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Index H


h

Overview (OVERVIEW)

H-key

H
h

h-key

H
h

H2

H2_G_QmodZ(G) : GrpAb -> GrpAb, Map

Hadamard

HadamardAutomorphismGroup(H) : AlgMatElt -> AlgMatElt
HadamardColumnDesign(H, i) : AlgMatElt, RngIntElt -> Dsgn
HadamardGraph(H: parameters) : Mtrx -> GrphUnd
HadamardNormalize(H) : AlgMatElt -> AlgMatElt
HadamardRowDesign(H, i) : AlgMatElt, RngIntElt -> Dsgn
IsHadamard(H) : AlgMatElt -> BoolElt
IsHadamardEquivalent(H, J) : AlgMatElt, AlgMatElt -> BoolElt

hadamard

Hadamard Matrices and their 3--Designs (INCIDENCE STRUCTURES AND DESIGNS)
Design_hadamard (Example H98E5)

HadamardAutomorphismGroup

HadamardAutomorphismGroup(H) : AlgMatElt -> AlgMatElt

HadamardColumnDesign

HadamardColumnDesign(H, i) : AlgMatElt, RngIntElt -> Dsgn

HadamardGraph

HadamardGraph(H: parameters) : Mtrx -> GrphUnd

HadamardNormalize

HadamardNormalize(H) : AlgMatElt -> AlgMatElt

HadamardRowDesign

HadamardRowDesign(H, i) : AlgMatElt, RngIntElt -> Dsgn

Half

UpperHalfPlaneWithCusps() : -> SpcHyp

Hall

Hall pi-Subgroups and Sylow Systems (FINITE SOLUBLE GROUPS)
HallSubgroup(G, S) : GrpPC, { RngIntElt } -> GrpPC
GrpPC_Hall (Example H24E17)

Hall-pi-Sylow

Hall pi-Subgroups and Sylow Systems (FINITE SOLUBLE GROUPS)

HallSubgroup

HallSubgroup(G, S) : GrpPC, { RngIntElt } -> GrpPC

Hamming

HammingAsymptoticBound(K, delta) : FldFin, FldPrElt -> FldPrElt
HammingCode(K, r) : FldFin, RngIntElt -> Code
WeightEnumerator(C): Code -> RngMPolElt

HammingAsymptoticBound

HammingAsymptoticBound(K, delta) : FldFin, FldPrElt -> FldPrElt

HammingCode

HammingCode(K, r) : FldFin, RngIntElt -> Code
CodeFld_HammingCode (Example H101E6)

HammingWeightEnumerator

HammingWeightEnumerator(C): Code -> RngMPolElt
WeightEnumerator(C): Code -> RngMPolElt

hand

Creation by Hand (RESOLUTION GRAPHS AND SPLICE DIAGRAMS)

Harmonic

HarmonicNumber(n) : RngIntElt -> RngIntElt

HarmonicNumber

HarmonicNumber(n) : RngIntElt -> RngIntElt

Has

HasAttribute(FldPr, "OutputPrecision") : Cat, MonStgElt -> BoolElt, RngIntElt
HasAttribute(FldPr, "Precision") : Cat, MonStgElt -> BoolElt, RngIntElt
HasAttribute(GrpMat, "FirstBasicOrbitBound") : Cat, MonStgElt -> BoolElt, RngIntElt
HasAttribute(FldFin, "PowerPrinting", l) : Cat, MonStgElt, BoolElt ->
HasAttribute(ModMPol, "MatrixPrinting", l) : Cat, MonStgElt, BoolElt ->
HasAttribute(F, "PowerPrinting") : FldFin, MonStgElt -> BoolElt, BoolElt
HasAttribute(A, s) : GrpAuto, MonStgElt -> BoolElt, .
HasAttribute(A, "GenWeights") : GrpAuto, MonStgElt -> BoolElt, [ RngIntElt ]
HasAttribute(A, "WeightSubgroupOrders") : GrpAuto, MonStgElt -> BoolElt, [ RngIntElt ]
HasAttribute(G, "IsVerified") : GrpMat, MonStgElt -> BoolElt
HasAttribute(G, "Base") : GrpMat, MonStgElt -> BoolElt, Tup
HasAttribute(G, "Order") : GrpMat, MonStgElt -> RngIntElt
HasAttribute(M, "MatrixPrinting") : ModMPol, MonStgElt -> BoolElt, BoolElt
HasAttribute(S, "Precision") : RngSer, MonStgElt -> BoolElt, RngIntElt
HasCentreType(X,i) : VSrfK3,RngIntElt -> BoolElt
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 }
HasClosedCosetTable(P) : GrpFPCosetEnumProc -> BoolElt
HasComplement(G, M) : GrpPerm, GrpPerm -> BoolElt, GrpPerm
HasComplement(M, S) : ModGrp, ModGrp -> BoolElt, ModGrp
HasComputableAbelianQuotient(G) : GrpFP -> BoolElt, GrpAb, Map
HasComputableLCS(G) : GrpGPC -> BoolElt
HasCurve(F) : FldFun -> BoolElt
HasDefinedModuleMap(C,n) : ModCpx, RngIntElt -> BoolElt
HasFiniteOrder(g) : GrpMatElt -> BoolElt, RngIntElt
HasFiniteOrder(A) : Mtrx -> BoolElt
HasGCD(R) : Rng -> BoolElt
HasGroebnerBasis(I) : RngMPol -> BoolElt
HasInfiniteComputableAbelianQuotient(G) : GrpFP -> BoolElt, GrpAb, Map
HasIrregularFibres(s) : GrphSpl -> BoolElt
HasLeviSubalgebra(L) : AlgLie -> BoolElt
HasLinearGrayMapImage(C) : Code -> BoolElt, Code
HasNonsingularPoint(X) : Sch -> BoolElt,Pt
HasOddDegreeModel(C) : CrvHyp -> BoolElt, CrvHyp, MapIsoSch
HasOrder(P, n) : JacHypPt, RngIntElt -> BoolElt
HasOutputFile() : -> BoolElt
HasPRoot(L) : RngLoc -> BoolElt
HasParallelClass(D) : Inc -> BoolElt, { IncBlk }
HasParallelism(D: parameters) : Inc, RngIntElt -> BoolElt, { SetEnum }
HasPointsOverExtension(X) : Sch -> BoolElt
HasPolynomial(N) : NwtnPgon -> BoolElt
HasPolynomialFactorization(R) : Rng -> BoolElt
HasRationalPoint(C) : CrvCon -> BoolElt, Pt
HasResolution(D) : Inc -> BoolElt, { SetEnum }, RngIntElt
HasResolution(D, lambda) : Inc, RngIntElt -> BoolElt, { SetEnum }
HasRoot(p) : RngUPolElt -> BoolElt, RngElt
HasRoot(g) : RngUPolElt -> BoolElt, RngLocElt
HasRoot(g) : RngUPolElt -> BoolElt, RngLocElt
HasRoot(f) : RngUPolElt -> BoolElt, RngSerElt
HasRoot(p, S) : RngUPolElt, Rng -> BoolElt, RngElt
HasSingularPointsOverExtension(C) : Sch -> BoolElt
HasSolubilityCertificate(C) : CrvCon -> BoolElt, SeqEnum
HasSolubilityCertificate(S) : SeqEnum[RngIntElt] -> BoolElt, SeqEnum
HasSparseRep(G) : Grph -> BoolElt
HasSparseRepOnly(G) : Grph -> BoolElt
HasDenseRepOnly(G) : Grph -> BoolElt
HasDenseAndSparseRep(G) : Grph -> BoolElt
HasSupplement(G, M) : GrpPerm, GrpPerm -> BoolElt, GrpPerm
HasValidCosetTable(P) : GrpFPCosetEnumProc -> BoolElt
HasValidIndex(P) : GrpFPCosetEnumProc -> BoolElt

HasAttribute

HasAttribute(FldPr, "OutputPrecision") : Cat, MonStgElt -> BoolElt, RngIntElt
HasAttribute(FldPr, "Precision") : Cat, MonStgElt -> BoolElt, RngIntElt
HasAttribute(GrpMat, "FirstBasicOrbitBound") : Cat, MonStgElt -> BoolElt, RngIntElt
HasAttribute(FldFin, "PowerPrinting", l) : Cat, MonStgElt, BoolElt ->
HasAttribute(ModMPol, "MatrixPrinting", l) : Cat, MonStgElt, BoolElt ->
HasAttribute(F, "PowerPrinting") : FldFin, MonStgElt -> BoolElt, BoolElt
HasAttribute(A, s) : GrpAuto, MonStgElt -> BoolElt, .
HasAttribute(A, "GenWeights") : GrpAuto, MonStgElt -> BoolElt, [ RngIntElt ]
HasAttribute(A, "WeightSubgroupOrders") : GrpAuto, MonStgElt -> BoolElt, [ RngIntElt ]
HasAttribute(G, "IsVerified") : GrpMat, MonStgElt -> BoolElt
HasAttribute(G, "Base") : GrpMat, MonStgElt -> BoolElt, Tup
HasAttribute(G, "Order") : GrpMat, MonStgElt -> RngIntElt
HasAttribute(M, "MatrixPrinting") : ModMPol, MonStgElt -> BoolElt, BoolElt
HasAttribute(S, "Precision") : RngSer, MonStgElt -> BoolElt, RngIntElt

HasCentreType

HasCentreType(X,i) : VSrfK3,RngIntElt -> BoolElt

HasClique

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 }

HasClosedCosetTable

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

HasComplement

HasComplement(G, M) : GrpPerm, GrpPerm -> BoolElt, GrpPerm
HasComplement(M, S) : ModGrp, ModGrp -> BoolElt, ModGrp

HasCompleteCosetTable

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

HasComputableAbelianQuotient

HasComputableAbelianQuotient(G) : GrpFP -> BoolElt, GrpAb, Map

HasComputableLCS

HasComputableLCS(G) : GrpGPC -> BoolElt

HasCurve

HasCurve(F) : FldFun -> BoolElt

HasDefinedModuleMap

HasDefinedModuleMap(C,n) : ModCpx, RngIntElt -> BoolElt

HasDenseAndSparseRep

HasDenseRep(G) : Grph -> BoolElt
HasSparseRepOnly(G) : Grph -> BoolElt
HasDenseRepOnly(G) : Grph -> BoolElt
HasDenseAndSparseRep(G) : Grph -> BoolElt
HasSparseRep(G) : Grph -> BoolElt

HasDenseRep

HasDenseRep(G) : Grph -> BoolElt
HasSparseRepOnly(G) : Grph -> BoolElt
HasDenseRepOnly(G) : Grph -> BoolElt
HasDenseAndSparseRep(G) : Grph -> BoolElt
HasSparseRep(G) : Grph -> BoolElt

HasDenseRepOnly

HasDenseRep(G) : Grph -> BoolElt
HasSparseRepOnly(G) : Grph -> BoolElt
HasDenseRepOnly(G) : Grph -> BoolElt
HasDenseAndSparseRep(G) : Grph -> BoolElt
HasSparseRep(G) : Grph -> BoolElt

HasFiniteOrder

HasFiniteOrder(g) : GrpMatElt -> BoolElt, RngIntElt
HasFiniteOrder(A) : Mtrx -> BoolElt

HasGCD

HasGCD(R) : Rng -> BoolElt

HasGroebnerBasis

HasGroebnerBasis(I) : RngMPol -> BoolElt

Hash

Hash(x) : Elt -> RngIntElt

HasInfiniteComputableAbelianQuotient

HasInfiniteComputableAbelianQuotient(G) : GrpFP -> BoolElt, GrpAb, Map

HasIrregularFibres

HasIrregularFibres(s) : GrphSpl -> BoolElt

HasLeviSubalgebra

HasLeviSubalgebra(L) : AlgLie -> BoolElt

HasLinearGrayMapImage

HasLinearGrayMapImage(C) : Code -> BoolElt, Code

HasNonsingularPoint

HasNonsingularPoint(X) : Sch -> BoolElt,Pt

HasOddDegreeModel

HasOddDegreeModel(C) : CrvHyp -> BoolElt, CrvHyp, MapIsoSch

HasOrder

HasOrder(P, n) : JacHypPt, RngIntElt -> BoolElt

HasOutputFile

HasOutputFile() : -> BoolElt

HasParallelClass

HasParallelClass(D) : Inc -> BoolElt, { IncBlk }

HasParallelism

HasParallelism(D: parameters) : Inc, RngIntElt -> BoolElt, { SetEnum }

HasPointsOverExtension

HasPointsOverExtension(X) : Sch -> BoolElt

HasPolynomial

HasPolynomial(N) : NwtnPgon -> BoolElt

HasPolynomialFactorization

HasPolynomialFactorization(R) : Rng -> BoolElt

HasPRoot

HasPRoot(L) : RngLoc -> BoolElt

HasRationalPoint

HasRationalPoint(C) : CrvCon -> BoolElt, Pt

HasResolution

HasResolution(D) : Inc -> BoolElt, { SetEnum }, RngIntElt
HasResolution(D, lambda) : Inc, RngIntElt -> BoolElt, { SetEnum }

HasRoot

HasRoot(p) : RngUPolElt -> BoolElt, RngElt
HasRoot(g) : RngUPolElt -> BoolElt, RngLocElt
HasRoot(g) : RngUPolElt -> BoolElt, RngLocElt
HasRoot(f) : RngUPolElt -> BoolElt, RngSerElt
HasRoot(p, S) : RngUPolElt, Rng -> BoolElt, RngElt

Hasse

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

HasseWittInvariant

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

HasSingularPointsOverExtension

HasSingularPointsOverExtension(C) : Sch -> BoolElt

HasSolubilityCertificate

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

HasSparseRep

HasDenseRep(G) : Grph -> BoolElt
HasSparseRepOnly(G) : Grph -> BoolElt
HasDenseRepOnly(G) : Grph -> BoolElt
HasDenseAndSparseRep(G) : Grph -> BoolElt
HasSparseRep(G) : Grph -> BoolElt

HasSparseRepOnly

HasDenseRep(G) : Grph -> BoolElt
HasSparseRepOnly(G) : Grph -> BoolElt
HasDenseRepOnly(G) : Grph -> BoolElt
HasDenseAndSparseRep(G) : Grph -> BoolElt
HasSparseRep(G) : Grph -> BoolElt

HasSupplement

HasSupplement(G, M) : GrpPerm, GrpPerm -> BoolElt, GrpPerm

HasValidCosetTable

HasValidCosetTable(P) : GrpFPCosetEnumProc -> BoolElt

HasValidIndex

HasValidIndex(P) : GrpFPCosetEnumProc -> BoolElt

Hecke

DiscriminantOfHeckeAlgebra(M : Bound) : ModSym -> RngIntElt
DualHeckeOperator(M, n) : ModSym, RngIntElt -> AlgMatElt
HeckeAlgebra(M : Bound) : ModSym -> AlgMat
HeckeBound(M) : ModSym -> RngIntElt
HeckeEigenvalueField(M) : ModSym -> Fld, Map
HeckeEigenvalueRing(M : parameters) : ModSym -> Rng, Map
HeckeOperator(M, n) : ModBrdt, RngIntElt -> AlgMatElt
HeckeOperator(M, n) : ModFrm, RngIntElt -> AlgMatElt
HeckeOperator(M, n) : ModSS, RngIntElt -> AlgMatElt
HeckeOperator(M, n) : ModSym, RngIntElt -> AlgMatElt
HeckePolynomial(M, n) : ModSym, RngIntElt -> RngUPolResElt
HeckePolynomial(M, n : parameters ) : ModFrm, RngIntElt -> RngUPolElt
IntegralHeckeOperator(M, n) : ModSym, RngIntElt -> AlgMatElt
SetHeckeBound(M, n) : ModSym, RngIntElt -> RngIntElt

hecke

Hecke Operators (BRANDT MODULES)
The Hecke Algebra (MODULAR SYMBOLS)

Hecke operators

ModSS_Hecke operators (Example H92E8)

hecke-algebra

The Hecke Algebra (MODULAR SYMBOLS)

hecke-operators

Hecke Operators (BRANDT MODULES)

HeckeAlgebra

HeckeAlgebra(M : Bound) : ModSym -> AlgMat
ModSym_HeckeAlgebra (Example H90E17)

HeckeBound

HeckeBound(M) : ModSym -> RngIntElt

HeckeEigenvalueField

HeckeEigenvalueField(M) : ModSym -> Fld, Map

HeckeEigenvalueRing

HeckeEigenvalueRing(M : parameters) : ModSym -> Rng, Map

HeckeOperator

HeckeOperator(M, n) : ModBrdt, RngIntElt -> AlgMatElt
HeckeOperator(M, n) : ModFrm, RngIntElt -> AlgMatElt
HeckeOperator(M, n) : ModSS, RngIntElt -> AlgMatElt
HeckeOperator(M, n) : ModSym, RngIntElt -> AlgMatElt

HeckeOperators

ModSym_HeckeOperators (Example H90E14)

HeckePolynomial

HeckePolynomial(M, n) : ModSym, RngIntElt -> RngUPolResElt
HeckePolynomial(M, n : parameters ) : ModFrm, RngIntElt -> RngUPolElt

HeckePolynomials

ModForm_HeckePolynomials (Example H93E13)

HeighestRoots

RootDtm_HeighestRoots (Example H33E10)

Height

AbsoluteLogarithmicHeight(a) : FldAlgElt -> FldPrElt
Height(P: parameters) : PtEll -> FldPrElt
Height(P: Precision) : JacHypPt -> FldPrElt
HeightConstant(J: parameters) : JacHyp -> FldPrElt, FldPrElt
HeightPairing(P, Q: parameters) : PtEll, PtEll -> FldPrElt
HeightPairing(P, Q: Precision) : JacHypPt, JacHypPt -> FldPrElt
HeightPairingMatrix(S: Precision) : [JacHypPt] -> AlgMat
LocalHeight(P, p) : PtEll, RngIntElt -> FldPrElt
NaiveHeight(P) : JacHypPt -> FldPrElt
NaiveHeight(P) : PtEll -> FldPrElt
RootHeight( RD, r ) : RootDtm, RngIntElt -> RngIntElt

height

Heights and Height Pairing (ELLIPTIC CURVES)

HeightConstant

HeightConstant(J: parameters) : JacHyp -> FldPrElt, FldPrElt

HeightPairing

HeightPairing(P, Q: parameters) : PtEll, PtEll -> FldPrElt
HeightPairing(P, Q: Precision) : JacHypPt, JacHypPt -> FldPrElt
CrvHyp_HeightPairing (Example H88E12)

HeightPairingMatrix

HeightPairingMatrix(S: Precision) : [JacHypPt] -> AlgMat

heights

Heights and Mordell--Weil Group (HYPERELLIPTIC CURVES)

Help

GetHelpExternalBrowser() : -> MonStgElt, MonStgElt
GetHelpExternalSystem() : -> MonStgElt
GetHelpUseExternal() : -> BoolElt, BoolElt
SetHelpExternalBrowser(S, T) : MonStgElt, MonStgElt ->
SetHelpExternalSystem(s) : MonStgElt ->
SetHelpUseExternalBrowser(b) : BoolElt ->
SetHelpUseExternalSystem(b) : BoolElt ->

help

Internal Help Browser (ENVIRONMENT AND OPTIONS)
Overview (OVERVIEW)
The Magma Help System (ENVIRONMENT AND OPTIONS)

HELP_

MAGMA_HELP_DIR

Hensel

HenselLift(g, r) : RngUPolElt, RngLocElt -> RngLocElt
HenselLift(g, r) : RngUPolElt, RngLocElt -> RngLocElt
HenselLift(g, r) : RngUPolElt, RngLocElt -> RngLocElt
HenselLift(g, r) : RngUPolElt, RngLocElt -> RngLocElt
HenselLift(g, r) : RngUPolElt, RngLocElt -> RngLocElt
HenselLift(g, r) : RngUPolElt, RngLocElt -> RngLocElt
HenselLift(g, r) : RngUPolElt, RngLocElt -> RngLocElt
HenselLift(g, r) : RngUPolElt, RngLocElt -> RngLocElt
HenselLift(f, g, h) : RngUPolElt, RngUPolElt, RngUPolElt -> RngUPolElt, RngUPolElt
HenselLift(f, g, h) : RngUPolElt, RngUPolElt, RngUPolElt -> RngUPolElt, RngUPolElt
HenselLift(f, s, P) : RngUPolElt, [ RngUPolElt ], RngUPol -> [ RngUPolElt ]
RngLoc_Hensel (Example H55E15)
RngPad_Hensel (Example H40E13)
RngPol_Hensel (Example H42E6)

hensel

Hensel Lifting (UNIVARIATE POLYNOMIAL RINGS)
Hensel Lifting of Roots (LOCAL RINGS AND FIELDS)
Hensel Lifting of Roots (p-ADIC RINGS AND FIELDS)

hensel-roots

Hensel Lifting of Roots (LOCAL RINGS AND FIELDS)
Hensel Lifting of Roots (p-ADIC RINGS AND FIELDS)

HenselLift

HenselLift(g, r) : RngUPolElt, RngLocElt -> RngLocElt
HenselLift(g, r) : RngUPolElt, RngLocElt -> RngLocElt
HenselLift(f, g, h) : RngUPolElt, RngUPolElt, RngUPolElt -> RngUPolElt, RngUPolElt
HenselLift(f, g, h) : RngUPolElt, RngUPolElt, RngUPolElt -> RngUPolElt, RngUPolElt
HenselLift(f, s, P) : RngUPolElt, [ RngUPolElt ], RngUPol -> [ RngUPolElt ]

Hermite

HermiteForm(X) : AlgMatElt -> AlgMatElt, AlgMatElt
HermiteForm(A) : Mtrx -> Mtrx, ModMatRngElt
HermitePolynomial(n) : RngIntElt -> RngUPolElt

HermiteForm

HermiteForm(X) : AlgMatElt -> AlgMatElt, AlgMatElt
HermiteForm(A) : Mtrx -> Mtrx, ModMatRngElt

HermitePolynomial

HermitePolynomial(n) : RngIntElt -> RngUPolElt

Hermitian

HermitianCode(q, r) : RngIntElt, RngIntElt -> Code
HermitianFunctionField(p, d) : RngIntElt, RngIntElt -> FldFun

HermitianCode

HermitianCode(q, r) : RngIntElt, RngIntElt -> Code

HermitianFunctionField

HermitianFunctionField(p, d) : RngIntElt, RngIntElt -> FldFun

Heron

RngMPol_Heron (Example H43E9)

Hessenberg

HessenbergForm(a) : AlgMatElt -> AlgMatElt
HessenbergForm(A) : Mtrx -> AlgMatElt

HessenbergForm

HessenbergForm(a) : AlgMatElt -> AlgMatElt
HessenbergForm(A) : Mtrx -> AlgMatElt

Hessian

HessianMatrix(X) : Sch -> ModMatRngElt
HessianMatrix(C) : Sch -> Mtrx
GrpPerm_Hessian (Example H20E3)

HessianMatrix

HessianMatrix(X) : Sch -> ModMatRngElt
HessianMatrix(C) : Sch -> Mtrx

Highest

DimensionOfHighestWeightModule(D, w) : RootDtm, [ ] -> RngIntElt
HighestRoot( RD ) : RootDtm -> .
HighestShortRoot( RD ) : RootDtm -> .
HighestWeightRepresentation(L, w) : AlgLie, [ ] -> UserProgram

HighestLongRoot

HighestLongRoot( RD ) : RootDtm -> .
HighestRoot( RD ) : RootDtm -> .

HighestRoot

HighestLongRoot( RD ) : RootDtm -> .
HighestRoot( RD ) : RootDtm -> .

HighestShortRoot

HighestShortRoot( RD ) : RootDtm -> .

HighestWeight

AlgLie_HighestWeight (Example H76E16)

HighestWeightRepresentation

HighestWeightRepresentation(L, w) : AlgLie, [ ] -> UserProgram

Hilber

HilberClassField(K) : FldAlg -> FldAb

HilberClassField

HilberClassField(K) : FldAlg -> FldAb

Hilbert

HilbertClassPolynomial(D) : RngIntElt -> RngUPolElt
HilbertClassPolynomial(D) : RngIntElt -> RngUPolElt
HilbertCoefficients(X,n) : VSrfK3,RngIntElt -> SeqEnum
HilbertForm(X) : VSrfK3 -> SeqEnum
HilbertGroebnerBasis(S, H) : [ RngMPolElt ], FldFunRatUElt -> BoolElt, [ RngMPolElt ]
HilbertNumerator(X) : VSrfK3 -> RngUPolElt
HilbertPolynomial(M) : RngMPol -> RngUPolElt, RngIntElt
R`HilbertSeries
HilbertSeries(M) : ModMPol -> FldFunElt
HilbertSeries(g,B) : RngIntElt,SeqEnum -> FldFunRatUElt
HilbertSeries(R) : RngInvar -> FldFunUElt
HilbertSeries(I) : RngMPol -> FldFunUElt
HilbertSeries(F,V) : SeqEnum,SeqEnum -> FldFunRatUElt
HilbertSeries(X) : VSrfK3 -> FldFunRatUElt
HilbertSeries(X,W) : VSrfK3,SeqEnum -> FldFunRatUElt
GB_Hilbert (Example H66E22)
PMod_Hilbert (Example H68E4)
PMod_Hilbert (Example H68E5)

hilbert

Hilbert Series and Hilbert Polynomial (IDEAL THEORY AND GRÖBNER BASES)
Hilbert-driven Gröbner Basis Construction (IDEAL THEORY AND GRÖBNER BASES)
FldAb_hilbert (Example H51E1)

hilbert-class-field

FldAb_hilbert-class-field (Example H51E6)

hilbert-groebner

Hilbert-driven Gröbner Basis Construction (IDEAL THEORY AND GRÖBNER BASES)

HilbertClassPolynomial

HilbertClassPolynomial(D) : RngIntElt -> RngUPolElt
HilbertClassPolynomial(D) : RngIntElt -> RngUPolElt

HilbertCoefficients

HilbertCoefficients(X,n) : VSrfK3,RngIntElt -> SeqEnum

HilbertForm

EnriquesForm(X) : VSrfK3 -> SeqEnum
NoetherForm(X) : VSrfK3 -> SeqEnum
HilbertForm(X) : VSrfK3 -> SeqEnum

HilbertGroebner

GB_HilbertGroebner (Example H66E23)

HilbertGroebnerBasis

HilbertGroebnerBasis(S, H) : [ RngMPolElt ], FldFunRatUElt -> BoolElt, [ RngMPolElt ]

HilbertNumerator

HilbertNumerator(X) : VSrfK3 -> RngUPolElt

HilbertPolynomial

HilbertPolynomial(M) : RngMPol -> RngUPolElt, RngIntElt

HilbertSeries

R`HilbertSeries
HilbertSeries(M) : ModMPol -> FldFunElt
HilbertSeries(g,B) : RngIntElt,SeqEnum -> FldFunRatUElt
HilbertSeries(R) : RngInvar -> FldFunUElt
HilbertSeries(I) : RngMPol -> FldFunUElt
HilbertSeries(F,V) : SeqEnum,SeqEnum -> FldFunRatUElt
HilbertSeries(X) : VSrfK3 -> FldFunRatUElt
HilbertSeries(X,W) : VSrfK3,SeqEnum -> FldFunRatUElt

Hirsch

HirschNumber(G) : GrpGPC -> RngIntElt

HirschNumber

HirschNumber(G) : GrpGPC -> RngIntElt

History

GetHistorySize() : ->
SetHistorySize(n) : RngIntElt ->

history

History (ENVIRONMENT AND OPTIONS)
History (OVERVIEW)
Magma Updates (OVERVIEW)

HN

GrpFP_1_HN (Example H19E32)

Holes

DeepHoles(L) : Lat -> [ ModTupFldElt ]
Holes(L) : Lat -> [ ModTupFldElt ]

Holomorphic

BasisOfHolomorphicDifferentials(F) : FldFunG -> SeqEnum[DiffFunElt]
BasisOfDifferentialsFirstKind(F) : FldFunG -> SeqEnum[DiffFunElt]
SpaceOfDifferentialsFirstKind(C) : Crv -> ModFld, Map
SpaceOfDifferentialsFirstKind(F) : FldFunG -> ModFld, Map

Hom

Hom(G, H) : GrpAb, GrpAb -> GrpAb, Map
Hom(M, N) : ModDed, ModDed -> ModDed, Map
Hom(M, N, "left") : ModMatRng, ModMatRng, MonStgElt -> ModMatRng
Hom(M, N, "right") : ModMatRng, ModMatRng, MonStgElt -> ModMatRng
Hom(M, N) : ModRng, ModRng -> ModMatRng
Hom(V, W) : ModTupFld, ModTupFld -> ModMat
Hom(M, N) : ModTupRng, ModTupRng -> ModMatRng
HomGenerators(G, H) : GrpAb, GrpAb -> GrpAb, Map
HomGenerators(G, U) : GrpPC, GrpPC -> [<AlgMatElt, RngIntElt>]

hom

Computation of Hom (ABELIAN GROUPS)
Endomorphisms (LATTICES)
Homomorphisms (ALGEBRAIC FUNCTION FIELDS)
Homomorphisms (OVERVIEW)
Homomorphisms (STRUCTURE CONSTANT ALGEBRAS)
Hom_(R)(M, N) for matrix modules (FREE MODULES)
hom< G -> H | x : -> e(x) > : Grp, Grp -> Map
hom< A -> B | x : -> e(x) > : Struct, Struct -> Map
hom< A -> B | Q > : AlgGen, AlgGen, [ AlgGenElt ] -> Map
hom< A -> B | f > : AlgMat, AlgMat, Map -> Map
hom< F -> R | r > : FldAlg, Rng, RngElt -> Map
hom< F -> G | x > : FldFin, Rng -> Map
hom<F -> R | g> : FldFun, Rng, RngElt -> Map
hom< P -> S | f, y_1, ..., y_n > : FldFunRat, Rng -> Map
hom< G -> H | L > : Grp, Grp -> Map
hom< A -> B | L> : Grp, Grp, List -> Map
hom<G | L> : GrpMat, List -> Map
hom< G -> H | L > : GrpPC, GrpPC, List -> Map
hom<G | L> : GrpPerm, List -> Map
hom<M -> N | T> : ModDed, ModDed, Map -> Map
hom< M -> N | X > : ModRng, ModRng, ModMatElt -> ModMatRng
hom< B -> G | S : parameters > : Struct , Struct -> Map
hom< G -> H | L: parameters> : GrpSLP, Grp -> Map
hom< P -> G | S : parameters> : Struct , Struct -> Map
hom< Z -> R | > : RngInt, Rng -> Map
hom< R -> S | > : RngIntRes, Rng -> Map
hom< P -> S | f, y_1, ..., y_n > : RngMPol, Rng -> Map
hom< O -> R | r > : RngOrd, Rng, RngElt -> Map
hom< P -> S | f, y > : RngUPol, Rng, Map, RngElt -> Map
hom< A -> G | S > : Struct , Struct -> Map
hom< M -> N | S > : Struct , Struct -> Map
hom< P -> G | S > : Struct , Struct -> Map
hom< R -> G | S > : Struct , Struct -> Map
hom< A -> B | G > : Struct, Struct -> Map
hom< A -> B | y_1, ..., y_n > : Struct, Struct -> Map
FldFunG_hom (Example H53E11)
FldQuad_hom (Example H49E2)
ModDed_hom (Example H63E6)
RngInt_hom (Example H38E1)

hom-spaces

Scheme_hom-spaces (Example H83E14)

Homeomorphic

IsHomeomorphic(G: parameters) : GraphUnd -> BoolElt

HomGenerators

HomGenerators(G, H) : GrpAb, GrpAb -> GrpAb, Map
HomGenerators(G, U) : GrpPC, GrpPC -> [<AlgMatElt, RngIntElt>]

Homogeneous

HomogeneousComponent(f, d) : RngMPolElt, RngIntElt -> RngMPolElt
HomogeneousComponents(f) : RngMPolElt -> [ RngMPolElt ]
HomogeneousModuleTest(P, S, F) : [ RngMPol ], [ RngMPol ], RngMPol -> BoolElt, [ RngMPol ]
HomogeneousModuleTest(P, S, F) : [ RngMPol ], [ RngMPol ], RngMPol -> BoolElt, [ RngMPol ]
HomogeneousModuleTest(P, S, L) : [ RngMPol ], [ RngMPol ], [ RngMPol ] -> [ BoolElt ], [ [ RngMPol ] ]
HomogeneousModuleTest(P, S, L) : [ RngMPol ], [ RngMPol ], [ RngMPol ] -> [ BoolElt ], [ [ RngMPol ] ]
HomogeneousModuleTestBasis(P, S, L) : [ RngMPol ], [ RngMPol ], [ RngMPol ] -> [ BoolElt ], [ [ RngMPol ] ]
IsHomogeneous(M) : ModMPol -> BoolElt
IsHomogeneous(I) : RngMPol -> BoolElt
IsHomogeneous(f) : RngMPolElt -> BoolElt
IsHomogeneous(X,f) : Sch,RngMPolElt -> BoolElt

HomogeneousComponent

HomogeneousComponent(f, d) : RngMPolElt, RngIntElt -> RngMPolElt

HomogeneousComponents

HomogeneousComponents(f) : RngMPolElt -> [ RngMPolElt ]

HomogeneousModuleTest

HomogeneousModuleTest(P, S, F) : [ RngMPol ], [ RngMPol ], RngMPol -> BoolElt, [ RngMPol ]
HomogeneousModuleTest(P, S, F) : [ RngMPol ], [ RngMPol ], RngMPol -> BoolElt, [ RngMPol ]
HomogeneousModuleTest(P, S, L) : [ RngMPol ], [ RngMPol ], [ RngMPol ] -> [ BoolElt ], [ [ RngMPol ] ]
HomogeneousModuleTest(P, S, L) : [ RngMPol ], [ RngMPol ], [ RngMPol ] -> [ BoolElt ], [ [ RngMPol ] ]

HomogeneousModuleTest1

GB_HomogeneousModuleTest1 (Example H66E27)

HomogeneousModuleTest2

RngInvar_HomogeneousModuleTest2 (Example H80E14)

HomogeneousModuleTestBasis

HomogeneousModuleTestBasis(P, S, L) : [ RngMPol ], [ RngMPol ], [ RngMPol ] -> [ BoolElt ], [ [ RngMPol ] ]

Homogenization

Homogenization(I, b) : RngMPol, RngIntElt, BoolElt -> RngMPol, Map

homogenization

Homogenization of Ideals (IDEAL THEORY AND GRÖBNER BASES)

Homological

HomologicalDimension(M) : ModMPol -> RngInt
HomologicalDimension(M) : ModMPol -> RngInt

HomologicalDimension

HomologicalDimension(M) : ModMPol -> RngInt
HomologicalDimension(M) : ModMPol -> RngInt

Homology

DimensionOfHomology(C, n) : ModCpx, RngIntElt -> RngIntElt
DimensionsOfHomology(C) : ModCpx -> SeqEnum
Homology(C) : ModCpx -> SeqEnum
Homology(C, n) : ModCpx, RngIntElt -> SeqEnum
InducedMapOnHomology(f,n) : MapChn, RngIntElt -> ModTupFldElt
LongExactSequenceOnHomology(f,g) : MapChn, MapChn -> ModCpx
SimpleHomologyDimensions(M) : ModAlg -> SeqEnum

homologymaps

Maps on Homology (CHAIN COMPLEXES)

HomologyOfChainComplex

HomologyOfChainComplex(C) : ModCpx -> SeqEnum
Homology(C) : ModCpx -> SeqEnum

Homomorphism

ConnectingHomomorphism(f,g,n) : MapChn, MapChn, RngIntElt -> ModMatFldElt
Homomorphism(A, B, gens, images) : Grp, Grp, [ GrpElt ], [ GrpElt ] -> Map
IdentityHomomorphism(G) : Grp -> Map
IdentityHomomorphism(G) : GrpPC -> Map
IsHomomorphism(G, H, Q) : GrpMat, GrpMat, SeqEnum[GrpMatElt] -> Bool, Map
IsHomomorphism(G, H, L) : GrpPC, GrpPC, SeqEnum -> BoolElt, Map
IsHomomorphism(G, H, Q) : GrpPerm, GrpPerm, SeqEnum[GrpPermElt] -> Bool, Map
IsModuleHomomorphism(X) : ModMatElt -> BoolElt
IsModuleHomomorphism(f) : ModMatFldElt -> BoolElt
LiftHomomorphism(x, n) : ModAlgElt, RngIntElt -> ModMatFldElt
LiftHomomorphism(X, S) : SeqEnum[ModAlgElt], SeqEnum[RngIntElt] -> ModMatFldElt
FldFunRat_Homomorphism (Example H44E2)
GrpFP_1_Homomorphism (Example H19E17)
GrpGPC_Homomorphism (Example H23E4)
GrpMat_Homomorphism (Example H21E7)
GrpPerm_Homomorphism (Example H20E6)
RngMPol_Homomorphism (Example H43E3)
RngPol_Homomorphism (Example H42E4)

homomorphism

Action on a G-Space (PERMUTATION GROUPS)
Coset Spaces: Induced Homomorphism (FINITELY PRESENTED GROUPS)
Creating Homomorphisms (MODULES OVER A MATRIX ALGEBRA)
Creation of Homomorphisms (MAPPINGS)
Creation of Homomorphisms (ORDERS AND ALGEBRAIC FIELDS)
Elements of M_n as Homomorphisms (MATRIX ALGEBRAS)
Hom(M, N) (MODULES OVER A MATRIX ALGEBRA)
Homomorphisms (AUTOMATIC GROUPS)
Homomorphisms (BRAID GROUPS)
Homomorphisms (FINITE FIELDS)
Homomorphisms (FINITELY PRESENTED GROUPS)
Homomorphisms (GROUPS DEFINED BY REWRITE SYSTEMS)
Homomorphisms (GROUPS)
Homomorphisms (MAPPINGS)
Homomorphisms (MATRIX GROUPS)
Homomorphisms (MODULES OVER A MATRIX ALGEBRA)
Homomorphisms (MONOIDS GIVEN BY REWRITE SYSTEMS)
Homomorphisms (MULTIVARIATE POLYNOMIAL RINGS)
Homomorphisms (OVERVIEW)
Homomorphisms (PERMUTATION GROUPS)
Homomorphisms (POLYCYCLIC GROUPS)
Homomorphisms (RATIONAL FIELD)
Homomorphisms (RATIONAL FUNCTION FIELDS)
Homomorphisms (REAL AND COMPLEX FIELDS)
Homomorphisms (RING OF INTEGERS)
Homomorphisms (RING OF INTEGERS)
Homomorphisms (UNIVARIATE POLYNOMIAL RINGS)
Modules (OVERVIEW)
Subgroups, Quotient Groups, Homomorphisms and Extensions (POLYCYCLIC GROUPS)
Subspaces, Quotient Spaces and Homomorphisms (VECTOR SPACES)
FldRat_homomorphism (Example H39E2)

homomorphism-element

Elements of M_n as Homomorphisms (MATRIX ALGEBRAS)

homomorphism_access

Accessing Homomorphisms (BRAID GROUPS)
Accessing Homomorphisms (FINITELY PRESENTED GROUPS)

homomorphism_constr

Construction of Homomorphisms (AUTOMATIC GROUPS)
Construction of Homomorphisms (BRAID GROUPS)
Construction of Homomorphisms (FINITELY PRESENTED GROUPS)
Construction of Homomorphisms (GROUPS DEFINED BY REWRITE SYSTEMS)
Construction of Homomorphisms (MONOIDS GIVEN BY REWRITE SYSTEMS)
Construction of Homomorphisms (POLYCYCLIC GROUPS)

homomorphism_general

General remarks (AUTOMATIC GROUPS)
General remarks (BRAID GROUPS)
General remarks (FINITELY PRESENTED GROUPS)
General remarks (GROUPS DEFINED BY REWRITE SYSTEMS)
General remarks (MONOIDS GIVEN BY REWRITE SYSTEMS)
General remarks (POLYCYCLIC GROUPS)

Homomorphisms

Homomorphisms(G, H) : GrpAb, GrpAb -> GrpAb, Map
Homomorphisms(G, H) : GrpPC, GrpPC -> SeqEnum
AlgBas_Homomorphisms (Example H81E3)
FldRe_Homomorphisms (Example H41E2)
GrpAbGen_Homomorphisms (Example H17E8)
GrpBrd_Homomorphisms (Example H30E4)
Grp_Homomorphisms (Example H16E1)
RngOrd_Homomorphisms (Example H48E8)

homomorphisms

Creating Homomorphisms (GROUPS OF STRAIGHT-LINE PROGRAMS)
Homomorphisms (BASIC ALGEBRAS)
Homomorphisms (FINITE SOLUBLE GROUPS)
Homomorphisms (FREE MODULES)
Homomorphisms (GENERIC ABELIAN GROUPS)
Homomorphisms between Modules (MODULES OVER DEDEKIND DOMAINS)

HomomorphismSpeed

GrpSLP_HomomorphismSpeed (Example H29E3)

Hook

HookLength(t, i, j) : Tbl, RngIntElt, RngIntElt -> RngIntElt
RandomHookWalk(P, i, j) : SeqEnum[RngIntElt], RngIntElt, RngIntElt -> RngIntElt, RngIntElt

HookLength

HookLength(t, i, j) : Tbl, RngIntElt, RngIntElt -> RngIntElt

Horizontal

HorizontalJoin(X, Y) : ModMatRngElt, ModMatRngElt -> ModMatRngElt
HorizontalJoin(X, Y) : Mtrx, Mtrx -> Mtrx
HorizontalJoin(Q) : [ ModMatRngElt ] -> ModMatRngElt
HorizontalJoin(Q) : [ Mtrx ] -> Mtrx

HorizontalJoin

HorizontalJoin(X, Y) : ModMatRngElt, ModMatRngElt -> ModMatRngElt
HorizontalJoin(X, Y) : Mtrx, Mtrx -> Mtrx
HorizontalJoin(Q) : [ ModMatRngElt ] -> ModMatRngElt
HorizontalJoin(Q) : [ Mtrx ] -> Mtrx

Hull

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

hyp

Heights and Mordell--Weil Group (HYPERELLIPTIC CURVES)

hypcurve

Creation of a Hyperelliptic Curve (HYPERELLIPTIC CURVES)
Creation Predicates (HYPERELLIPTIC CURVES)

hyperbolic

Hyperbolic Functions (REAL AND COMPLEX FIELDS)
Hyperbolic Functions and their Inverses (POWER, LAURENT AND PUISEUX SERIES)
Inverse Hyperbolic Functions (REAL AND COMPLEX FIELDS)

Hypercenter

Hypercenter(G) : GrpAb -> GrpAb
Hypercentre(G) : GrpAb -> GrpAb
Hypercentre(G) : GrpFin -> GrpFin
Hypercentre(G) : GrpPC -> GrpPC
Hypercentre(G) : GrpPerm -> GrpPerm

Hypercentre

Hypercenter(G) : GrpAb -> GrpAb
Hypercentre(G) : GrpAb -> GrpAb
Hypercentre(G) : GrpFin -> GrpFin
Hypercentre(G) : GrpPC -> GrpPC
Hypercentre(G) : GrpPerm -> GrpPerm

Hyperelliptic

HyperellipticCurve(E) : CrvEll -> CrvHyp, Map
HyperellipticCurve(h, f) : RngUPolElt, RngUPolElt -> CrvHyp
HyperellipticCurveFromIgusaClebsch(S) : SeqEnum -> CrvHyp
HyperellipticCurveOfGenus(g, h, f) : RngIntElt, RngUPolElt, RngUPolElt -> CrvHyp
HyperellipticPolynomials(C) : CrvHyp -> RngUPolElt, RngUPolElt
IsHyperellipticCurve([h, g]) : [ RngUPolElt ] -> BoolElt, CrvHyp
IsHyperellipticCurveOfGenus(g, [h, f]) : RngIntElt, [RngUPolElt] -> BoolElt, CrvHyp
IsHyperellipticWeierstrass(C) : Crv -> BoolElt

hyperelliptic

RationalPoints(J, P) : JacHyp, SrfKumPt -> SetIndx
HYPERELLIPTIC CURVES

hyperelliptic-curve

RationalPoints(J, P) : JacHyp, SrfKumPt -> SetIndx
HYPERELLIPTIC CURVES

HyperellipticCurve

HyperellipticCurve(E) : CrvEll -> CrvHyp, Map
HyperellipticCurve(h, f) : RngUPolElt, RngUPolElt -> CrvHyp

HyperellipticCurveFromIgusaClebsch

HyperellipticCurveFromIgusaClebsch(S) : SeqEnum -> CrvHyp

HyperellipticCurveOfGenus

HyperellipticCurveOfGenus(g, h, f) : RngIntElt, RngUPolElt, RngUPolElt -> CrvHyp

HyperellipticPolynomials

HyperellipticPolynomials(C) : CrvHyp -> RngUPolElt, RngUPolElt

Hypergeometric

HypergeometricSeries(a,b,c, z) : RngElt, RngElt, RngElt, RngElt -> RngElt
HypergeometricSeries(a,b,c, z) : RngElt, RngElt, RngElt, RngElt -> RngElt
HypergeometricU(a, b, s) : FldPrElt, FldPrElt, FldPrElt -> FldPrElt

hypergeometric

The Hypergeometric Function (REAL AND COMPLEX FIELDS)
The Hypergeometric series (POWER, LAURENT AND PUISEUX SERIES)

HypergeometricSeries

HypergeometricSeries(a,b,c, z) : RngElt, RngElt, RngElt, RngElt -> RngElt
HypergeometricSeries(a,b,c, z) : RngElt, RngElt, RngElt, RngElt -> RngElt

HypergeometricU

HypergeometricU(a, b, s) : FldPrElt, FldPrElt, FldPrElt -> FldPrElt

Hyperplane

HyperplaneAtInfinity(X) : Sch -> Sch

HyperplaneAtInfinity

HyperplaneAtInfinity(X) : Sch -> Sch

Hypersurface

IsHypersurface(X) : Sch -> BoolElt, RngMPolElt

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