generalizations (LINEAR CODES OVER FINITE FIELDS)

BCHBound

BCHBound(C) : Code -> RngIntElt, RngIntElt

BCHCode

BCHCode(K, n, d, b) : FldFin, RngIntElt, RngIntElt, RngIntElt -> Code
CodeFld_BCHCode (Example H97E26)

BDLC

BestDimensionLinearCode(K, n, d) : FldFin,RngIntElt,RngIntElt -> Code
BDLC(K, n, d) : FldFin,RngIntElt,RngIntElt -> Code

BDLCLower

BDLCLowerBound(F, n, d) : FldFin, RngIntElt, RngIntElt -> RngIntElt

BDLCLowerBound

BDLCLowerBound(F, n, d) : FldFin, RngIntElt, RngIntElt -> RngIntElt

BDLCUpper

BDLCUpperBound(F, n, d) : FldFin, RngIntElt, RngIntElt -> RngIntElt

BDLCUpperBound

BDLCUpperBound(F, n, d) : FldFin, RngIntElt, RngIntElt -> RngIntElt

Beep

GetBeep() : -> BoolElt
SetBeep(b) : BoolElt ->

begin

Overview (OVERVIEW)

Berlekamp

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

BerlekampMassey

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

Bernoulli

BernoulliApproximation(n) : RngIntElt -> FldPrElt
BernoulliApproximation(n) : RngIntElt -> FldPrElt
BernoulliNumber(n) : RngIntElt -> FldRatElt
BernoulliNumber(n) : RngIntElt -> RngIntElt
BernoulliPolynomial(n) : RngIntElt -> RngUPolElt
BernoulliPolynomial(n) : RngIntElt -> RngUPolElt
RngSer_Bernoulli (Example H60E3)

bernoulli

The Bernoulli Polynomial (UNIVARIATE POLYNOMIAL RINGS)

bernoulli-polynomial

The Bernoulli Polynomial (UNIVARIATE POLYNOMIAL RINGS)

BernoulliApproximation

BernoulliApproximation(n) : RngIntElt -> FldPrElt
BernoulliApproximation(n) : RngIntElt -> FldPrElt

BernoulliNumber

BernoulliNumber(n) : RngIntElt -> FldRatElt
BernoulliNumber(n) : RngIntElt -> RngIntElt

BernoulliPolynomial

BernoulliPolynomial(n) : RngIntElt -> RngUPolElt
BernoulliPolynomial(n) : RngIntElt -> RngUPolElt

Bessel

BesselFunction(n, r) : RngIntElt, FldReElt -> FldReElt

bessel

KBessel2(n, s) : FldPrElt, FldPrElt -> FldPrElt
Gamma, Bessel and Associated Functions (REAL AND COMPLEX FIELDS)

BesselFunction

BesselFunction(n, r) : RngIntElt, FldReElt -> FldReElt

Best

BestDimensionLinearCode(K, n, d) : FldFin,RngIntElt,RngIntElt -> 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
BestApproximation(r, n) : FldPrElt, RngIntElt -> FldPrElt
BestTranslation( T ) : Tup -> Tup

best

Best Known Bounds for Linear Codes (LINEAR CODES OVER FINITE FIELDS)
Best Known Linear Codes (LINEAR CODES OVER FINITE FIELDS)

best-bounds

Best Known Bounds for Linear Codes (LINEAR CODES OVER FINITE FIELDS)

best-codes

Best Known Linear Codes (LINEAR CODES OVER FINITE FIELDS)

BestApproximation

BestApproximation(r, n) : FldPrElt, RngIntElt -> FldPrElt

BestDimensionLinearCode

BestDimensionLinearCode(K, n, d) : FldFin,RngIntElt,RngIntElt -> Code
BDLC(K, n, d) : FldFin,RngIntElt,RngIntElt -> Code

BestKnownLinearCode

BestKnownLinearCode(K, n, k) : FldFin,RngIntElt,RngIntElt -> Code
BKLC(K, n, k) : FldFin,RngIntElt,RngIntElt -> Code

BestLengthDimension

CodeFld_BestLengthDimension (Example H97E40)

BestLengthLinearCode

BestLengthLinearCode(K, k, d) : FldFin,RngIntElt,RngIntElt -> Code, BoolElt
BLLC(K, k, d) : FldFin,RngIntElt,RngIntElt -> Code, BoolElt

BestTranslation

BestTranslation( T ) : Tup -> Tup

Between

SubcodeBetweenCode(C1, C2, k) : Code,Code,RngIntElt -> Code

BFSTree

BFSTree(u) : GrphVert -> Grph
BreadthFirstSearchTree(u) : GrphVert -> Grph

bibliography

Bibliography for Database of Irreducible Soluble Subgroups of GL(n,p) for n > 1 and p^n < 256 (OVERVIEW)
Bibliography for Database of Simple Groups (OVERVIEW)

Bicomponents

Bicomponents(G) : GrphUnd -> [GrphUnd]

Big

O(x) : RngLocElt -> RngLocElt
BigO(x) : RngLocElt -> RngLocElt
BigO(x) : RngLocElt -> RngLocElt
BigO(f) : RngSerElt -> RngIntElt

bigger

Comparison (OVERVIEW)

BigO

O(x) : RngLocElt -> RngLocElt
BigO(x) : RngLocElt -> RngLocElt
BigO(x) : RngLocElt -> RngLocElt
BigO(f) : RngSerElt -> RngIntElt

Bijective

IsBijective(a) : ModMatRngElt -> BoolElt

Bilinear

ScalarsSymmetricBilinearForm(G) : GrpMat -> SeqEnum
SymmetricBilinearForm(G) : GrpMat -> AlgMatElt
SymmetricBilinearForm(f) : RngMPolElt -> ModMatRngElt

Binary

QuadraticForms(D) : RngIntElt -> QuadBin
BinaryQuadraticForms(D) : RngIntElt -> QuadBin

binary

Binary Set Operators (SETS)

BinaryQuadraticForms

QuadraticForms(D) : RngIntElt -> QuadBin
BinaryQuadraticForms(D) : RngIntElt -> QuadBin

binding

Key Bindings (Emacs and VI mode) (ENVIRONMENT AND OPTIONS)
Key Bindings in Emacs mode only (ENVIRONMENT AND OPTIONS)
Key Bindings in VI mode only (ENVIRONMENT AND OPTIONS)

Binomial

Binomial(n, r) : RngIntElt, RngIntElt -> RngIntElt
Binomial(n, r) : RngIntElt, RngIntElt -> RngIntElt

bInvariants

bInvariants(E) : CrvEll -> [ RngElt ]

Bipartite

BipartiteGraph(m, n) : RngIntElt, RngIntElt -> GrphUnd
IsBipartite(G) : GrphUnd -> BoolElt

BipartiteGraph

BipartiteGraph(m, n) : RngIntElt, RngIntElt -> GrphUnd

Bipartition

Bipartition(G) : GrphUnd -> [ { GrphVert } ]

Biquadratic

BiquadraticResidueSymbol(a, b) : RngQuadElt, RngQuadElt -> RngQuadElt

BiquadraticResidueSymbol

BiquadraticResidueSymbol(a, b) : RngQuadElt, RngQuadElt -> RngQuadElt

Bits

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

BKLC

BestKnownLinearCode(K, n, k) : FldFin,RngIntElt,RngIntElt -> Code
BKLC(K, n, k) : FldFin,RngIntElt,RngIntElt -> Code

BKLCLower

BKLCLowerBound(F, n, k) : FldFin, RngIntElt, RngIntElt -> RngIntElt

BKLCLowerBound

BKLCLowerBound(F, n, k) : FldFin, RngIntElt, RngIntElt -> RngIntElt

BKLCUpper

BKLCUpperBound(F, n, k) : FldFin, RngIntElt, RngIntElt -> RngIntElt

BKLCUpperBound

BKLCUpperBound(F, n, k) : FldFin, RngIntElt, RngIntElt -> RngIntElt

blackbox

Groups (OVERVIEW)
GROUPS WHOSE ELEMENTS ARE STRAIGHT-LINE PROGRAMS

BLLC

BestLengthLinearCode(K, k, d) : FldFin,RngIntElt,RngIntElt -> Code, BoolElt
BLLC(K, k, d) : FldFin,RngIntElt,RngIntElt -> Code, BoolElt

BLLCLower

BLLCLowerBound(F, k, d) : FldFin, RngIntElt, RngIntElt -> RngIntElt

BLLCLowerBound

BLLCLowerBound(F, k, d) : FldFin, RngIntElt, RngIntElt -> RngIntElt

BLLCUpper

BLLCUpperBound(F, k, d) : FldFin, RngIntElt, RngIntElt -> RngIntElt

BLLCUpperBound

BLLCUpperBound(F, k, d) : FldFin, RngIntElt, RngIntElt -> RngIntElt

Block

Block(D, i) : Inc, RngIntElt -> IncBlk
BlockDegree(D) : Dsgn -> RngIntElt
BlockDegree(D, B) : Inc, IncBlk -> RngIntElt
# B : IncBlk -> RngIntElt
BlockDegrees(D) : Inc -> [ RngIntElt ]
BlockGraph(D) : Inc -> Grph
BlockGraph(D) : Inc -> GrphUnd
BlockGroup(D) : Inc -> GrpPerm
BlockSet(D) : Inc -> IncBlkSet
BlockSystem(G) : GrpMat -> Rec
InsertBlock(~a, b, i, j) : AlgMatElt, ModHomElt, RngIntElt, RngIntElt -> AlgMatElt
InsertBlock(A, B, i, j) : Mtrx, Mtrx, RngIntElt, RngIntElt -> Mtrx
IsBlock(G, S) : GrpPerm, { Elt } -> BoolElt
IsBlock(D, S) : Inc, IncBlk -> BoolElt, IncBlk
IsBlockTransitive(D) : Inc -> BoolElt
IsolMinBlockSize(n, p, i) : RngIntElt, RngIntElt, RngIntElt -> RngIntElt
Line(D, p, q) : Inc, IncPt, IncPt -> IncBlk
Submatrix(a, i, j, p, q) : AlgMatElt, RngIntElt, RngIntElt, RngIntElt, RngIntElt -> ModMatRngElt
Submatrix(A, i, j, p, q) : Mtrx, RngIntElt, RngIntElt, RngIntElt, RngIntElt -> Mtrx
SubmatrixRange(A, i, j, r, s) : Mtrx, RngIntElt, RngIntElt, RngIntElt, RngIntElt -> Mtrx

block

Creating Points and Blocks (INCIDENCE STRUCTURES AND DESIGNS)
Operations on Points and Blocks (INCIDENCE STRUCTURES AND DESIGNS)
The Point--Set and Block--Set of an Incidence Structure (INCIDENCE STRUCTURES AND DESIGNS)

BlockDegree

BlockSize(D) : Dsgn -> RngIntElt
BlockDegree(D) : Dsgn -> RngIntElt
BlockDegree(D, B) : Inc, IncBlk -> RngIntElt

BlockDegrees

BlockSizes(D) : Inc -> [ RngIntElt ]
BlockDegrees(D) : Inc -> [ RngIntElt ]

BlockGraph

BlockGraph(D) : Inc -> Grph
BlockGraph(D) : Inc -> GrphUnd

BlockGroup

BlockGroup(D) : Inc -> GrpPerm

Blocks

Blocks(D) : Inc -> { IncBlk }
BlocksAction(G, P) : GrpPerm, GSet -> Hom(GrpPerm), GrpPerm, GrpPerm
BlocksImage(G) : GrpMat -> GrpPerm
BlocksImage(G, P) : GrpPerm, GSet -> GrpPerm
BlocksKernel(G, P) : GrpPerm, GSet -> GrpPerm
NumberOfBlocks(D) : Inc -> RngIntElt

BlocksAction

BlocksAction(G, P) : GrpPerm, GSet -> Hom(GrpPerm), GrpPerm, GrpPerm

BlocksActions

GrpPerm_BlocksActions (Example H20E22)

BlockSet

BlockSet(D) : Inc -> IncBlkSet

BlocksImage

BlocksImage(G) : GrpMat -> GrpPerm
BlocksImage(G, P) : GrpPerm, GSet -> GrpPerm

BlockSize

BlockSize(D) : Dsgn -> RngIntElt
BlockDegree(D) : Dsgn -> RngIntElt
BlockDegree(D, B) : Inc, IncBlk -> RngIntElt

BlockSizes

BlockSizes(D) : Inc -> [ RngIntElt ]
BlockDegrees(D) : Inc -> [ RngIntElt ]

BlocksKernel

BlocksKernel(G, P) : GrpPerm, GSet -> GrpPerm

BlockSystem

BlockSystem(G) : GrpMat -> Rec

blow

Resolution of Singularities (PLANE ALGEBRAIC CURVES)

blow-ups

Resolution of Singularities (PLANE ALGEBRAIC CURVES)

Blowup

Blowup(C) : Crv -> Crv, Crv
Blowup(C,M) : Crv,Mtrx -> Crv, RngIntElt, RngIntElt

Blum

BlumBlumShubModulus(b) : RngIntElt -> RngIntElt
BBSModulus(b) : RngIntElt -> RngIntElt
RandomSequenceBlumBlumShub(b, t) : RngIntElt, RngIntElt -> SeqEnum
RandomSequenceBlumBlumShub(n, s, t) : RngIntElt, RngIntElt, RngIntElt -> SeqEnum

BlumBlumShub

BlumBlumShub(b, t) : RngIntElt, RngIntElt -> SeqEnum
RandomSequenceBlumBlumShub(b, t) : RngIntElt, RngIntElt -> SeqEnum
RandomSequenceBlumBlumShub(n, s, t) : RngIntElt, RngIntElt, RngIntElt -> SeqEnum

BlumBlumShubModulus

BlumBlumShubModulus(b) : RngIntElt -> RngIntElt
BBSModulus(b) : RngIntElt -> RngIntElt

book

Documentation (OVERVIEW)

Boolean

Boolean Functions (INPUT AND OUTPUT)
Boolean Functions and Operators (SETS)
Boolean Operators for Elements (FINITELY PRESENTED ALGEBRAS)
Boolean Operators on Ideals (INTRODUCTION [BASIC RINGS])
Boolean Predicates (LINEAR CODES OVER FINITE RINGS)
Booleans (OVERVIEW)
Comparison of Words (FINITELY PRESENTED GROUPS)
Elementary Graph Predicates (GRAPHS)
Equality (TUPLES AND CARTESIAN PRODUCTS)
Equality and Comparison (ABELIAN GROUPS)
Equality and Comparison (FINITELY PRESENTED SEMIGROUPS)
Equality and Comparison (GROUPS WHOSE ELEMENTS ARE STRAIGHT-LINE PROGRAMS)
Equality and Membership (ALGEBRAICALLY CLOSED FIELDS)
Equality and Membership (FINITE FIELDS)
Equality and Membership (GALOIS RINGS)
Equality and Membership (INTRODUCTION [BASIC RINGS])
Equality and Membership (RATIONAL FIELD)
Equality and Membership (RING OF INTEGERS)
Equality and Membership (RING OF INTEGERS)
Field Predicates (ORDERS AND ALGEBRAIC FIELDS)
General Group Properties (ABELIAN GROUPS)
General Properties of Subgroups (ABELIAN GROUPS)
Membership and Equality (ABELIAN GROUPS)
Membership and Equality (AUTOMATIC GROUPS)
Membership and Equality (FREE MODULES)
Membership and Equality (GROUPS DEFINED BY REWRITE SYSTEMS)
Membership and Equality (GROUPS WHOSE ELEMENTS ARE STRAIGHT-LINE PROGRAMS)
Membership and Equality (GROUPS)
Membership and Equality (LINEAR CODES OVER FINITE FIELDS)
Membership and Equality (MATRIX ALGEBRAS)
Membership and Equality (MATRIX GROUPS)
Membership and Equality (MODULES OVER A MATRIX ALGEBRA)
Membership and Equality (MONOIDS GIVEN BY REWRITE SYSTEMS)
Membership and Equality (PERMUTATION GROUPS)
Membership and Equality (VECTOR SPACES)
Order Predicates (ORDERS AND ALGEBRAIC FIELDS)
Predicates (MATRIX ALGEBRAS)
Predicates and Booleans (CHARACTERS OF FINITE GROUPS)
Predicates for Matrices (MATRIX GROUPS)
Predicates on Ideals (ORDERS AND ALGEBRAIC FIELDS)
Predicates on Ring Elements (ALGEBRAICALLY CLOSED FIELDS)
Predicates on Ring Elements (FINITE FIELDS)
Predicates on Ring Elements (GALOIS RINGS)
Predicates on Ring Elements (INTRODUCTION [BASIC RINGS])
Predicates on Ring Elements (MULTIVARIATE POLYNOMIAL RINGS)
Predicates on Ring Elements (POWER, LAURENT AND PUISEUX SERIES)
Predicates on Ring Elements (RATIONAL FIELD)
Predicates on Ring Elements (RATIONAL FUNCTION FIELDS)
Predicates on Ring Elements (RING OF INTEGERS)
Predicates on Ring Elements (RING OF INTEGERS)
Predicates on Ring Elements (UNIVARIATE POLYNOMIAL RINGS)
Predicates on Sequences (SEQUENCES)
Properties of a Automatic Group (AUTOMATIC GROUPS)
Properties of a Rewrite Group (GROUPS DEFINED BY REWRITE SYSTEMS)
Properties of a Rewrite Monoid (MONOIDS GIVEN BY REWRITE SYSTEMS)
Properties of Codes (LINEAR CODES OVER FINITE FIELDS)
Properties of Subgroups (FINITELY PRESENTED GROUPS)
Ring Predicates (ORDERS AND ALGEBRAIC FIELDS)
Ring Predicates and Booleans (RATIONAL FIELD)
Ring Predicates and Booleans (REAL AND COMPLEX FIELDS)
Ring Predicates and Booleans (RING OF INTEGERS)

boolean

Boolean Operations (BINARY QUADRATIC FORMS)
Boolean values (STATEMENTS AND EXPRESSIONS)
Comparison Operators for Elements (POLYCYCLIC GROUPS)
Elementary Properties of Incidence Structures and Designs (INCIDENCE STRUCTURES AND DESIGNS)
General Group Properties (POLYCYCLIC GROUPS)
General Properties of Subgroups (POLYCYCLIC GROUPS)
Membership and Equality (GENERIC ABELIAN GROUPS)
Membership and Equality (POLYCYCLIC GROUPS)
Predicates on Elements (ALGEBRAIC FUNCTION FIELDS)
Predicates on Elements (ALGEBRAIC FUNCTION FIELDS)
Predicates on Elements (ALGEBRAIC FUNCTION FIELDS)
Predicates on Elements (ALGEBRAIC FUNCTION FIELDS)
Predicates on Elements (ORDERS AND ALGEBRAIC FIELDS)
Predicates on Ideals (ALGEBRAIC FUNCTION FIELDS)
Properties of Planes (FINITE PLANES)
Properties of Subgroups Requiring a Nil-po-tent Covering Group (POLYCYCLIC GROUPS)
Ring Predicates and Booleans (MULTIVARIATE POLYNOMIAL RINGS)
Ring Predicates and Booleans (POWER, LAURENT AND PUISEUX SERIES)
Ring Predicates and Booleans (UNIVARIATE POLYNOMIAL RINGS)

boolean-operations

Boolean Operations (BINARY QUADRATIC FORMS)

Booleans

Booleans() : Nil -> Bool
State_Booleans (Example H1E8)

Bordered

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

BorderedDoublyCirculantQRCode

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

Borel

BorelSubgroup(C) : CosetGeom -> GrpPerm
Borel(C) : CosetGeom -> GrpPerm

BorelSubgroup

BorelSubgroup(C) : CosetGeom -> GrpPerm
Borel(C) : CosetGeom -> GrpPerm

Bottom

Bottom(L) : SubFldLat -> SubFldLatElt
Bottom(L): SubGrpLat -> SubGrpLatElt
Bottom(L): SubModLat -> SubModLatElt

Bound

BDLCLowerBound(F, n, d) : FldFin, RngIntElt, RngIntElt -> RngIntElt
BDLCUpperBound(F, n, d) : FldFin, RngIntElt, RngIntElt -> RngIntElt
BKLCLowerBound(F, n, k) : FldFin, RngIntElt, RngIntElt -> RngIntElt
BKLCUpperBound(F, n, k) : FldFin, RngIntElt, RngIntElt -> RngIntElt
BLLCLowerBound(F, k, d) : FldFin, RngIntElt, RngIntElt -> RngIntElt
BLLCUpperBound(F, k, d) : FldFin, RngIntElt, RngIntElt -> RngIntElt
BachBound(K) : FldNum -> RngIntElt
ClassGroupGenerationBound(F) : FldFun -> RngIntElt
ClassGroupGenerationBound(q, g) : RngIntElt, RngIntElt -> RngIntElt
ClassNumberApproximationBound(q, g, e) : RngIntElt, RngIntElt, -> RngIntElt
EliasAsymptoticBound(K, delta) : FldFin, FldPrElt -> FldPrElt
EliasBound(K, n, d) : FldFin, RngIntElt, RngIntElt -> RngIntElt
GilbertVarshamovAsymptoticBound(K, delta) : FldFin, FldPrElt -> FldPrElt
GilbertVarshamovBound(K, n, d) : FldFin, RngIntElt, RngIntElt -> RngIntElt
GilbertVarshamovLinearBound(K, n, d) : FldFin,RngIntElt,RngIntElt -> RngIntElt
GriesmerBound(K, n, d) : FldFin, RngIntElt, RngIntElt -> RngIntElt
GriesmerLengthBound(K, k, d) : FldFin,RngIntEt,RngIntElt -> RngIntElt
GriesmerMinimumWeightBound(K, n, k) : FldFin,RngIntElt,RngIntElt->RngIntElt
HammingAsymptoticBound(K, delta) : FldFin, FldPrElt -> FldPrElt
HeckeBound(M) : ModSym -> RngIntElt
IharaBound(F) : FldFun -> RngIntElt
JohnsonBound(n, d) : RngIntElt, RngIntElt -> RngIntElt
LevenshteinBound(K, n, d) : FldFin, RngIntElt, RngIntElt -> RngIntElt
McElieceEtAlAsymptoticBound(delta) : FldPrElt -> FldPrElt
MinkowskiBound(K) : FldNum -> RngIntElt
NumberOfPlacesOfDegreeOneBound(F) : FldFun -> RngIntElt
NumberOfPlacesOfDegreeOneBound(F, m) : FldFun, RngIntElt -> RngIntElt
PlotkinAsymptoticBound(K, delta) : FldFin, FldPrElt -> FldPrElt
PlotkinBound(K, n, d) : FldFin, RngIntElt, RngIntElt -> RngIntElt
PrecisionBound(M : parameters) : ModFrm -> RngIntElt
RegulatorLowerBound(O) : RngOrd -> FldPrElt
SerreBound(F) : FldFun -> RngIntElt
SetHeckeBound(M, n) : ModSym, RngIntElt -> RngIntElt
SetLowerBound(L, n, b) : LP, RngIntElt, RngElt ->
SetUpperBound(L, n, b) : LP, RngIntElt, RngElt ->
SilvermanBound(H) : SetPtEll -> FldPrElt
SingletonAsymptoticBound(delta) : FldPrElt -> FldPrElt
SingletonBound(K, n, d) : FldFin, RngIntElt, RngIntElt -> RngIntElt
SpherePackingBound(K, n, d) : FldFin, RngIntElt, RngIntElt -> RngIntElt
TorsionBound(J, n) : JacHyp, RngIntElt -> RngIntElt
TorsionBound(M, maxp) : ModSym, RngIntElt -> RngIntElt
VanLintBound(K, n, d) : FldFin, RngIntElt, RngIntElt -> RngIntElt
VerifyMinimumDistanceLowerBound(C, d) : Code, RngIntElt -> BoolElt, RngIntElt, BoolElt
VerifyMinimumDistanceUpperBound(C, d) : Code, RngIntElt -> BoolElt, RngIntElt, BoolElt

bound

Asymptotic Bounds on the Information Rate (LINEAR CODES OVER FINITE FIELDS)
Bounds (LINEAR CODES OVER FINITE FIELDS)
Bounds on the Minimum Distance (LINEAR CODES OVER FINITE FIELDS)

Boundary

BoundaryMap(C, n) : ModCpx, RngIntElt -> ModMatFldElt
BoundaryMap(M) : ModSym -> ModMatFldElt
BoundaryMaps(C) : ModCpx -> List
IsBoundary(N, p) : NwtnPgon,Tup -> BoolElt
LayerBoundary(G,i,j,k) : GrpPC, RngIntElt, RngIntElt, RngIntElt -> RngIntElt
MinorBoundary(G,i,j) : GrpPC, RngIntElt, RngIntElt -> RngIntElt
NilpotentBoundary(G,i) : GrpPC, RngIntElt -> RngIntElt

BoundaryMap

BoundaryMap(C, n) : ModCpx, RngIntElt -> ModMatFldElt
BoundaryMap(M) : ModSym -> ModMatFldElt
ModSym_BoundaryMap (Example H88E13)

BoundaryMaps

BoundaryMaps(C) : ModCpx -> List

Bounded

OrbitActionBounded(G, T, b) : GrpMat, Elt, RngIntElt -> BoolElt, Hom(Grp), GrpPerm, GrpMat
OrbitBounded(G, y, b) : GrpMat, Elt, RngIntElt -> BoolElt, SetEnum
OrbitImageBounded(G, T, b) : GrpMat, Set, RngIntElt -> BoolElt, GrpPerm
OrbitKernelBounded(G, T, b) : GrpMat, Set, RngIntElt -> BoolElt, GrpMat
WordsOfBoundedWeight(C, l, u) : Code, RngIntElt, RngIntElt -> { ModTupFldElt }

Bounds

MordellWeilRankBounds(H: parameters) : SetPtEll -> RngIntElt, RngIntElt
RankBounds(H: parameters) : SetPtEll -> RngIntElt, RngIntElt
UnsetBounds(L) : LP ->

bounds

Best Known Bounds for Linear Codes (LINEAR CODES OVER FINITE FIELDS)

brace

Sets (OVERVIEW)

bracestar *}

{* e_1, e_2, ..., e_n *} : Elt, ..., Elt -> SetMulti
{* *} : Null -> SetMulti
{* U | *} : Struct -> SetMulti
{* U | e_1, e_2, ..., e_m *} : Struct, Elt, ..., Elt -> SetMulti
{* e(x) : x in E | P(x) *}
{* U | e(x) : x in E | P(x) *}
{* e(x_1,...,x_k) : x_1 in E_1, ..., x_kin E_k | P(x_1, ..., x_k) *}
{* U | e(x_1,...,x_k) : x_1 in E_1, ...,x_k in E_k | P(x_1, ..., x_k) *}

Bracket

(a, b) : AlgAssElt, AlgAssElt -> AlgAssElt
LieBracket(a, b) : AlgAssElt, AlgAssElt -> AlgAssElt

bracket

Expression (OVERVIEW)
Generator Assignment (OVERVIEW)
Sequences (OVERVIEW)
Sets (OVERVIEW)

Braid

BraidGroup( W ) : GrpCox -> GrpFP, Map
BraidGroup( F ) : GrpFP -> GrpFP, Map
BraidGroup(n) : RngIntElt -> GrpFP
PureBraidGroup( W ) : GrpCox -> GrpFP, Map
PureBraidGroup( F ) : GrpFP -> GrpFP, Map

braid

Braid groups (COXETER GROUPS)

BraidGroup

BraidGroup( W ) : GrpCox -> GrpFP, Map
BraidGroup( F ) : GrpFP -> GrpFP, Map
BraidGroup(n) : RngIntElt -> GrpFP

BraidGroups

GrpCox_BraidGroups (Example H36E17)

Branch

BranchVertexPath(u,v) : GrphVert,GrphVert -> SeqEnum

BranchVertexPath

BranchVertexPath(u,v) : GrphVert,GrphVert -> SeqEnum

Brandt

BrandtModule(A) : AlgQuatOrd -> ModBrdt
BrandtModule(D) : RngIntElt, RngIntElt -> ModBrdt
BrandtModuleDimension(D,N) : RngIntElt, RngIntElt -> RngIntElt

brandt

BRANDT MODULES

brandt-modules

BRANDT MODULES

BrandtModule

BrandtModule(A) : AlgQuatOrd -> ModBrdt
BrandtModule(D) : RngIntElt, RngIntElt -> ModBrdt

BrandtModuleDimension

BrandtModuleDimension(D,N) : RngIntElt, RngIntElt -> RngIntElt

Bravais

BravaisGroup(G) : GrpMat -> GrpMat

BravaisGroup

BravaisGroup(G) : GrpMat -> GrpMat

Breadth

BFSTree(u) : GrphVert -> Grph
BreadthFirstSearchTree(u) : GrphVert -> Grph

BreadthFirstSearchTree

BFSTree(u) : GrphVert -> Grph
BreadthFirstSearchTree(u) : GrphVert -> Grph

break

Early Exit from Iterative Statements (STATEMENTS AND EXPRESSIONS)
The break statement (OVERVIEW)
State_break (Example H1E15)

Browser

GetHelpExternalBrowser() : -> MonStgElt, MonStgElt
SetHelpExternalBrowser(S, T) : MonStgElt, MonStgElt ->
SetHelpUseExternalBrowser(b) : BoolElt ->

browser

Internal Help Browser (ENVIRONMENT AND OPTIONS)

Bruhat

Bruhat( g ) : GrpLieElte -> GrpLieElt, GrpLieElt, GrpLieElt, GrpLieElt
GrpLie_Bruhat (Example H37E6)

bruhat

Bruhat normalisation (GROUPS OF LIE TYPE)

BSD

ModSym_BSD (Example H88E22)

BSD389A

ModSym_BSD389A (Example H88E26)

BSGS

Base and Strong Generating Set (MATRIX GROUPS)
Base and Strong Generating Set (PERMUTATION GROUPS)
BSGS(G) : GrpMat ->
BSGS(G) : GrpPerm ->
GrpPerm_BSGS (Example H20E32)

BSGS-base-strong-generator

Base and Strong Generating Set (MATRIX GROUPS)
Base and Strong Generating Set (PERMUTATION GROUPS)

Buffer

SetBufferSize(D, n) : DB, RngIntElt ->

bug

Magma Updates (OVERVIEW)

build

Building the K3 Database (THE K3 DATABASE)
Gathering the Data (THE K3 DATABASE)
Working with the Raw Elements (THE K3 DATABASE)

building

Building Permutation Groups (PERMUTATION GROUPS)

building-groups

Building Permutation Groups (PERMUTATION GROUPS)

BuildSubgroups

GrpFP_1_BuildSubgroups (Example H22E44)

builtin

Intrinsics (OVERVIEW)

Burnside

BurnsideMatrix(G) : GrpPC -> AlgMatElt
DisplayBurnsideMatrix(G) : GrpPC ->

BurnsideMatrix

BurnsideMatrix(G) : GrpPC -> AlgMatElt

By

IsDivisibleBy(a, b) : FldFunElt, FldFunElt -> BoolElt, FldFunElt
IsDivisibleBy(a, b) : RngFunOrdElt, RngFunOrdElt -> BoolElt, RngFunOrdElt
IsDivisibleBy(n, d) : RngIntElt, RngIntElt -> BoolElt, RngIntElt
IsDivisibleBy(a, b) : RngMPolElt, RngMPolElt -> BoolElt, RngMPolElt
MultiplicationByMMap(E, m) : CrvEll, RngIntElt -> Map

by

Call by Value Evaluation (MAGMA SEMANTICS)
Creation by Hand (RESOLUTION GRAPHS AND SPLICE DIAGRAMS)
Definition of Subgroups by Generators (FINITE SOLUBLE GROUPS)
Expression (OVERVIEW)
Sequences (OVERVIEW)
Sets (OVERVIEW)
The for statement (OVERVIEW)

bye

Control-C key (OVERVIEW)
Quitting (OVERVIEW)

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