Subindex: <B><B>O</B> .. One</B>

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Subindex: O .. One

O

   O(x) : RngPadElt -> RngPadElt
   BigO(x) : RngPadElt -> RngPadElt
   BigO(f) : RngSerElt -> RngIntElt
   O(s) : RngDiffElt -> RngDiffElt

o

o`CyclotomicExtensions : RngOrd -> [Rec]

object

The Error Objects (STATEMENTS AND EXPRESSIONS)

Objective

ObjectiveFunction(L) : LP -> Mtrx
SetObjectiveFunction(L, F) : LP, Mtrx ->

ObjectiveFunction

ObjectiveFunction(L) : LP -> Mtrx

Objects

Combinatorial Objects (SYMMETRIC FUNCTIONS)

Obstruction

   Obstruction(G) : GrphMultUnd -> GrphMultUnd
   Obstruction(G) : GrphUnd -> GrphUnd
   ObstructionDescentBuildingBlock(M) : ModSym -> SeqEnum

ObstructionDescentBuildingBlock

ObstructionDescentBuildingBlock(M) : ModSym -> SeqEnum

Odd

   HasOddDegreeModel(C) : CrvHyp -> BoolElt, CrvHyp, MapIsoSch
   IsOdd(x) : GrpDrchElt -> BoolElt
   IsOdd(n) : RngIntElt -> BoolElt
   LRatioOddPart(M, j) : ModSym, RngIntElt -> FldRatElt
   OddGraph(n) : RngIntElt -> GrphUnd

OddGraph

OddGraph(n) : RngIntElt -> GrphUnd
EnumComb_OddGraph (Example H114E1)

of

   Conjugacy of Subgroups of the Classical Groups (MATRIX GROUPS OVER FINITE FIELDS)
   Differential Operators of Algebraic Functions (DIFFERENTIAL RINGS, FIELDS AND OPERATORS)
   Searching For Points (HYPERELLIPTIC CURVES)
   Structure of Congruence Subgroups (SUBGROUPS OF PSL_2(R))
   Twisted Groups of Lie Type (GROUPS OF LIE TYPE)

ofe

RngLoc_ofe (Example H59E12)

Old

   OldQuotient(A) : ModAbVar -> ModAbVar, MapModAbVar
   OldQuotient(A, r) : ModAbVar, RngIntElt -> ModAbVar, MapModAbVar
   OldSubvariety(A) : ModAbVar -> ModAbVar, MapModAbVar
   OldSubvariety(A, r) : ModAbVar, RngIntElt -> ModAbVar, MapModAbVar

OldQuotient

OldQuotient(A) : ModAbVar -> ModAbVar, MapModAbVar
OldQuotient(A, r) : ModAbVar, RngIntElt -> ModAbVar, MapModAbVar

OldSubvariety

OldSubvariety(A) : ModAbVar -> ModAbVar, MapModAbVar
OldSubvariety(A, r) : ModAbVar, RngIntElt -> ModAbVar, MapModAbVar

Omega

   AutomorphismOmega(U) : AlgQUE -> Map
   IsogenyMapOmega(I) : Map -> RngMPolElt
   Omega(G, i) : GrpAb, RngIntElt -> GrpAb
   Omega(G, i) : GrpPC, RngIntElt -> GrpPC
   Omega(n, q) : RngIntElt, RngIntElt -> GrpMat
   OmegaMinus(n, q) : RngIntElt, RngIntElt -> GrpMat
   OmegaPlus(n, q) : RngIntElt, RngIntElt -> GrpMat
   ProjectiveOmega(arguments)
   ProjectiveOmegaMinus(arguments)
   ProjectiveOmegaPlus(arguments)

OmegaMinus

OmegaMinus(n, q) : RngIntElt, RngIntElt -> GrpMat

OmegaPlus

OmegaPlus(n, q) : RngIntElt, RngIntElt -> GrpMat

omit

Multiple Assignment (OVERVIEW)

On

   FrobeniusActionOnPoints(s, q : parameters) : [ PtEll ], RngIntElt -> AlgMatElt
   FrobeniusActionOnReducibleFiber(L) : < Tup > -> AlgMatElt
   FrobeniusActionOnTrivialLattice(E) : CrvEll -> AlgMatElt
   GammaOrbitOnRoots(R,r) : RootDtm, RngIntElt -> GSetEnum
   GammaOrbitsOnRoots(R) : RootDtm -> SeqEnum[GSetEnum]
   HeightOnAmbient(P) : Pt -> FldReElt
   InducedMapOnHomology(f, n) : MapChn, RngIntElt -> ModTupFldElt
   LongExactSequenceOnHomology(f, g) : MapChn, MapChn -> ModCpx
   NumberOfPointsOnSurface(E, e) : CrvEll, RngIntElt -> RngIntElt
   NumberOfStandardTableauxOnWeight(n) : RngIntElt -> RngIntElt
   NumberOfTableauxOnAlphabet(P, m) : SeqEnum,RngIntElt -> RngIntElt
   NumbersOfPointsOnSurface(E, e) : CrvEll, RngIntElt -> [ RngIntElt ], [ RngIntElt ]
   SetDebugOnError(f) : BoolElt ->
   SetQuitOnError(b) : BoolElt ->
   TableauxOnShapeWithContent(S, C) : SeqEnum[RngIntElt], SeqEnum[RngIntElt] -> SetEnum

on

SUPERSINGULAR DIVISORS ON MODULAR CURVES

One

   One(O) : AlgAssVOrd -> AlgAssVOrdElt
   O ! 1 : AlgAssVOrd, RngIntElt -> AlgAssVOrdElt
   U ! 1 : AlgPBW, RngIntElt -> AlgPBWElt
   A ! 1 : AlgQuat, RngIntElt -> AlgQuatElt
   U ! 1 : AlgQUE, RngIntElt -> AlgQUEElt
   DegreeOnePrimeIdeals(O, B) : RngOrd, RngIntElt -> [ RngOrdIdl ]
   DivisorOfDegreeOne(C) : Crv[FldFin] -> DivCrvElt
   DivisorOfDegreeOne(F) : FldFun -> DivFunElt
   DoubleGenusOneModel(model) : ModelG1 -> ModelG1
   ExtendedOneCocycle(alpha) : OneCoC -> SetEnum[OneCoC]
   GenusOneModel(C) : Crv -> ModelG1
   GenusOneModel(mat) : Mtrx -> ModelG1
   GenusOneModel(n,E) : RngIntElt, CrvEll -> ModelG1, Crv, MapSch, MapSch
   GenusOneModel(n,seq) : RngIntElt, [RngElt] -> ModelG1
   GenusOneModel(mats) : SeqEnum -> ModelG1
   HasMultiplicityOne(A) : ModAbVar -> BoolElt
   Id(R) : AlgChtr -> AlgChtrElt
   IdentifyOneCocycle(CM, s) : ModCoho, UserProgram -> ModTupRngElt
   IdentityAutomorphism(G) : GrpLie -> GrpLieAutoElt
   InducedOneCocycle(AmodB, alpha) : GGrp, OneCoC -> OneCoC
   IsGenusOneModel(f) : RngMPolElt -> BoolElt, ModelG1
   IsMinusOne(a) : AlgGenElt -> BoolElt
   IsMinusOne(a) : AlgMatElt -> BoolElt
   IsMinusOne(a) : FldACElt -> BoolElt
   IsMinusOne(A) : Mtrx -> BoolElt
   IsMinusOne(a) : RngElt -> BoolElt
   IsMinusOne(a) : RngOrdResElt -> BoolElt
   IsMinusOne(x) : RngPadElt -> BoolElt
   IsMinusOne(s) : RngPowLazElt -> BoolElt
   IsOne(a) : AlgGenElt -> BoolElt
   IsOne(a) : AlgMatElt -> BoolElt
   IsOne(a) : FldACElt -> BoolElt
   IsOne(u) : MonFPElt -> BoolElt
   IsOne(A) : Mtrx -> BoolElt
   IsOne(s) : RngDiffElt -> BoolElt
   IsOne(L) : RngDiffOpElt -> BoolElt
   IsOne(a) : RngElt -> BoolElt
   IsOne(I) : RngFunOrdIdl -> BoolElt
   IsOne(a) : RngOrdResElt -> BoolElt
   IsOne(x) : RngPadElt -> BoolElt
   IsOne(s) : RngPowLazElt -> BoolElt
   IsOneCocycle(A, imgs) : GGrp, SeqEnum[GrpElt] -> BoolElt, OneCoC
   MaximalZeroOneSolution(LHS, relations, RHS, objective) : Mtrx, Mtrx, Mtrx, Mtrx -> Mtrx, RngIntElt
   MinimalZeroOneSolution(LHS, relations, RHS, objective) : Mtrx, Mtrx, Mtrx, Mtrx -> Mtrx, RngIntElt
   NumberOfPlacesOfDegreeOne(m, U) : DivFunElt, GrpAb -> RngIntElt
   NumberOfPlacesOfDegreeOneECFBound(C) : Crv -> RngIntElt
   NumberOfPlacesOfDegreeOneECFBound(F) : FldFun -> RngIntElt
   NumberOfPlacesOfDegreeOneOverExactConstantField(C) : Crv[FldFin] -> RngIntElt
   NumberOfPlacesOfDegreeOneOverExactConstantField(C, m) : Crv[FldFin], RngIntElt -> RngIntElt
   NumberOfPlacesOfDegreeOneOverExactConstantField(F) : FldFun -> RngIntElt
   NumberOfPlacesOfDegreeOneOverExactConstantField(F, m) : FldFun -> RngIntElt
   NumberOfPlacesOfDegreeOneOverExactConstantField(F, m) : FldFun, RngIntElt -> RngIntElt
   NumberOfPlacesOfDegreeOneOverExactConstantFieldBound(F, m) : FldFun, RngIntElt -> RngIntElt
   One(A) : AlgGen -> AlgGenElt
   One(R) : Rng -> RngElt
   One(R) : RngDiff -> RngDiffElt
   One(R) : RngDiffOp -> RngDiffOpElt
   One(L) : RngPad -> RngPadElt
   OneCocycle(A, imgs) : GGrp, SeqEnum[GrpElt] -> OneCoC
   OneCocycle(CM, s) : ModCoho, SeqEnum -> UserProgram
   OneCohomology(A) : GGrp -> SetEnum[OneCoC]
   RandomGenusOneModel(n) : RngIntElt -> ModelG1
   TrivialOneCocycle(A) : GGrp -> OneCoC

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