[____] [____] [_____] [____] [__] [Index] [Root]
Index S
S-algebras (FINITELY PRESENTED ALGEBRAS)
DivisorGroup(K) : FldNum -> DivNum
Creation of structures (ORDERS AND ALGEBRAIC FIELDS)
S-algebras (FINITELY PRESENTED ALGEBRAS)
S
s
IsSatisfied(U, E) : { RelElt }, [ GrpElt ] -> BoolElt
CosetSatisfying(P : parameters) : GrpFPCosetEnumProc -> { GrpFPElt }
CosetsSatisfying(P : parameters) : GrpFPCosetEnumProc -> { GrpFPElt }
CosetsSatisfying(T, S: parameters) : Map, { GrpFPElt }: -> { GrpFPCosElt }
ExistsCosetSatisfying(P : parameters) : GrpFPCosetEnumProc -> BoolElt, GrpFPElt
IsolGroupOfDegreeFieldSatisfying(d,{p, f}) : RngIntElt, RngIntElt, Predicate -> GrpMat
IsolGroupOfDegreeSatisfying(d, f) : RngIntElt, Predicate -> GrpMat
IsolGroupSatisfying(f) : Predicate -> GrpMat
IsolGroupsOfDegreeFieldSatisfying(d,{p, f}) : RngIntElt, RngIntElt, Predicate -> SeqEnum
IsolGroupsOfDegreeSatisfying(d, f) : RngIntElt, Predicate -> SeqEnum
IsolGroupsSatisfying(f) : Predicate -> SeqEnum
Saving and restoring Magma states (OVERVIEW)
save "filename";
Saving and restoring Magma states (OVERVIEW)
IsScalar(u) : AlgFPElt -> BoolElt
IsScalar(a) : AlgMatElt -> BoolElt
IsScalar(g) : GrpMatElt -> BoolElt
IsScalar(A) : Mtrx -> BoolElt
ScalarMatrix(R, t) : AlgMat, RngElt -> AlgMatElt
ScalarMatrix(R, n, s) : Rng, RngIntElt, RngElt -> Mtrx
ScalarMatrix(n, s) : RngIntElt, RngElt -> Mtrx
ScalarMatrix(R, t) : AlgMat, RngElt -> AlgMatElt
ScalarMatrix(R, n, s) : Rng, RngIntElt, RngElt -> Mtrx
ScalarMatrix(n, s) : RngIntElt, RngElt -> Mtrx
ScalarsQuadraticForm(G) : GrpMat -> SeqEnum
ScalarsSymmetricBilinearForm(G) : GrpMat -> SeqEnum
ScalarsSymplecticForm(G) : GrpMat -> SeqEnum
ScalarsUnitaryForm(G) : GrpMat -> SeqEnum
ScalarsQuadraticForm(G) : GrpMat -> SeqEnum
ScalarsSymmetricBilinearForm(G) : GrpMat -> SeqEnum
ScalarsSymplecticForm(G) : GrpMat -> SeqEnum
ScalarsUnitaryForm(G) : GrpMat -> SeqEnum
ScaledIgusaInvariants(f): RngUPolElt -> SeqEnum
ScaledIgusaInvariants(h, f): RngUPolElt, RngUPolElt -> SeqEnum
ScaledLattice(L,n) : Lat, RngIntElt -> Lat
ScaledIgusaInvariants(f): RngUPolElt -> SeqEnum
ScaledIgusaInvariants(h, f): RngUPolElt, RngUPolElt -> SeqEnum
ScaledLattice(L,n) : Lat, RngIntElt -> Lat
BaseScheme(L) : LinSys -> SchProj
BaseScheme(f) : MapSch -> Sch
Scheme(p) : Pt -> Sch
Scheme(p) : Pt -> Sch
Scheme(X,f) : Sch,RngMPolElt -> Sch
Scheme(P) : SetPt -> Sch
Scheme(H) : SetPtEll -> CrvEll
Scheme(P) : SetPtEll -> CrvEll
SubgroupScheme(E,P) : CrvEll, Pt -> CrvEllSubgroup
SubgroupScheme(G, f) : SchGrpEll, RngUPolElt -> SchGrpEll
TorsionSubgroupScheme(G, n) : SchGrpEll, RngIntElt -> SchGrpEll
A Pair of Twisted Cubics (SCHEMES)
Advanced Examples (SCHEMES)
Curves in Space (SCHEMES)
Advanced Examples (SCHEMES)
Curves in Space (SCHEMES)
A Pair of Twisted Cubics (SCHEMES)
Scheme_scheme-equality (Example H83E5)
Scheme_scheme-points (Example H83E6)
Affine and Projective Spaces (SCHEMES)
Base Change for Schemes (SCHEMES)
Basic Attributes of Schemes (SCHEMES)
Constructing Schemes (SCHEMES)
Different Types of Scheme (SCHEMES)
Functions and Homogeneity on Ambient Spaces (SCHEMES)
Functions of the Ambient Space (SCHEMES)
Global Geometry of Schemes (SCHEMES)
Introduction (SCHEMES)
Local Geometry of Schemes (SCHEMES)
Maps and Schemes (SCHEMES)
Prelude to Points (SCHEMES)
Projective Closure and Affine Patches (SCHEMES)
Rational Points and Point Sets (SCHEMES)
SCHEMES
Schemes (SCHEMES)
Schemes (SCHEMES)
Scrolls and Products (SCHEMES)
Zero-dimensional Schemes (SCHEMES)
Introduction (SCHEMES)
Projective Closure and Affine Patches (SCHEMES)
Functions and Homogeneity on Ambient Spaces (SCHEMES)
Prelude to Points (SCHEMES)
Base Change for Schemes (SCHEMES)
Basic Attributes of Schemes (SCHEMES)
Functions of the Ambient Space (SCHEMES)
Zero-dimensional Schemes (SCHEMES)
Name(X,i) : Sch,RngIntElt -> RngMPolElt
Constructing Schemes (SCHEMES)
Scheme_schemes-creation (Example H83E4)
Global Geometry of Schemes (SCHEMES)
Local Geometry of Schemes (SCHEMES)
Rational Points and Point Sets (SCHEMES)
Scheme_schemes-points-example1 (Example H83E2)
Scheme_schemes-prime-components (Example H83E8)
Scrolls and Products (SCHEMES)
Affine and Projective Spaces (SCHEMES)
Different Types of Scheme (SCHEMES)
RandomSchreier(G: parameters) : GrpMat ->
RandomSchreier(G: parameters) : GrpPerm : ->
SchreierGenerators(G, H : parameters) : GrpFP, GrpFP -> { GrpFPElt }
SchreierGraph(A, B) : Grp, Grp -> GrphDir
SchreierSystem(G, H) : GrpFP, GrpFP -> {@ GrpFPElt @}, Map
SchreierVector(G, i) : GrpPerm, RngIntElt -> [RngIntElt]
SchreierVectors(G) : GrpPerm -> [ [RngIntElt] ]
SimsSchreier(G: parameters) : GrpPerm : ->
SolubleSchreier(G: parameters) : GrpPerm : ->
ToddCoxeterSchreier(G) : GrpMat : ->
ToddCoxeterSchreier(G: parameters) : GrpPerm : ->
SchreierGenerators(G, H : parameters) : GrpFP, GrpFP -> { GrpFPElt }
GrpFP_1_SchreierGenerators (Example H19E42)
UnlabelledSchreierGraph(A, B) : Grp, Grp -> GrphDir
SchreierGraph(A, B) : Grp, Grp -> GrphDir
Transversal(G, H) : GrpFP, GrpFP -> {@ GrpFPElt @}, Map
SchreierSystem(G, H) : GrpFP, GrpFP -> {@ GrpFPElt @}, Map
SchreierVector(G, i) : GrpPerm, RngIntElt -> [RngIntElt]
SchreierVectors(G) : GrpPerm -> [ [RngIntElt] ]
AbsolutelyIrreducibleModulesSchur(G, K: parameters) : GrpPC, Rng -> List[GModule]
AbsolutelyIrreducibleRepresentationsSchur(G, k: parameters) : GrpPC, Rng -> List[Map]
IrreducibleModulesSchur(G, K: parameters) : GrpPC, Rng -> List[GModule]
IrreducibleRepresentationsSchur(G, k: parameters) : GrpPC, Rng -> List[Map]
Schur(x, k) : AlgChtrElt, RngIntElt -> FldCycElt
SClassGroup(S) : SetEnum[PlcFunElt] -> GrpAb, Map, Map
SClassGroupAbelianInvariants(S) : SetEnum[PlcFunElt] -> SeqEnum
SClassGroupExactSequence(S) : SetEnum[PlcFunElt] -> Map, Map, Map
SClassNumber(S) : SetEnum[PlcFunElt] -> RngIntElt
SClassGroup(S) : SetEnum[PlcFunElt] -> GrpAb, Map, Map
SClassGroupAbelianInvariants(S) : SetEnum[PlcFunElt] -> SeqEnum
SClassGroupExactSequence(S) : SetEnum[PlcFunElt] -> Map, Map, Map
SClassNumber(S) : SetEnum[PlcFunElt] -> RngIntElt
Scope (MAGMA SEMANTICS)
AbsoluteRationalScroll(k,N) : Rng,SeqEnum -> PrjScrl
Scheme_scroll-map-base-points (Example H83E19)
Scrolls and Products (SCHEMES)
R sdiff S : SetEnum, SetEnum -> SetEnum
SEA(H: parameters) : SetPtEll -> RngIntElt
CrvEll_SEA (Example H87E27)
BFSTree(u) : GrphVert -> Grph
BreadthFirstSearchTree(u) : GrphVert -> Grph
DepthFirstSearchTree(u) : GrphVert -> Grph
Search(~P: parameters) : Process(Tietze) ->
SearchEqual(~P: parameters) : Process(Tietze) ->
SearchForDecomposition(G, S) : GrpMat, [GrpMatElt] -> BoolElt
SearchEqual(~P: parameters) : Process(Tietze) ->
SearchForDecomposition(G, S) : GrpMat, [GrpMatElt] -> BoolElt
Searching the Database (THE K3 DATABASE)
Searching with predicates (DATABASES OF GROUPS)
Sec(c) : FldComElt -> FldComElt
Sec(f) : RngSerElt -> RngSerElt
Automorphisms (RATIONAL CURVES AND CONICS)
Introduction (RATIONAL CURVES AND CONICS)
Isomorphisms (RATIONAL CURVES AND CONICS)
Rational Curves and Conics (RATIONAL CURVES AND CONICS)
Conics (RATIONAL CURVES AND CONICS)
Rational Points on Conics (RATIONAL CURVES AND CONICS)
AllSecants(P, A) : Plane, { PlanePt } -> { PlaneLn }
Sech(s) : FldPrElt -> FldPrElt
ChebyshevU(n) : RngIntElt -> RngUPolElt
ChebyshevSecond(n) : RngIntElt -> RngUPolElt
DicksonSecond(n, a) : RngIntElt, RngElt -> RngUPolElt
DicksonSecond(n, a) : RngIntElt, RngElt -> RngUPolElt
StirlingSecond(m, n) : RngIntElt, RngIntElt -> RngIntElt
StirlingSecond(m, n) : RngIntElt, RngIntElt -> RngIntElt
Crv_second-affine-patch (Example H84E8)
IrreducibleSecondaryInvariants(R) : RngInvar -> [ RngMPolElt ]
R`SecondaryInvariants
SecondaryInvariants(R) : RngInvar -> [ RngMPolElt ]
SecondaryInvariants(R, H) : RngInvar, Grp -> [ RngMPolElt ]
Secondary Invariants (INVARIANT RINGS OF FINITE GROUPS)
R`SecondaryInvariants
SecondaryInvariants(R) : RngInvar -> [ RngMPolElt ]
SecondaryInvariants(R, H) : RngInvar, Grp -> [ RngMPolElt ]
RngInvar_SecondaryInvariants (Example H80E7)
AbelianSection(SQP: parameter) : SQProc -> BoolElt, SQProc
ElementaryAbelianSection(SQP: parameter) : SQProc -> BoolElt, SQProc
NilpotentSection(SQP: parameter) : SQProc -> BoolElt, SQProc
NonsplitSection(SQP: parameter) : SQProc -> BoolElt, SQProc
NonsplitElementaryAbelianSection(SQP: parameter) : SQProc -> BoolElt, SQProc
RefineSection(G, M, N) : GrpPerm, GrpPerm, GrpPerm -> [ GrpPerm ]
SectionCentraliser(G, H, K) : GrpPerm, GrpPerm, GrpPerm -> GrpPerm
SplitAbelianSection(SQP: parameter) : SQProc -> BoolElt, SQProc
SplitElementaryAbelianSection(SQP: parameter) : SQProc -> BoolElt, SQProc
SplitSection(SQP: parameter) : SQProc -> BoolElt, SQProc
Action on an Elementary Abelian Section (K[G]-MODULES AND GROUP REPRESENTATIONS)
Action on an Elementary Abelian Section (K[G]-MODULES AND GROUP REPRESENTATIONS)
SectionCentralizer(G, H, K) : GrpPerm, GrpPerm, GrpPerm -> GrpPerm
SectionCentraliser(G, H, K) : GrpPerm, GrpPerm, GrpPerm -> GrpPerm
SectionCentralizer(G, H, K) : GrpPerm, GrpPerm, GrpPerm -> GrpPerm
SectionCentraliser(G, H, K) : GrpPerm, GrpPerm, GrpPerm -> GrpPerm
Sections(L) : LinSys -> SeqEnum
Calculation of Standard Sections (FP GROUPS - ADVANCED FEATURES)
GetSeed() : -> RngIntElt, RngIntElt
SetSeed(s, c) : RngIntElt ->
SetSeed(s, c) : RngIntElt ->
SetSeed(s, c) : RngIntElt ->
SetSeed(s, c) : RngIntElt ->
Seek(F, o, p) : File, RngIntElt, RngIntElt ->
Expression (OVERVIEW)
The select expression (OVERVIEW)
IsSelfOrthogonal(C) : Code -> BoolElt
IsSelfDual(C) : Code -> BoolElt
IsSelfDual(C) : Code -> BoolElt
IsSelfDual(C) : Code -> BoolElt
IsSelfDual(D) : Inc -> BoolElt
IsSelfDual(P) : PlaneProj -> BoolElt
IsSelfNormalising(G, H) : GrpGPC, GrpGPC -> BoolElt
IsSelfNormalizing(G, H) : GrpFin, GrpFin -> BoolElt
IsSelfNormalizing(G, H) : GrpFP, GrpFP -> BoolElt
IsSelfNormalizing(G, H) : GrpPC, GrpPC -> BoolElt
IsSelfNormalizing(G, H) : GrpPerm, GrpPerm -> BoolElt
IsWeaklySelfDual(C) : Code -> BoolElt
IsWeaklySelfDual(C) : Code -> BoolElt
IsWeaklySelfDual(C) : Code -> BoolElt
Self(n) : RngIntElt -> Elt
SelfIntersections(g) : GrphRes -> SeqEnum
Seq_Self (Example H8E5)
CodeFld_SelfDual (Example H101E17)
CodeRng_SelfDualZ4 (Example H102E7)
ModifySelfintersection(~v,n) : GrphResVert,RngIntElt ->
SelfIntersections(g) : GrphRes -> SeqEnum
TwoSelmerGroupData(J: parameters) : JacHyp -> RngIntElt, RngIntElt, Tup, List
The 2-Selmer Group (HYPERELLIPTIC CURVES)
FldAb_Selmer-group (Example H51E3)
MAGMA SEMANTICS
IsNegativeSemiDefinite(F) : ModMatRngElt -> BoolElt
IsPositiveSemiDefinite(F) : ModMatRngElt -> BoolElt
IsSemiLinear(G) : GrpMat -> BoolElt
SemiLinearGroup(G, S) : GrpMat, FldFin -> GrpMat
SemiSimpleLieAlgebra(X, F) : MonStgElt, Fld -> AlgLie
SemiSimpleType(L) : AlgLie -> AlgLie
Semidir(G, Q) : GrpMat, SeqEnum -> GrpPerm
FreeSemigroup(n) : RngIntElt -> SgpFP
Semigroup< generators | relations > : SgpFPElt, ..., SgpFPElt, Rel, ...Rel -> SgpFP
Semigroups (OVERVIEW)
Semigroups (OVERVIEW)
SemiLinearGroup(G, S) : GrpMat, FldFin -> GrpMat
GrpMat_Semilinearity (Example H21E32)
Semilinearity (MATRIX GROUPS)
IsSemiregular(G, Y) : GrpPerm, GSet -> BoolElt
IsSemiregular(G, Y, S) : GrpPerm, GSet, SetEnum -> BoolElt
IsSemisimple(A) : AlgGen -> BoolElt
IsSemisimple( G ) : GrpLie-> BoolElt
IsSemisimple(M) : ModAlg -> BoolElt, SeqEnum
IsSemisimple(M) : ModGrp -> BoolElt
IsSemisimple( RD ) : RootDtm-> BoolElt
SemisimpleEFAModuleMaps(G) : GrpGPC -> [ModGrp]
SemisimpleEFAModules(G) : GrpGPC -> [ModGrp]
SemisimpleEFASeries(G) : GrpGPC -> [GrpGPC]
SemisimpleRank( G ) : GrpLie -> RngIntElt
The Type of a Semisimple Lie Algebra (LIE ALGEBRAS)
The Type of a Semisimple Lie Algebra (LIE ALGEBRAS)
SemisimpleEFAModuleMaps(G) : GrpGPC -> [ModGrp]
SemisimpleEFAModules(G) : GrpGPC -> [ModGrp]
SemisimpleEFASeries(G) : GrpGPC -> [GrpGPC]
SemiSimpleLieAlgebra(X, F) : MonStgElt, Fld -> AlgLie
SemisimpleRank( G ) : GrpLie -> RngIntElt
SemiSimpleType(L) : AlgLie -> AlgLie
AlgLie_SemiSimpleType (Example H76E10)
IsMDS(C) : Code -> BoolElt
IsMaximumDistanceSeparable(C) : Code -> BoolElt
IsSeparable(G) : GrphUnd -> BoolElt
IsSeparable(f) : RngUPolElt -> BoolElt
IsSeparating(a) : FldFunGElt -> BoolElt
SeparatingElement(F) : FldFunG -> FldFunGElt
SeparatingElement(F) : FldFunG -> FldFunGElt
EltSeq(P): PtEll -> [ RngElt ]
ElementToSequence(P): PtEll -> [ RngElt ]
Seq(G) : GrpAtc -> SeqEnum
Seq(G, a, b) : GrpAtc, RngIntElt, RngIntElt -> SeqEnum
Seq(G) : GrpRWS -> SeqEnum
Seq(G, a, b) : GrpRWS, RngIntElt, RngIntElt -> SeqEnum
Seq(M) : MonRWS -> SeqEnum
Seq(M, a, b) : MonRWS, RngIntElt, RngIntElt -> SeqEnum
SeqFact(s) : SeqEnum -> RngIntEltFact
Seqelt(s, F) : [ FldFinElt ] -> FldFinElt
SequenceToElement(s, F) : [ FldFinElt ] -> FldFinElt
Sequences (OVERVIEW)
SequenceToFactorization(s) : SeqEnum -> RngIntEltFact
SeqFact(s) : SeqEnum -> RngIntEltFact
Seqint(s, b) : [RngIntElt], RngIntElt -> RngIntElt
SequenceToInteger(s, b) : [RngIntElt], RngIntElt -> RngIntElt
Seqlist(Q) : SeqEnum -> List
SequenceToList(Q) : SeqEnum -> List
SequenceToSet(S) : SeqEnum -> SetEnum
Seqset(S) : SeqEnum -> SetEnum
ClassGroupExactSequence(F) : FldFun -> Map, Map, Map
ClassGroupExactSequence(O) : RngFunOrd -> Map, Map, Map
Coefficients(f) : RngSerElt -> [ RngElt ], RngIntElt, RngIntElt
Coefficients(p) : RngUPolElt -> [ RngElt ]
DegreeSequence(G) : Grph -> [ { GrphVert } ]
DifferentiationSequence(x, n, a) : FldFunGElt, RngIntElt, FldFunGElt -> SeqEnum
ElementSequence(G) : GrpPC -> SeqEnum
ElementToSequence(a) : AlgGenElt -> SeqEnum
ElementToSequence(a) : AlgGrpElt -> SeqEnum
ElementToSequence(a) : AlgMatElt -> [ RngElt ]
ElementToSequence(x) : AlgQuatOrdElt -> SeqEnum
Coordinates(x) : AlgQuatElt -> SeqEnum
ElementToSequence(a) : FldAlgElt -> [ FldAlgElt ]
ElementToSequence(a) : FldFinElt -> [ FldFinElt ]
ElementToSequence(a, E) : FldFinElt, FldFin -> [ FldFinElt ]
ElementToSequence(a) : FldFunElt -> SeqEnum[FldFunRatUElt]
ElementToSequence(a) : FldRatElt -> [FldRatElt]
ElementToSequence(x) : GrpAbElt -> [RngIntElt]
ElementToSequence(u) : GrpAtcElt -> [ RngIntElt ]
ElementToSequence(u) : GrpBrdElt -> [ RngIntElt ]
ElementToSequence(w) : GrpFPElt -> [ RngIntElt ]
ElementToSequence(x) : GrpGPCElt -> [RngIntElt]
ElementToSequence(g) : GrpMatElt -> [ RngElt ]
ElementToSequence(x) : GrpPCElt -> [RngIntElt]
ElementToSequence(g) : GrpPermElt -> [ Elt ]
ElementToSequence(u) : GrpRWSElt -> [ RngIntElt ]
ElementToSequence(v) : LatElt -> [ RngElt ]
ElementToSequence(a) : ModDedElt -> SeqEnum
ElementToSequence(u) : ModTupFldElt -> [RngElt]
ElementToSequence(u) : ModTupRngElt -> [RngElt]
ElementToSequence(u) : ModTupRngElt -> [RngElt]
ElementToSequence(w) : MonOrdElt -> SeqEnum
ElementToSequence(u) : MonRWSElt -> [ RngIntElt ]
ElementToSequence(s) : MonStgElt -> [ MonStgElt ]
ElementToSequence(A) : Mtrx -> [ RngElt ]
ElementToSequence(l) : PlaneLn -> [ FldFinElt ]
ElementToSequence(p) : PlanePt -> [ FldFinElt ]
ElementToSequence(P): PtEll -> [ RngElt ]
ElementToSequence(a) : RngGalElt -> [ RngIntResElt ]
ElementToSequence(x) : RngLocElt -> [ RngElt ]
ElementToSequence(x) : RngLocElt -> [ RngIntElt ]
ElementToSequence(u) : SgpFPElt -> [ SgpFPElt ]
Eltseq(P) : PtHyp -> SeqEnum
Eltseq(P) : PtHyp -> SeqEnum, RngIntElt
Eltseq(f) : QuadBinElt -> SeqEnum[RngIntElt]
Eltseq(f) : RngIntEltFact -> SeqEnum
Eltseq(a) : RngOrdResElt -> []
Eltseq(P) : SrfKumPt -> SeqEnum
GeneratorsSequence(G) : GrpPerm -> [ GrpPermElt ]
IndexedSetToSequence(S) : SetIndx -> SeqEnum
IntegerToSequence(n, b) : RngIntElt, RngIntElt -> [RngIntElt]
IsShortExactSequence(f, g) : MapChn, MapChn -> BoolElt
IsShortExactSequence(C) : ModCpx -> BoolElt, RngIntElt
LongExactSequenceOnHomology(f,g) : MapChn, MapChn -> ModCpx
MaximalIncreasingSequence(w) : MonOrdElt -> RngIntElt
PowerSequence(R) : Struct -> PowSeqEnum
RandomSequenceBlumBlumShub(b, t) : RngIntElt, RngIntElt -> SeqEnum
RandomSequenceBlumBlumShub(n, s, t) : RngIntElt, RngIntElt, RngIntElt -> SeqEnum
RandomSequenceRSA(b, t) : RngIntElt, RngIntElt -> SeqEnum
RandomSequenceRSA(n, e, s, t) : RngIntElt, RngIntElt, RngIntElt,RngIntElt -> SeqEnum
Representation(g) : GrpAbGenElt -> [RngIntElt]
SClassGroupExactSequence(S) : SetEnum[PlcFunElt] -> Map, Map, Map
SeqFact(s) : SeqEnum -> RngIntEltFact
Seqset(S) : SeqEnum -> SetEnum
SequenceToElement(s, F) : [ FldFinElt ] -> FldFinElt
SequenceToInteger(s, b) : [RngIntElt], RngIntElt -> RngIntElt
SequenceToList(Q) : SeqEnum -> List
SequenceToMultiset(Q) : SeqEnum -> SetMulti
Setseq(S) : SetEnum -> SeqEnum
StringToIntegerSequence(s) : MonStgElt -> [ RngIntElt ]
VarietySequence(I) : RngMPol -> [ [ RngElt ] ]
aInvariants(E) : CrvEll -> [ RngElt ]
Eltseq(x) : GrpAbElt -> [RngIntElt]
Deconstruction of an Element (ABELIAN GROUPS)
Factorization Sequences (RING OF INTEGERS)
Parents of Sets and Sequences (INTRODUCTION [SETS, SEQUENCES, AND MAPPINGS])
Power Sequences (SEQUENCES)
Sequence Conversions (ALGEBRAIC FUNCTION FIELDS)
Sequence Conversions (FINITE FIELDS)
Sequence Conversions (GALOIS RINGS)
Sequence Conversions (LOCAL RINGS AND FIELDS)
Sequence Conversions (p-ADIC RINGS AND FIELDS)
Sequence Conversions (RATIONAL FIELD)
Sequences (OVERVIEW)
MaximalIncreasingSequences(w, k) : SeqEnum,RngIntElt -> RngIntElt
PSEUDO-RANDOM BIT SEQUENCES
Seqelt(s, F) : [ FldFinElt ] -> FldFinElt
SequenceToElement(s, F) : [ FldFinElt ] -> FldFinElt
SequenceToFactorization(s) : SeqEnum -> RngIntEltFact
SeqFact(s) : SeqEnum -> RngIntEltFact
Seqint(s, b) : [RngIntElt], RngIntElt -> RngIntElt
SequenceToInteger(s, b) : [RngIntElt], RngIntElt -> RngIntElt
Seqlist(Q) : SeqEnum -> List
SequenceToList(Q) : SeqEnum -> List
SequenceToMultiset(Q) : SeqEnum -> SetMulti
SequenceToSet(S) : SeqEnum -> SetEnum
Seqset(S) : SeqEnum -> SetEnum
CharacteristicSeries(A) : GrpAuto -> SeqEnum
ChiefSeries(G) : GrpAb -> [GrpAb]
ChiefSeries(G) : GrpMat -> [ GrpMat ], [ <RngIntElt, RngIntElt, RngIntElt, RngIntElt> ]
ChiefSeries(G) : GrpPC -> [GrpPC]
ChiefSeries(G) : GrpPerm -> [ GrpPerm ], [ <RngIntElt, RngIntElt, RngIntElt, RngIntElt> ]
CompositionSeries(A) : AlgGen -> [ AlgGen ], [ AlgGen ], AlgMatElt
CompositionSeries(G) : GrpPC -> [GrpPC]
CompositionSeries(G, i) : GrpPC, RngIntElt -> [GrpPC]
CompositionSeries(M) : ModRng, ModRng -> [ ModRng ], [ ModRng ], AlgMatElt
DerivedSeries(L) : AlgLie -> [ AlgLie ]
DerivedSeries(G) : GrpAb -> [GrpAb]
DerivedSeries(G) : GrpFin -> [ GrpFin ]
DerivedSeries(G) : GrpGPC -> [GrpGPC]
DerivedSeries(G) : GrpMat -> [ GrpMat ]
DerivedSeries(G) : GrpPC -> [GrpPC]
DerivedSeries(G) : GrpPerm -> [ GrpPerm ]
EisensteinSeries(M) : ModFrm -> List
ElementaryAbelianSeries(G) : GrpAb -> [GrpAb]
ElementaryAbelianSeries(G) : GrpPC -> [GrpPC]
ElementaryAbelianSeries(G: parameters) : GrpPerm -> [ GrpPerm ]
ElementaryAbelianSeries(G: parameters) : GrpPerm -> [ GrpPerm ]
FittingSeries(G) : GrpGPC -> [GrpGPC]
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
HypergeometricSeries(a,b,c, z) : RngElt, RngElt, RngElt, RngElt -> RngElt
HypergeometricSeries(a,b,c, z) : RngElt, RngElt, RngElt, RngElt -> RngElt
IsEisensteinSeries(f) : ModFrmElt -> BoolElt
IsEisensteinSeries(f) : ModFrmElt -> BoolElt
JenningsSeries(G) : GrpFin -> [ GrpFin ]
JenningsSeries(G) : GrpMat -> [ GrpMat ]
JenningsSeries(G) : GrpPC -> [GrpPC]
JenningsSeries(G) : GrpPerm -> [ GrpPerm ]
LaurentSeriesRing(R) : Rng -> RngSerLaur
LazyPowerSeriesRing(C, n) : Rng, RngIntElt -> RngPowLaz
LazySeries(R, f) : RngPowLaz, RngMPolElt -> RngPowLazElt
LowerCentralSeries(L) : AlgLie -> [ AlgLie ]
LowerCentralSeries(G) : GrpFin -> [ GrpFin ]
LowerCentralSeries(G) : GrpGPC -> [GrpGPC]
LowerCentralSeries(G) : GrpMat -> [ GrpMat ]
LowerCentralSeries(G) : GrpPC -> [GrpPC]
LowerCentralSeries(G) : GrpPerm -> [ GrpPerm ]
MolienSeries(G) : GrpMat -> FldFunUElt
PowerSeriesRing(R) : Rng -> RngSerPow
PrintSeries(SQP) : SQProc ->
PuiseuxSeriesRing(R) : Rng -> RngSerPuis
SocleSeries(G) : GrpPerm -> [ GrpPerm ]
SocleSeries(M) : ModRng -> [ ModRng ], [ ModRng ], AlgMatElt
SubnormalSeries(G, H) : GrpAb, GrpAb -> [GrpAb]
SubnormalSeries(G, H) : GrpFin, GrpFin -> [ GrpFin ]
SubnormalSeries(G, H) : GrpMat, GrpMat -> [ GrpMat ]
SubnormalSeries(G, H) : GrpPC, GrpPC -> [GrpPC]
SubnormalSeries(G, H) : GrpPerm, GrpPerm -> [ GrpPerm ]
ThetaSeries(L, n) : Lat, RngIntElt -> RngSerElt
ThetaSeries(x, y, prec) : ModBrdtElt, ModBrdtElt, RngIntElt -> RngSerElt
ThetaSeries(f, n) : QuadBinElt, RngIntElt -> RngSerElt
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 ]
WeierstrassSeries(z, t) : FldPrElt, RngSerElt -> RngSerElt
WeierstrassSeries(z, q, p) : RngElt, RngSerElt, RngIntElt -> RngSerElt
WeierstrassSeries(z, F) : RngSerElt, QuadBinElt -> RngSerElt
WeierstrassSeries(z, f) : RngSerElt, QuadBinElt -> RngSerElt
WeierstrassSeries(z, q) : RngSerElt, RngSerElt -> RngSerElt
WeierstrassSeries(z, L) : RngSerElt, SeqEnum -> RngSerElt
pCentralSeries(G, p) : GrpFin, RngIntElt -> [ GrpFin ]
pCentralSeries(G, p) : GrpMat, RngIntElt -> [ GrpMat ]
pCentralSeries(G, p) : GrpPC, RngIntElt -> [GrpPC]
pCentralSeries(G, p) : GrpPerm, RngIntElt -> [ GrpPerm ]
qEigenform(M, prec) : ModSym, RngIntElt -> RngSerPowElt
qExpansion(f) : ModFrmElt -> RngSerPowElt
AlgLie_Series (Example H76E7)
GrpMat_Series (Example H21E26)
GrpPerm_Series (Example H20E23)
Characteristic Subgroups and Normal Series (PERMUTATION GROUPS)
Characteristic Subgroups and Subgroup Series (ABELIAN GROUPS)
Characteristic Subgroups and Subgroup Series (GROUPS)
Characteristic Subgroups and Subgroup Series (MATRIX GROUPS)
Characteristic Subgroups and Subgroup Series (POLYCYCLIC GROUPS)
Composition and Chief Series (PERMUTATION GROUPS)
Composition Series (MODULES OVER A MATRIX ALGEBRA)
Eisenstein Series (MODULAR FORMS)
Normal Subgroups and Subgroup Series (FINITE SOLUBLE GROUPS)
POWER, LAURENT AND PUISEUX SERIES
Rings, Fields, and Algebras (OVERVIEW)
Series (LIE ALGEBRAS)
Socle Series (MODULES OVER A MATRIX ALGEBRA)
Special Values of L-functions (MODULAR SYMBOLS)
Subgroup Series (FINITE SOLUBLE GROUPS)
Tools for the calculation of specific normal series (FP GROUPS - ADVANCED FEATURES)
POWER, LAURENT AND PUISEUX SERIES
RngLoc_series-print (Example H55E2)
RngPad_series-print (Example H40E1)
SerreBound(F) : FldFun -> RngIntElt
SerreBound(F) : FldFun -> RngIntElt
GetViMode() : -> BoolElt
Set and Get (ENVIRONMENT AND OPTIONS)
Set Operations (AUTOMATIC GROUPS)
Set Operations (GROUPS DEFINED BY REWRITE SYSTEMS)
Set Operations (MONOIDS GIVEN BY REWRITE SYSTEMS)
E(m) : CrvEll, Map -> SetPtEll
E(L) : CrvEll, Rng -> SetPtEll
BlockSet(D) : Inc -> IncBlkSet
DifferenceSet(p, t) : RngIntElt, MonStgElt -> { RngIntResElt }
EdgeSet(G) : Grph -> GrphEdgeSet
ElementSet(G, H) : GrpPerm, GrpPerm -> { GrpPermElt }
FormalSet(M) : Struct -> SetForm
HasAttribute(A, s) : GrpAuto, MonStgElt -> BoolElt, .
IndexedSetToSequence(S) : SetIndx -> SeqEnum
IndexedSetToSet(S) : SetIndx -> SetEnum
InformationSet(C) : Code -> [ RngIntElt ]
IsDifferenceSet(B) : SetEnum -> BoolElt, RngIntElt
LeftDescentSet( W, w ) : GrpCox, GrpPermElt -> { }
LineSet(P) : Plane -> PlaneLnSet
MaximumIndependentSet(G: parameters) : GrphUnd -> { GrphVert }
MinimumDominatingSet(G) : GrphUnd -> SetEnum
MultisetToSet(S) : SetMulti -> SetEnum
PointSet(D) : Inc -> IncPtSet
PointSet(P) : Plane -> PlanePtSet
PowerFormalSet(R) : Struct -> PowSetIndx
PowerIndexedSet(R) : Struct -> PowSetIndx
PowerSet(R) : Struct -> PowSetEnum
RightDescentSet( W, w ) : GrpCox, GrpPermElt -> { }
Seqset(S) : SeqEnum -> SetEnum
Set(F) : FldFin -> SetEnum
Set(G) : GrpAtc -> SetEnum
Set(G, a, b) : GrpAtc, RngIntElt, RngIntElt -> SetEnum
Set(G) : GrpRWS -> SetEnum
Set(G, a, b) : GrpRWS, RngIntElt, RngIntElt -> SetEnum
Set(B) : IncBlk -> { IncPt }
Set(M) : MonRWS -> SetEnum
Set(M, a, b) : MonRWS, RngIntElt, RngIntElt -> SetEnum
Set(l) : PlaneLn -> { PlanePt }
Set(R) : RngIntRes -> SetEnum
Set(M) : Struct -> SetEnum
SetAFR(~DB) : SeqEnum ->
SetAllInvariantsOfDegree(R, d, Q) : RngInvar, RngIntElt, [ RngMPolElt ] ->
SetAssertions(b) : BoolElt ->
SetAutoColumns(b) : BoolElt ->
SetAutoCompact(b) : BoolElt ->
SetBeep(b) : BoolElt ->
SetBufferSize(D, n) : DB, RngIntElt ->
SetColumns(n) : RngIntElt ->
SetDefaultRealField(R) : FldRe ->
SetDisplayLevel(~P, Level) : Process(pQuot), RngIntElt ->
SetEchoInput(b) : BoolElt ->
SetEchoInput(b) : BoolElt ->
SetEntry(~A, i, j, x) : MtrxSprs, RngIntElt, RngIntElt, RngElt ->
SetExtraspecialSigns( RD, s ) : RootDtm, . ->
SetGlobalTCParameters(: parameters) : ->
SetHeckeBound(M, n) : ModSym, RngIntElt -> RngIntElt
SetHelpExternalBrowser(S, T) : MonStgElt, MonStgElt ->
SetHelpExternalSystem(s) : MonStgElt ->
SetHelpUseExternalBrowser(b) : BoolElt ->
SetHelpUseExternalSystem(b) : BoolElt ->
SetHistorySize(n) : RngIntElt ->
SetIgnorePrompt(b) : BoolElt ->
SetIgnoreSpaces(b) : BoolElt ->
SetIndent(n) : RngIntElt ->
SetIntegerSolutionVariables(L, I, m) : LP, SeqEnum[RngIntElt], BoolElt ->
SetKantPrecision(O, n) : RngOrd, RngIntElt ->
SetKantPrinting(f) : BoolElt -> BoolElt
SetLibraries(s) : MonStgElt ->
SetLibraryRoot(s) : MonStgElt ->
SetLineEditor(b) : BoolElt ->
SetLogFile(F) : MonStgElt ->
SetLogFile(F) : MonStgElt ->
SetLowerBound(L, n, b) : LP, RngIntElt, RngElt ->
SetMaximiseFunction(L, m) : LP, BoolElt ->
SetMemoryLimit(n) : RngIntElt ->
SetNormalising( G, Normalising ) : GrpLie, BoolElt -> .
SetObjectiveFunction(L, F) : LP, Mtrx ->
SetOptions(~P : parameters) : Process(Tietze) ->
SetOrderMaximal(O, b) : RngOrd, BoolElt ->
SetOrderTorsionUnit(O, e, r) : RngOrd, RngOrdElt, RngIntElt ->
SetOrderUnitsAreFundamental(O) : RngOrd ->
SetOutputFile(F) : MonStgElt ->
SetOutputFile(F) : MonStgElt ->
SetPath(s) : MonStgElt ->
SetPowerPrinting(F, l) : FldFin, BoolElt ->
SetPrecision(M, prec) : ModFrm, RngIntElt ->
SetPreviousSize(n) : RngIntElt ->
SetPrimitiveElement(F, x) : FldFin, FldFinElt ->
SetPrintLevel(l) : MonStgElt ->
SetProcessParameters(~P: parameters) : GrpFPCosetEnumProc ->
SetPrompt(s) : MonStgElt ->
SetQuitOnError(b) : BoolElt ->
SetRows(n) : RngIntElt ->
SetSeed(s, c) : RngIntElt ->
SetSeed(s, c) : RngIntElt ->
SetToIndexedSet(E) : SetEnum -> SetIndx
SetToMultiset(E) : SetEnum -> SetMulti
SetTraceback(n) : BoolElt ->
SetUpperBound(L, n, b) : LP, RngIntElt, RngElt ->
SetVerbose("Cunningham", b) : MonStgElt, Boolean ->
SetVerbose("Buchberger", v) : MonStgElt, RngIntElt ->
SetVerbose("CrvHypRed", v) : MonStgElt, RngIntElt ->
SetVerbose("Decomposition", v) : MonStgElt, RngIntElt ->
SetVerbose("Factorization", v) : MonStgElt, RngIntElt ->
SetVerbose("Faugere", v) : MonStgElt, RngIntElt ->
SetVerbose("FFLog", v) : MonStgElt, RngIntElt ->
SetVerbose("FGLM", v) : MonStgElt, RngIntElt ->
SetVerbose("Groebner", v) : MonStgElt, RngIntElt ->
SetVerbose("GroebnerWalk", v) : MonStgElt, RngIntElt ->
SetVerbose("HilbertGroebner", v) : MonStgElt, RngIntElt ->
SetVerbose("Invariants", v) : MonStgElt, RngIntElt ->
SetVerbose("JacHypCnt", v) : MonStgElt, RngIntElt ->
SetVerbose("KBMAG", v) : MonStgElt, RngIntElt ->
SetVerbose("KBMAG", v) : MonStgElt, RngIntElt ->
SetVerbose("KBMAG", v) : MonStgElt, RngIntElt ->
SetVerbose("LLL", v) : MonStgElt, RngIntElt ->
SetVerbose("Newton", v) : MonStgElt, RngIntElt ->
SetVerbose("NilpotentQuotient", n) : MonStgElt, RngIntElt ->
SetVerbose("PolyFact", v) : MonStgElt, RngIntElt ->
SetVerbose("PolyFact", v) : MonStgElt, RngIntElt ->
SetVerbose("SEA", v) : MonStgElt, RngIntElt ->
SetVerbose("SparseMatrix", v) : MonStgElt, RngIntElt ->
SetVerbose("SubgroupLattice", i) : MonStgElt, RngIntElt ->
SetVerbose("SubmoduleLattice", i) : MonStgElt, RngIntElt ->
SetVerbose("SupersingularModule", n) : MonStgElt, RngIntElt ->
SetVerbose(s, i) : MonStgElt, RngIntElt ->
SetVerbose(s, n) : MonStgElt, RngIntElt ->
SetViMode(b) : BoolElt ->
Setseq(S) : SetEnum -> SeqEnum
SingerDifferenceSet(n, q) : RngIntElt, RngIntElt -> { RngIntResElt }
VertexSet(G) : Grph -> GrphVertSet
X(L) : Sch,Rng -> SetPt
GrpAtc_Set (Example H28E6)
GrpPC_Set (Example H24E11)
GrpRWS_Set (Example H27E6)
MonRWS_Set (Example H15E6)
Cliques, Independent Sets (GRAPHS)
Parents of Sets and Sequences (INTRODUCTION [SETS, SEQUENCES, AND MAPPINGS])
Power Sets (SETS)
Set Operations (FINITE SOLUBLE GROUPS)
Set Operations (GROUPS)
Set Operations (MATRIX GROUPS)
Set Operations (PERMUTATION GROUPS)
Set-Theoretic Operations (ABELIAN GROUPS)
Set-Theoretic Operations (GENERIC ABELIAN GROUPS)
Set-Theoretic Operations (GROUPS OF STRAIGHT-LINE PROGRAMS)
Set-Theoretic Operations in a Group (POLYCYCLIC GROUPS)
Sets (OVERVIEW)
The Information Space and Information Sets (LINEAR CODES OVER FINITE FIELDS)
The Point-Set and Block-Set of an Incidence Structure (INCIDENCE STRUCTURES AND DESIGNS)
The Point-Set and Line-Set of a Plane (FINITE PLANES)
The Vertex--Set and Edge--Set of a Graph (GRAPHS)
GetViMode() : -> BoolElt
Set and Get (ENVIRONMENT AND OPTIONS)
Set Operations (FINITE SOLUBLE GROUPS)
GrpPC_set_ops (Example H24E10)
SetAFR(~DB) : SeqEnum ->
SetAllInvariantsOfDegree(R, d, Q) : RngInvar, RngIntElt, [ RngMPolElt ] ->
GetAssertions() : -> BoolElt
SetAssertions(b) : BoolElt ->
SetAttribute(A, s, v) : GrpAuto, MonStgElt, . ->
HasAttribute(A, s) : GrpAuto, MonStgElt -> BoolElt, .
GetAutoColumns() : -> BoolElt
SetAutoColumns(b) : BoolElt ->
GetAutoCompact() : -> BoolElt
SetAutoCompact(b) : BoolElt ->
GetBeep() : -> BoolElt
SetBeep(b) : BoolElt ->
SetBufferSize(D, n) : DB, RngIntElt ->
GetColumns() : -> RngIntElt
SetColumns(n) : RngIntElt ->
SetDefaultRealField(R) : FldRe ->
SetDisplayLevel(~P, Level) : Process(pQuot), RngIntElt ->
GetEchoInput() : ->
SetEchoInput(b) : BoolElt ->
SetEchoInput(b) : BoolElt ->
SetEntry(~A, i, j, x) : MtrxSprs, RngIntElt, RngIntElt, RngElt ->
Sets (OVERVIEW)
SetExtraspecialSigns( RD, s ) : RootDtm, . ->
Sets (OVERVIEW)
SetGlobalTCParameters(: parameters) : ->
SetHeckeBound(M, n) : ModSym, RngIntElt -> RngIntElt
SetHelpExternalBrowser(S, T) : MonStgElt, MonStgElt ->
SetHelpExternalSystem(s) : MonStgElt ->
SetHelpUseExternalBrowser(b) : BoolElt ->
SetHelpUseExternalSystem(b) : BoolElt ->
GetHistorySize() : ->
SetHistorySize(n) : RngIntElt ->
GetIgnorePrompt() : -> BoolElt
SetIgnorePrompt(b) : BoolElt ->
GetIgnoreSpaces() : -> BoolElt
SetIgnoreSpaces(b) : BoolElt ->
GetIndent() : -> RngIntElt
SetIndent(n) : RngIntElt ->
Sets (OVERVIEW)
SetIntegerSolutionVariables(L, I, m) : LP, SeqEnum[RngIntElt], BoolElt ->
SetKantPrecision(O, n) : RngOrd, RngIntElt ->
SetKantPrinting(f) : BoolElt -> BoolElt
GetLibraries() : -> MonStgElt
SetLibraries(s) : MonStgElt ->
GetLibraryRoot() : -> MonStgElt
SetLibraryRoot(s) : MonStgElt ->
GetLineEditor() : BoolElt ->
SetLineEditor(b) : BoolElt ->
UnsetLogFile() : ->
SetLogFile(F) : MonStgElt ->
SetLogFile(F) : MonStgElt ->
SetLowerBound(L, n, b) : LP, RngIntElt, RngElt ->
SetMaximiseFunction(L, m) : LP, BoolElt ->
GetMemoryLimit() : -> RngIntElt
SetMemoryLimit(n) : RngIntElt ->
SetNormalizing( G, Normalising ) : GrpLie, BoolElt -> .
SetNormalising( G, Normalising ) : GrpLie, BoolElt -> .
SetNormalizing( G, Normalising ) : GrpLie, BoolElt -> .
SetNormalising( G, Normalising ) : GrpLie, BoolElt -> .
SetObjectiveFunction(L, F) : LP, Mtrx ->
GrpPerm_SetOperations (Example H20E10)
Grp_SetOperations (Example H16E13)
SetOptions(~P : parameters) : Process(Tietze) ->
SetOrderMaximal(O, b) : RngOrd, BoolElt ->
SetOrderTorsionUnit(O, e, r) : RngOrd, RngOrdElt, RngIntElt ->
SetOrderUnitsAreFundamental(O) : RngOrd ->
SetOutputFile(F) : MonStgElt ->
SetOutputFile(F) : MonStgElt ->
GetPath() : -> MonStgElt
SetPath(s) : MonStgElt ->
AssertAttribute(F, "PowerPrinting", l) : FldFin, MonStgElt, BoolElt ->
SetPowerPrinting(F, l) : FldFin, BoolElt ->
SetPrecision(M, prec) : ModFrm, RngIntElt ->
SetPreviousSize(n) : RngIntElt ->
SetPrimitiveElement(F, x) : FldFin, FldFinElt ->
GetPrintLevel() : -> MonStgElt
SetPrintLevel(l) : MonStgElt ->
SetProcessParameters(~P: parameters) : GrpFPCosetEnumProc ->
GetPrompt() : -> MonStgElt
SetPrompt(s) : MonStgElt ->
SetQuitOnError(b) : BoolElt ->
GetRows() : -> RngIntElt
SetRows(n) : RngIntElt ->
AllInformationSets(C) : Code -> [ [ RngIntElt ] ]
G-Sets (PERMUTATION GROUPS)
Places (PLANE ALGEBRAIC CURVES)
Sets (OVERVIEW)
Sets of Places (PLANE ALGEBRAIC CURVES)
GetSeed() : -> RngIntElt, RngIntElt
SetSeed(s, c) : RngIntElt ->
SetSeed(s, c) : RngIntElt ->
SetToSequence(S) : SetEnum -> SeqEnum
Setseq(S) : SetEnum -> SeqEnum
Setting Properties of Orders (ORDERS AND ALGEBRAIC FIELDS)
SetToIndexedSet(E) : SetEnum -> SetIndx
SetToMultiset(E) : SetEnum -> SetMulti
SetToSequence(S) : SetEnum -> SeqEnum
Setseq(S) : SetEnum -> SeqEnum
GetTraceback() : -> BoolElt
SetTraceback(n) : BoolElt ->
SetUpperBound(L, n, b) : LP, RngIntElt, RngElt ->
SetVerbose("Cunningham", b) : MonStgElt, Boolean ->
SetVerbose("Buchberger", v) : MonStgElt, RngIntElt ->
SetVerbose("CrvHypRed", v) : MonStgElt, RngIntElt ->
SetVerbose("Decomposition", v) : MonStgElt, RngIntElt ->
SetVerbose("Factorization", v) : MonStgElt, RngIntElt ->
SetVerbose("Faugere", v) : MonStgElt, RngIntElt ->
SetVerbose("FFLog", v) : MonStgElt, RngIntElt ->
SetVerbose("FGLM", v) : MonStgElt, RngIntElt ->
SetVerbose("Groebner", v) : MonStgElt, RngIntElt ->
SetVerbose("GroebnerWalk", v) : MonStgElt, RngIntElt ->
SetVerbose("HilbertGroebner", v) : MonStgElt, RngIntElt ->
SetVerbose("Invariants", v) : MonStgElt, RngIntElt ->
SetVerbose("JacHypCnt", v) : MonStgElt, RngIntElt ->
SetVerbose("KBMAG", v) : MonStgElt, RngIntElt ->
SetVerbose("KBMAG", v) : MonStgElt, RngIntElt ->
SetVerbose("KBMAG", v) : MonStgElt, RngIntElt ->
SetVerbose("LLL", v) : MonStgElt, RngIntElt ->
SetVerbose("Newton", v) : MonStgElt, RngIntElt ->
SetVerbose("NilpotentQuotient", n) : MonStgElt, RngIntElt ->
SetVerbose("PolyFact", v) : MonStgElt, RngIntElt ->
SetVerbose("PolyFact", v) : MonStgElt, RngIntElt ->
SetVerbose("SEA", v) : MonStgElt, RngIntElt ->
SetVerbose("SparseMatrix", v) : MonStgElt, RngIntElt ->
SetVerbose("SubgroupLattice", i) : MonStgElt, RngIntElt ->
SetVerbose("SubmoduleLattice", i) : MonStgElt, RngIntElt ->
SetVerbose("SupersingularModule", n) : MonStgElt, RngIntElt ->
SetVerbose(s, i) : MonStgElt, RngIntElt ->
SetVerbose(s, n) : MonStgElt, RngIntElt ->
GetViMode() : -> BoolElt
SetViMode(b) : BoolElt ->
Seysen(L) : Lat -> Lat, AlgMatElt
Seysen(X) : ModMatRngElt -> ModMatRngElt, AlgMatElt
SeysenGram(F) : ModMatRngElt -> ModMatRngElt, AlgMatElt, RngIntElt
Lat_Seysen (Example H64E13)
Seysen Reduction (LATTICES)
SeysenGram(F) : ModMatRngElt -> ModMatRngElt, AlgMatElt, RngIntElt
GrpData_sg-process (Example H22E13)
GrpData_sg-process (Example H22E2)
Database of Almost-Simple Groups (DATABASES OF GROUPS)
GrpData_sgdb (Example H22E11)
Semigroups (OVERVIEW)
Shadow(D, I, F) : IncGeom, Set, Set -> SetIndx
ShadowSpace(D,I) : IncGeom, Set -> Inc
Shadow Spaces (INCIDENCE GEOMETRY)
Shadow Spaces (INCIDENCE GEOMETRY)
Shadows (INCIDENCE GEOMETRY)
ShadowSpace(D,I) : IncGeom, Set -> Inc
OuterShape(t) : Tbl -> SeqEnum
Shape(t) : Tbl -> SeqEnum[RngIntElt]
SkewShape(t) : Tbl -> SeqEnum[RngIntElt]
TableauxOfShape(S, m) : SeqEnum[RngIntElt], RngIntElt -> SetEnum
TableauxOnShapeWithContent(S, C) : SeqEnum[RngIntElt], SeqEnum[RngIntElt] -> SetEnum
IsSharplyTransitive(G, Y, k) : GrpPerm, GSet, RngIntElt -> BoolElt
Performing shell commands from Magma (OVERVIEW)
Performing shell commands from Magma (OVERVIEW)
ShephardTodd(n) : RngIntElt -> GrpMat, Fld
ShephardTodd(n) : RngIntElt -> GrpMat, Fld
Shift(C, n) : ModCpx, RngIntElt -> ModCpx
ShiftToDegreeZero(C) : ModCpx -> ModCpx
ShiftToDegreeZero(C) : ModCpx -> ModCpx
HighestShortRoot( RD ) : RootDtm -> .
IsShortExactSequence(f, g) : MapChn, MapChn -> BoolElt
IsShortExactSequence(C) : ModCpx -> BoolElt, RngIntElt
IsShortRoot( RD, r ) : RootDtm, RngIntElt -> BoolElt
ShortBasis(D : parameters) : DivFunElt -> [RngElt], [RngIntElt]
ShortVectors(L, u) : Lat, RngElt -> [ <LatElt, RngElt> ]
ShortVectorsMatrix(L, u) : Lat, RngElt -> ModMatRngElt
ShortVectorsProcess(L, u) : Lat, RngElt -> LatEnumProc
Short and Close Vectors (LATTICES)
Short and Close Vectors (LATTICES)
ShortBasis(D : parameters) : DivFunElt -> [RngElt], [RngIntElt]
Mat_ShortCuts (Example H59E2)
Mat_Shortcuts (Example H59E3)
Shortcuts (MATRICES)
ShortenCode(C, i) : Code, RngIntElt -> Code
ShortenCode(C, i) : Code, RngIntElt -> Code
ShortenCode(C, S) : Code, { RngIntElt } -> Code
ShortenCode(C, S) : Code, { 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
ShortestVectors(L) : Lat -> [ LatElt ], RngElt
ShortestVectorsMatrix(L) : Lat -> ModMatRngElt
Shortest and Closest Vectors (LATTICES)
Shortest and Closest Vectors (LATTICES)
ShortestVectors(L) : Lat -> [ LatElt ], RngElt
ShortestVectorsMatrix(L) : Lat -> ModMatRngElt
ShortVectors(L, u) : Lat, RngElt -> [ <LatElt, RngElt> ]
ShortVectorsMatrix(L, u) : Lat, RngElt -> ModMatRngElt
ShortVectorsProcess(L, u) : Lat, RngElt -> LatEnumProc
ShowIdentifiers() : ->
ShowMemoryUsage() : ->
ShowOptions(~P : parameters) : Process(Tietze) ->
ShowPrevious() : ->
ShowPrevious(i) : RngIntElt ->
ShowValues() : ->
ShowIdentifiers() : ->
ShowMemoryUsage() : ->
ShowOptions(~P : parameters) : Process(Tietze) ->
ShowPrevious() : ->
ShowPrevious(i) : RngIntElt ->
ShowValues() : ->
ShrikhandeGraph() : -> GrphUnd
GewirtzGraph() : -> GrphUnd
ClebschGraph() : -> GrphUnd
ShrikhandeGraph() : -> GrphUnd
GewirtzGraph() : -> GrphUnd
ClebschGraph() : -> GrphUnd
ShrinkingGenerator(C1, S1, C2, S2, t) : RngUPolElt, SeqEnum, RngUPolElt,SeqEnum, RngIntElt -> SeqEnum
ShrinkingGenerator(C1, S1, C2, S2, t) : RngUPolElt, SeqEnum, RngUPolElt,SeqEnum, RngIntElt -> SeqEnum
BlumBlumShubModulus(b) : RngIntElt -> RngIntElt
BBSModulus(b) : RngIntElt -> RngIntElt
RandomSequenceBlumBlumShub(b, t) : RngIntElt, RngIntElt -> SeqEnum
RandomSequenceBlumBlumShub(n, s, t) : RngIntElt, RngIntElt, RngIntElt -> SeqEnum
RootSide(v) : GrphVert -> GrphVert
TwoSidedIdealClasses(S) : AlgQuatOrd -> [AlgQuatOrd]
PolynomialSieve( T ) : Tup -> SeqEnum
Sieve(K) : FldFin ->
ASigmaL(arguments)
AffineSigmaLinearGroup(arguments)
DivisorSigma(i, n) : RngIntElt, RngIntElt -> RngIntElt
ProjectiveSigmaLinearGroup(arguments)
ProjectiveSigmaSymplecticGroup(arguments)
ProjectiveSigmaUnitaryGroup(arguments)
Sign(s) : FldPrElt -> RngIntElt
Sign(q) : FldRatElt -> RngIntElt
Sign(g) : GrpPermElt -> RngIntElt
Sign(x) : Infty -> RngIntElt
Sign(n) : RngIntElt -> RngIntElt
Sign(f) : RngMPolElt -> RngIntElt
Sign(p) : RngUPolElt -> RngIntElt
SignDecomposition(D) : DivCrvElt -> DivElt,DivElt
Absolute Value and Sign (RATIONAL FIELD)
Signature(Q) : FldRat -> RngIntElt, RngIntElt
Signature(Z) : RngInt -> RngIntElt, RngIntElt
Signature(O) : RngOrd -> RngIntElt, RngIntElt
Signature (OVERVIEW)
ListSignatures(C) : Cat ->
SignDecomposition(D) : DivCrvElt -> DivElt,DivElt
SetExtraspecialSigns( RD, s ) : RootDtm, . ->
SilvermanBound(H) : SetPtEll -> FldPrElt
SilvermanBound(H) : SetPtEll -> FldPrElt
Database of Simple Groups: Permutations, Presentations, Conjugacy Classes, Maximal Subgroups and Sylow Subgroups (OVERVIEW)
IsSimilar(A, B) : AlgMatElt, AlgMatElt -> BoolElt, AlgMatElt
IsSimilar(a, b) : AlgMatElt, AlgMatElt -> BoolElt, AlgMatElt
AlmostSimpleGroupDatabase() : -> DB
IdentifyAlmostSimpleGroup(G) : GrpPerm -> Map, GrpPerm
IrreducibleModule(B, i) : AlgBas, RngIntElt -> ModAlg
IsSimple(A) : AlgGen -> BoolElt
IsSimple(F) : FldAlg -> BoolElt
IsSimple(G) : GrpAb -> BoolElt
IsSimple(G) : GrpFin -> BoolElt
IsSimple(G) : GrpGPC -> BoolElt
IsSimple( G ) : GrpLie -> BoolElt
IsSimple(G) : GrpMat -> BoolElt
IsSimple(G) : GrpPC -> BoolElt
IsSimple(G) : GrpPerm -> BoolElt
IsSimple(D) : Inc -> BoolElt
NameSimple(G) : GrpPerm -> <RngIntElt, RngIntElt, RngIntElt>
SemiSimpleLieAlgebra(X, F) : MonStgElt, Fld -> AlgLie
SemiSimpleType(L) : AlgLie -> AlgLie
SimpleCohomologyDimensions(M) : ModAlg -> SeqEnum
SimpleExtension(F) : FldAlg -> FldAlg
SimpleHomologyDimensions(M) : ModAlg -> SeqEnum
SimpleLieAlgebra(X, n, F) : MonStgElt, RngIntElt, Fld -> AlgLie
SimpleReflectionMatrices( RD ) : RootDtm -> []
SimpleReflectionPermutations( RD ) : RootDtm -> []
SimpleRoots( W ) : GrpCox -> Mtrx
SimpleRoots( RD ) : RootDtm -> Mtrx
SimpleSubgroups(G: parameters) : GrpFin -> [ rec< Grp, RngIntElt, RngIntElt, GrpFP> ]
SimpleSubgroups(G: parameters) : GrpPerm -> [ rec< GrpPerm, RngIntElt, RngIntElt, GrpFP> ]
Construction of Semisimple Lie Algebras (LIE ALGEBRAS)
Construction of Simple Linear Codes (LINEAR CODES OVER FINITE RINGS)
Database of Simple Groups: Permutations, Presentations, Conjugacy Classes, Maximal Subgroups and Sylow Subgroups (OVERVIEW)
Other Elementary Functions (RING OF INTEGERS)
Positive and Simple Roots (ROOT DATA FOR LIE THEORY)
Simple Assignment (STATEMENTS AND EXPRESSIONS)
Simple Element Functions (REAL AND COMPLEX FIELDS)
Some Trivial Linear Codes (LINEAR CODES OVER FINITE FIELDS)
Simple Assignment (STATEMENTS AND EXPRESSIONS)
CodeFld_SimpleCodeChain (Example H101E4)
SimpleCohomologyDimensions(M) : ModAlg -> SeqEnum
SimpleCoreflectionMatrices( RD ) : RootDtm -> []
SimpleReflectionMatrices( RD ) : RootDtm -> []
SimpleCoroots( W ) : GrpCox -> Mtrx
SimpleRoots( W ) : GrpCox -> Mtrx
SimpleRoots( RD ) : RootDtm -> Mtrx
SimpleExtension(F) : FldAlg -> FldAlg
SimpleHomologyDimensions(M) : ModAlg -> SeqEnum
SimpleLieAlgebra(X, n, F) : MonStgElt, RngIntElt, Fld -> AlgLie
AlgLie_SimpleLieAlgebra (Example H76E1)
SimpleModule(B, i) : AlgBas, RngIntElt -> ModAlg
IrreducibleModule(B, i) : AlgBas, RngIntElt -> ModAlg
SimpleCoreflectionMatrices( RD ) : RootDtm -> []
SimpleReflectionMatrices( RD ) : RootDtm -> []
SimpleReflectionPermutations( RD ) : RootDtm -> []
SimpleCoroots( W ) : GrpCox -> Mtrx
SimpleRoots( W ) : GrpCox -> Mtrx
SimpleRoots( RD ) : RootDtm -> Mtrx
SimpleSubgroups(G: parameters) : GrpFin -> [ rec< Grp, RngIntElt, RngIntElt, GrpFP> ]
SimpleSubgroups(G: parameters) : GrpPerm -> [ rec< GrpPerm, RngIntElt, RngIntElt, GrpFP> ]
Simplex(A) : Prj -> SeqEnum
SimplexCode(r) : RngIntElt -> Code
TranslationOfSimplex(P,Q) : Prj, [Pt] -> MapSch
SimplexCode(r) : RngIntElt -> Code
Simplification (FINITELY PRESENTED GROUPS)
IsSimplifiedModel(E) : CrvEll -> BoolElt
SimplifiedModel(E): CrvEll -> CrvEll, Map, Map
SimplifiedModel(C) : CrvHyp -> CrvHyp, MapIsoSch
SimplifiedModel(E): CrvEll -> CrvEll, Map, Map
SimplifiedModel(C) : CrvHyp -> CrvHyp, MapIsoSch
Simplify(A) : FldAC ->
Simplify(D) : Inc -> Inc
Simplify(G: parameters) : GrpFP -> GrpFP
Simplify(~P : parameters) : Process(Tietze) ->
Simplify(O) : RngOrd -> RngOrd
SimplifyLength(G: parameters) : GrpFP -> GrpFP
SimplifyLength(~P : parameters) : Process(Tietze) ->
Simplification (ALGEBRAICALLY CLOSED FIELDS)
GrpFP_1_Simplify1 (Example H19E54)
SimplifyLength(G: parameters) : GrpFP -> GrpFP
SimplifyLength(~P : parameters) : Process(Tietze) ->
SimplifyPresentation(~P : parameters) : Process(Tietze) ->
Simplify(~P : parameters) : Process(Tietze) ->
IsSimplyConnected( G ) : GrpLie-> BoolElt
IsSimplyConnected( RD ) : RootDtm-> BoolElt
IsSimplyLaced( G ) : GrpLie-> BoolElt
IsSimplyLaced( RD ) : RootDtm-> BoolElt
SimpsonQuadrature(f, a, b, n) : Program, FldPrElt, FldPrElt, RngIntElt -> FldPrElt
SimpsonQuadrature(f, a, b, n) : Program, FldPrElt, FldPrElt, RngIntElt -> FldPrElt
SimsSchreier(G: parameters) : GrpPerm : ->
SimsSchreier(G: parameters) : GrpPerm : ->
Sin(c) : FldComElt -> FldComElt
Sin(f) : RngSerElt -> RngSerElt
Sin(f) : RngSerElt -> RngSerElt
Release Notes V1.20-1 (8 January 1996) since June 1995 (OVERVIEW)
Sincos(s) : FldPrElt -> FldPrElt, FldPrElt
Sincos(f) : RngSerElt -> RngSerElt
Sincos(f) : RngSerElt -> RngSerElt
Singularity Analysis (PLANE ALGEBRAIC CURVES)
Singularity Analysis (PLANE ALGEBRAIC CURVES)
SingerDifferenceSet(n, q) : RngIntElt, RngIntElt -> { RngIntResElt }
SingerDifferenceSet(n, q) : RngIntElt, RngIntElt -> { RngIntResElt }
InverseRSKCorrespondenceSingleWord(t1, t2) : Tbl, Tbl -> MonOrdElt
IsSinglePrecision(n) : RngIntElt -> BoolElt
The `single use' Rule (MAGMA SEMANTICS)
The `single use' Rule (MAGMA SEMANTICS)
SingletonAsymptoticBound(delta) : FldPrElt -> FldPrElt
SingletonBound(K, n, d) : FldFin, RngIntElt, RngIntElt -> RngIntElt
SingletonAsymptoticBound(delta) : FldPrElt -> FldPrElt
SingletonBound(K, n, d) : FldFin, RngIntElt, RngIntElt -> RngIntElt
HasSingularPointsOverExtension(C) : Sch -> BoolElt
IsSingular(A) : Mtrx -> BoolElt
IsSingular(C) : Sch -> BoolElt
IsSingular(X) : Sch -> BoolElt
IsSingular(p) : Sch,Pt -> BoolElt
IsSingular(p) : Sch,Pt -> BoolElt
IsSingular(p) : Sch,Pt -> BoolElt
SingularPoints(C) : Sch -> SetIndx
SingularSubscheme(X) : Sch -> Sch
Lat_SingularElements (Example H64E9)
IsOrdinarySingularity(p) : Sch,Pt -> BoolElt
IsOrdinarySingularity(p) : Sch,Pt -> BoolElt
IsOrdinarySingularity(p) : Sch,Pt -> BoolElt
GrphRes_singularity (Example H85E1)
SingularPoints(C) : Sch -> SetIndx
SingularSubscheme(X) : Sch -> Sch
Sinh(s) : FldPrElt -> FldPrElt
Sinh(f) : RngSerElt -> RngSerElt
Sinh(f) : RngSerElt -> RngSerElt
IsSIntegral(P, S) : PtEll, SeqEnum -> BoolElt
SIntegralDesbovesPoints(Q, S) : [ RngIntElt ], [ RngIntElt ] -> [ SeqEnum ]
SIntegralLjunggrenPoints(Q, S) : [ RngIntElt ], [ RngIntElt ] -> [ SeqEnum ]
SIntegralPoints(E, S) : CrvEll, SeqEnum -> [ PtEll ], [ Tup ]
SIntegralQuarticPoints(Q, S) : [ RngIntElt ], [ RngIntElt ] -> [ SeqEnum ]
S-integral Points (ELLIPTIC CURVES)
SIntegralDesbovesPoints(Q, S) : [ RngIntElt ], [ RngIntElt ] -> [ SeqEnum ]
SIntegralLjunggrenPoints(Q, S) : [ RngIntElt ], [ RngIntElt ] -> [ SeqEnum ]
SIntegralPoints(E, S) : CrvEll, SeqEnum -> [ PtEll ], [ Tup ]
CrvEll_SIntegralPoints (Example H87E23)
SIntegralQuarticPoints(Q, S) : [ RngIntElt ], [ RngIntElt ] -> [ SeqEnum ]
BlockSize(D) : Dsgn -> RngIntElt
BlockDegree(D) : Dsgn -> RngIntElt
BlockDegree(D, B) : Inc, IncBlk -> RngIntElt
GetPreviousSize() : -> RngIntElt
IsolMinBlockSize(n, p, i) : RngIntElt, RngIntElt, RngIntElt -> RngIntElt
SetBufferSize(D, n) : DB, RngIntElt ->
SetHistorySize(n) : RngIntElt ->
SetPreviousSize(n) : RngIntElt ->
Size(G) : Grph -> RngIntElt
Size(g) : GrphRes -> RngIntElt
Size(s) : GrphRes -> RngIntElt
VarietySizeOverAlgebraicClosure(I) : RngMPol -> RngIntElt
Groups (OVERVIEW)
Rings, Fields, and Algebras (OVERVIEW)
Sets (OVERVIEW)
BlockSizes(D) : Inc -> [ RngIntElt ]
BlockDegrees(D) : Inc -> [ RngIntElt ]
ColumnSkewLength(t, j) : Tbl,RngIntElt -> RngIntElt
IsSkew(t) : Tbl -> BoolElt
NumberOfSkewRows(t) : Tbl -> RngIntElt
RowSkewLength(t, i) : Tbl,RngIntElt -> RngIntElt
SkewShape(t) : Tbl -> SeqEnum[RngIntElt]
SkewWeight(t) : Tbl -> RngIntElt
OptimalSkewness(F) : RngMPolElt -> FldReElt, FldReElt
InnerShape(t) : Tbl -> SeqEnum[RngIntElt]
SkewShape(t) : Tbl -> SeqEnum[RngIntElt]
SkewWeight(t) : Tbl -> RngIntElt
SL(arguments)
SpecialLinearGroup(arguments)
Slope(l) : PlaneLn -> FldFinElt
SLPGroup(n) : RngIntElt -> GrpSLP
GrpSLP_SLPGroup (Example H29E1)
IsInSmallGroupDatabase(o) : RngIntElt -> RngIntElt
IsSoluble(D, o, n) : DB, RngIntElt, RngIntElt -> Grp
SmallGroupIsSoluble(o, n) : RngIntElt, RngIntElt -> Grp
SmallGroupIsSolvable(o, n) : RngIntElt, RngIntElt -> Grp
NumberOfSmallGroups(o) : RngIntElt -> RngIntElt
PresentationIsSmall(G) : GrpGPC -> BoolElt
SmallGroup(o: parameters) : RngIntElt -> Grp
SmallGroup(o, f: parameters) : RngIntElt, Program -> Grp
SmallGroup(o, f: parameters) : RngIntElt, Program -> Grp
SmallGroup(o, f: parameters) : RngIntElt, Program -> Grp
SmallGroup(o, f: parameters) : RngIntElt, Program -> Grp
SmallGroup(o, n) : RngIntElt, RngIntElt -> Grp
SmallGroupDatabase() : -> DB
SmallGroupDatabaseLimit() : -> RngIntElt
SmallGroupDecoding(c, o) : RngIntElt, RngIntElt -> GrpPC
SmallGroupEncoding(G) : GrpPC -> RngIntElt, RngIntElt
SmallGroupIsInsoluble(o, n) : RngIntElt, RngIntElt -> Grp
SmallGroupProcess(o: parameters) : RngIntElt -> Process
SmallGroupProcess(o, f: parameters) : RngIntElt, Program -> Process
SmallGroupProcess(S: parameters) : [RngIntElt] -> Process
SmallGroupProcess(S, f: parameters) : [RngIntElt], Program -> Process
SmallGroups(o: parameters) : RngIntElt -> [* Grp *]
SmallGroups(o, f: parameters) : RngIntElt, Program -> [* Grp *]
SmallGroups(S: parameters) : [RngIntElt] -> [* Grp *]
SmallGroups(S, f: parameters) : [RngIntElt], Program -> [* Grp *]
IsOverSmallerField(G) : GrpMat -> BoolElt, GrpMat
IsOverSmallerField(G, d) : GrpMat, RngIntElt -> BoolElt, GrpMat
IsRealisableOverSmallerField(M) : ModGrp -> BoolElt, ModGrp
ModuleOverSmallerField(M, F) : ModGrp, FldFin -> ModGrp
ModulesOverSmallerField(Q, F) : SeqEnum, FldFin -> ModGrp
WriteOverSmallerField(G, F) : GrpMat, FldFin -> GrpMat, Map
WriteOverSmallerField(M, F) : ModGrp, FldFin -> ModGrp, Map
Comparison (OVERVIEW)
SmallGroup(o: parameters) : RngIntElt -> Grp
SmallGroup(o, f: parameters) : RngIntElt, Program -> Grp
SmallGroup(o, f: parameters) : RngIntElt, Program -> Grp
SmallGroup(o, n) : RngIntElt, RngIntElt -> Grp
OpenSmallGroupDatabase() : -> DB
SmallGroupDatabase() : -> DB
SmallGroupDatabaseLimit() : -> RngIntElt
SmallGroupDecoding(c, o) : RngIntElt, RngIntElt -> GrpPC
SmallGroupEncoding(G) : GrpPC -> RngIntElt, RngIntElt
SmallGroupIsInsolvable(o, n) : RngIntElt, RngIntElt -> Grp
SmallGroupIsInsoluble(o, n) : RngIntElt, RngIntElt -> Grp
SmallGroupIsInsolvable(o, n) : RngIntElt, RngIntElt -> Grp
SmallGroupIsInsoluble(o, n) : RngIntElt, RngIntElt -> Grp
IsSolvable(D, o, n) : DB, RngIntElt, RngIntElt -> Grp
SmallGroupIsSoluble(o, n) : RngIntElt, RngIntElt -> Grp
SmallGroupIsSolvable(o, n) : RngIntElt, RngIntElt -> Grp
IsSoluble(D, o, n) : DB, RngIntElt, RngIntElt -> Grp
IsSolvable(D, o, n) : DB, RngIntElt, RngIntElt -> Grp
SmallGroupIsSoluble(o, n) : RngIntElt, RngIntElt -> Grp
SmallGroupIsSolvable(o, n) : RngIntElt, RngIntElt -> Grp
IsSoluble(D, o, n) : DB, RngIntElt, RngIntElt -> Grp
SmallGroupProcess(o: parameters) : RngIntElt -> Process
SmallGroupProcess(o, f: parameters) : RngIntElt, Program -> Process
SmallGroupProcess(S: parameters) : [RngIntElt] -> Process
SmallGroupProcess(S, f: parameters) : [RngIntElt], Program -> Process
SmallGroups(o: parameters) : RngIntElt -> [* Grp *]
SmallGroups(o, f: parameters) : RngIntElt, Program -> [* Grp *]
SmallGroups(S: parameters) : [RngIntElt] -> [* Grp *]
SmallGroups(S, f: parameters) : [RngIntElt], Program -> [* Grp *]
GrpData_SmallGroups (Example H22E1)
GrpData_SmallIdentify (Example H22E3)
GrpData_SmallInternal (Example H22E4)
SPARSE MATRICES
SmithForm(a) : AlgMatElt -> AlgMatElt, AlgMatElt, AlgMatElt
SmithForm(A) : ModMatRngElt -> ModMatRngElt, ModMatRngElt, ModMatRngElt
SmithForm(a) : AlgMatElt -> AlgMatElt, AlgMatElt, AlgMatElt
SmithForm(A) : ModMatRngElt -> ModMatRngElt, ModMatRngElt, ModMatRngElt
The Database of Small Groups (DATABASES OF GROUPS)
The Database of Small Groups (DATABASES OF GROUPS)
NumberOfSmoothDivisors(n, m, P) : RngIntElt, RngIntElt, SeqEnum[RngElt] -> RngElt
SO(arguments)
SpecialOrthogonalGroup(arguments)
Socle(G) : GrpPerm -> GrpPerm
Socle(M) : ModAlg -> ModAlg
Socle(M) : ModRng -> ModRng
SocleAction(G) : GrpPerm -> Hom, GrpPerm, GrpPerm
SocleFactor(G) : GrpPerm -> GrpPerm
SocleFactors(G) : GrpPerm -> [ GrpPerm ]
SocleFactors(M) : ModRng -> [ ModRng ]
SocleImage(G) : GrpPerm -> GrpPerm
SocleKernel(G) : GrpPerm -> GrpPerm
SocleQuotient(G) : GrpPerm -> GrpPerm, Hom, GrpPerm
SocleSeries(G) : GrpPerm -> [ GrpPerm ]
SocleSeries(M) : ModRng -> [ ModRng ], [ ModRng ], AlgMatElt
Socle Series (MODULES OVER A MATRIX ALGEBRA)
The Socle (PERMUTATION GROUPS)
SocleAction(G) : GrpPerm -> Hom, GrpPerm, GrpPerm
SocleFactor(G) : GrpPerm -> GrpPerm
SocleFactors(G) : GrpPerm -> [ GrpPerm ]
SocleFactors(M) : ModRng -> [ ModRng ]
SocleImage(G) : GrpPerm -> GrpPerm
SocleKernel(G) : GrpPerm -> GrpPerm
SocleQuotient(G) : GrpPerm -> GrpPerm, Hom, GrpPerm
SocleSeries(G) : GrpPerm -> [ GrpPerm ]
SocleSeries(M) : ModRng -> [ ModRng ], [ ModRng ], AlgMatElt
The Schur Algorithm for Soluble Groups (K[G]-MODULES AND GROUP REPRESENTATIONS)
Database of Soluble Groups (OVERVIEW)
InverseMattsonSolomonTransform(A, n) : RngUPolElt, RngIntElt -> RngUPolElt
MattsonSolomonTransform(f, n) : RngUPolElt, RngIntElt -> RngUPolElt
ReedSolomonCode(K, d, b) : FldFin, RngIntElt, RngIntElt -> Code
ReedSolomonCode(n, d) : RngIntElt, RngIntElt -> Code
Mattson--Solomon Transforms (LINEAR CODES OVER FINITE FIELDS)
Reed--Solomon and Justesen Codes (LINEAR CODES OVER FINITE FIELDS)
HasSolubilityCertificate(C) : CrvCon -> BoolElt, SeqEnum
HasSolubilityCertificate(S) : SeqEnum[RngIntElt] -> BoolElt, SeqEnum
SolubilityCertificate(C) : CrvCon -> SeqEnum
Solubility Certificates (RATIONAL CURVES AND CONICS)
SolubilityCertificate(C) : CrvCon -> SeqEnum
IsSolvable(D, o, n) : DB, RngIntElt, RngIntElt -> Grp
SmallGroupIsSoluble(o, n) : RngIntElt, RngIntElt -> Grp
SmallGroupIsSolvable(o, n) : RngIntElt, RngIntElt -> Grp
IsSoluble(D, o, n) : DB, RngIntElt, RngIntElt -> Grp
SmallGroupIsSoluble(o, n) : RngIntElt, RngIntElt -> Grp
SmallGroupIsSolvable(o, n) : RngIntElt, RngIntElt -> Grp
IsSoluble(G) : GrpAb -> BoolElt
IsSoluble(A) : GrpAuto -> BoolElt
IsSoluble(G) : GrpFin -> BoolElt
IsSoluble(G) : GrpGPC -> BoolElt
IsSoluble(G) : GrpMat -> BoolElt
IsSoluble(G) : GrpPC -> BoolElt
IsSoluble(G) : GrpPerm -> BoolElt
Radical(G) : GrpMat -> GrpMat
Radical(G) : GrpPerm -> GrpPerm
SolubleQuotient(G) : Grp -> GrpPC, Map
SolubleQuotient(F, n : parameters): GrpFP, RngIntElt -> GrpPC, Map, SeqEnum, MonStgElt
SolubleQuotientProcess(F : parameters): GrpFP -> SQProc
SolubleResidual(G) : GrpFin -> GrpFin
SolubleResidual(G) : GrpMat -> GrpMat
SolubleResidual(G) : GrpPerm -> GrpPerm
SolubleSchreier(G: parameters) : GrpPerm : ->
SolubleSubgroups(G: parameters) : GrpFin -> [ rec< Grp, RngIntElt, RngIntElt, GrpFP> ]
SolvableQuotient(G): GrpMat -> GrpPC, Map
SolvableQuotient(G): GrpPerm, RngIntElt -> GrpPC, Map, SeqEnum, MonStgElt
SolvableQuotient(G : parameters): GrpFP, RngIntElt -> GrpPC, Map, SeqEnum, MonStgElt
SolvableQuotient(F, n : parameters): GrpFP, RngIntElt -> GrpPC, Map, SeqEnum, MonStgElt
Calculation of Standard Sections (FP GROUPS - ADVANCED FEATURES)
Database of Irreducible Soluble Subgroups of GL(n,p) for n > 1 and p^n < 256 (OVERVIEW)
Database of Soluble Groups (OVERVIEW)
FINITE SOLUBLE GROUPS
Initialisation (FP GROUPS - ADVANCED FEATURES)
Miscellaneous Functions (FP GROUPS - ADVANCED FEATURES)
Soluble Matrix Groups (MATRIX GROUPS)
Soluble Quotient (FINITELY PRESENTED GROUPS)
Soluble Quotient Process Tools (FP GROUPS - ADVANCED FEATURES)
Soluble Quotient Processes (FP GROUPS - ADVANCED FEATURES)
Soluble Quotients (FP GROUPS - ADVANCED FEATURES)
The Soluble Radical and its Quotient (MATRIX GROUPS)
The Soluble Radical and its Quotient (PERMUTATION GROUPS)
Invariants(G) : GrpMat -> [ RngIntElt ]
Soluble Matrix Groups (MATRIX GROUPS)
Soluble Quotient (FINITELY PRESENTED GROUPS)
Soluble Quotient Processes (FP GROUPS - ADVANCED FEATURES)
Soluble Quotients (FP GROUPS - ADVANCED FEATURES)
The Soluble Radical and its Quotient (MATRIX GROUPS)
The Soluble Radical and its Quotient (PERMUTATION GROUPS)
SolvableQuotient(G) : Grp -> GrpPC, Map
SolubleQuotient(G) : Grp -> GrpPC, Map
SolubleQuotient(F, n : parameters): GrpFP, RngIntElt -> GrpPC, Map, SeqEnum, MonStgElt
SolvableQuotient(G): GrpMat -> GrpPC, Map
SolvableQuotient(G): GrpPerm, RngIntElt -> GrpPC, Map, SeqEnum, MonStgElt
SolvableQuotient(G : parameters): GrpFP, RngIntElt -> GrpPC, Map, SeqEnum, MonStgElt
SolvableQuotient(F, n : parameters): GrpFP, RngIntElt -> GrpPC, Map, SeqEnum, MonStgElt
GrpFP_2_SolubleQuotient (Example H32E13)
GrpFP_1_SolubleQuotient1 (Example H19E26)
GrpFP_1_SolubleQuotient2 (Example H19E27)
SolubleQuotientProcess(F : parameters): GrpFP -> SQProc
SolubleRadical(G) : GrpMat -> GrpMat
SolvableRadical(G) : GrpMat -> GrpMat
Radical(G) : GrpMat -> GrpMat
Radical(G) : GrpPerm -> GrpPerm
SolvableResidual(G) : GrpFin -> GrpFin
SolubleResidual(G) : GrpFin -> GrpFin
SolubleResidual(G) : GrpMat -> GrpMat
SolubleResidual(G) : GrpPerm -> GrpPerm
SolvableSchreier(G: parameters) : GrpPerm : ->
SolubleSchreier(G: parameters) : GrpPerm : ->
SolvableSubgroups(G: parameters) : GrpFin -> [ rec< Grp, RngIntElt, RngIntElt, GrpFP> ]
SolubleSubgroups(G: parameters) : GrpFin -> [ rec< Grp, RngIntElt, RngIntElt, GrpFP> ]
IntegerSolutionVariables(L) : LP -> SeqEnum
MaximalIntegerSolution(LHS, relations, RHS, objective) : Mtrx, Mtrx, Mtrx, Mtrx -> Mtrx, RngIntElt
MaximalSolution(LHS, relations, RHS, objective) : Mtrx, Mtrx, Mtrx, Mtrx -> Mtrx, RngIntElt
MaximalZeroOneSolution(LHS, relations, RHS, objective) : Mtrx, Mtrx, Mtrx, Mtrx -> Mtrx, RngIntElt
MinimalIntegerSolution(LHS, relations, RHS, objective) : Mtrx, Mtrx, Mtrx, Mtrx -> Mtrx, RngIntElt
MinimalSolution(LHS, relations, RHS, objective) : Mtrx, Mtrx, Mtrx, Mtrx -> Mtrx, RngIntElt
MinimalZeroOneSolution(LHS, relations, RHS, objective) : Mtrx, Mtrx, Mtrx, Mtrx -> Mtrx, RngIntElt
ModularSolution(A, M) : MtrxSprs, RngIntElt -> ModTupRng
SetIntegerSolutionVariables(L, I, m) : LP, SeqEnum[RngIntElt], BoolElt ->
Solution(L) : LP -> Mtrx, RngIntElt
Solution(A, W) : ModMatRngElt, ModTupRng -> ModTupRngElt, ModTupRng
Solution(A, w) : ModMatRngElt, ModTupRng -> ModTupRngElt, ModTupRng
Solution(A, Q) : ModMatRngElt, [ ModTupRng ] -> [ ModTupRngElt ], ModTupRng
Solution(A, W) : ModMatRngElt, [ ModTupRng ] -> [ ModTupRngElt ], ModTupRng
Solution(a, b, m) : RngIntElt, RngIntElt, RngIntElt -> RngIntElt, RngIntElt
Solution(a, b) : RngIntResElt, RngIntResElt -> RngIntResElt
Solution(A, B, N) : [RngIntElt], [RngIntElt],[RngIntElt] -> RngIntElt
Mat_Solution (Example H59E8)
Linear Systems (Structured Gaussian Elimination) (SPARSE MATRICES)
Matrix Invariants (SPARSE MATRICES)
Nullspace (SPARSE MATRICES)
Nullspaces and Solutions of Systems (MATRICES)
Solutions of Systems of Linear Equations (MATRIX ALGEBRAS)
Matrix Invariants (SPARSE MATRICES)
Nullspace (SPARSE MATRICES)
Nullspaces and Solutions of Systems (MATRICES)
Solutions of Systems of Linear Equations (MATRIX ALGEBRAS)
Solutions(t, a) : Thue, RngIntElt -> [ [ RngIntElt, RngIntElt ] ]
DeleteNonsplitSolutionspace(SQP, p, i, k): SQProc, RngIntElt, RngIntElt, RngIntElt ->
DeleteSplitSolutionspace(SQP, p, i, k): SQProc, RngIntElt, RngIntElt, RngIntElt ->
IsSolvable(D, o, n) : DB, RngIntElt, RngIntElt -> Grp
SmallGroupIsSoluble(o, n) : RngIntElt, RngIntElt -> Grp
SmallGroupIsSolvable(o, n) : RngIntElt, RngIntElt -> Grp
IsSoluble(D, o, n) : DB, RngIntElt, RngIntElt -> Grp
SmallGroupIsSoluble(o, n) : RngIntElt, RngIntElt -> Grp
SmallGroupIsSolvable(o, n) : RngIntElt, RngIntElt -> Grp
IsSoluble(G) : GrpAb -> BoolElt
IsSoluble(A) : GrpAuto -> BoolElt
IsSoluble(G) : GrpFin -> BoolElt
IsSoluble(G) : GrpGPC -> BoolElt
IsSoluble(G) : GrpMat -> BoolElt
IsSoluble(G) : GrpPC -> BoolElt
IsSoluble(G) : GrpPerm -> BoolElt
IsSolvable(L) : AlgLie -> BoolElt
Radical(G) : GrpMat -> GrpMat
Radical(G) : GrpPerm -> GrpPerm
SolubleQuotient(G) : Grp -> GrpPC, Map
SolubleQuotient(F, n : parameters): GrpFP, RngIntElt -> GrpPC, Map, SeqEnum, MonStgElt
SolubleResidual(G) : GrpFin -> GrpFin
SolubleResidual(G) : GrpMat -> GrpMat
SolubleResidual(G) : GrpPerm -> GrpPerm
SolubleSchreier(G: parameters) : GrpPerm : ->
SolubleSubgroups(G: parameters) : GrpFin -> [ rec< Grp, RngIntElt, RngIntElt, GrpFP> ]
SolvableQuotient(G): GrpMat -> GrpPC, Map
SolvableQuotient(G): GrpPerm, RngIntElt -> GrpPC, Map, SeqEnum, MonStgElt
SolvableQuotient(G : parameters): GrpFP, RngIntElt -> GrpPC, Map, SeqEnum, MonStgElt
SolvableQuotient(F, n : parameters): GrpFP, RngIntElt -> GrpPC, Map, SeqEnum, MonStgElt
SolvableRadical(L) : AlgLie -> AlgLie
SolvableSubgroups(G: parameters) : GrpPerm -> [ rec< GrpPerm, RngIntElt, RngIntElt, GrpFP> ]
SolvableQuotient(G) : Grp -> GrpPC, Map
SolubleQuotient(G) : Grp -> GrpPC, Map
SolubleQuotient(F, n : parameters): GrpFP, RngIntElt -> GrpPC, Map, SeqEnum, MonStgElt
SolvableQuotient(G): GrpMat -> GrpPC, Map
SolvableQuotient(G): GrpPerm, RngIntElt -> GrpPC, Map, SeqEnum, MonStgElt
SolvableQuotient(G : parameters): GrpFP, RngIntElt -> GrpPC, Map, SeqEnum, MonStgElt
SolvableQuotient(F, n : parameters): GrpFP, RngIntElt -> GrpPC, Map, SeqEnum, MonStgElt
SolubleRadical(G) : GrpMat -> GrpMat
SolvableRadical(G) : GrpMat -> GrpMat
Radical(G) : GrpMat -> GrpMat
Radical(G) : GrpPerm -> GrpPerm
SolvableRadical(L) : AlgLie -> AlgLie
SolvableResidual(G) : GrpFin -> GrpFin
SolubleResidual(G) : GrpFin -> GrpFin
SolubleResidual(G) : GrpMat -> GrpMat
SolubleResidual(G) : GrpPerm -> GrpPerm
SolvableSchreier(G: parameters) : GrpPerm : ->
SolubleSchreier(G: parameters) : GrpPerm : ->
SolvableSubgroups(G: parameters) : GrpFin -> [ rec< Grp, RngIntElt, RngIntElt, GrpFP> ]
SolubleSubgroups(G: parameters) : GrpFin -> [ rec< Grp, RngIntElt, RngIntElt, GrpFP> ]
SolvableSubgroups(G: parameters) : GrpPerm -> [ rec< GrpPerm, RngIntElt, RngIntElt, GrpFP> ]
SOMinus(arguments)
SpecialOrthogonalGroupMinus(arguments)
SOPlus(arguments)
SpecialOrthogonalGroupPlus(arguments)
Sort(~S) : SeqEnum ->
Sort(~S, C) : SeqEnum, UserProgram ->
SortDecomposition(D) : [ModBrdt] -> SeqEnum
SortDecomposition(D) : [ModSym] -> SeqEnum
SortDecomposition(D) : [ModBrdt] -> SeqEnum
SortDecomposition(D) : [ModSym] -> SeqEnum
PSigmaSp(arguments)
ProjectiveSigmaSymplecticGroup(arguments)
SymplecticGroup(arguments)
Newton_sp-vertices-ex (Example H54E4)
AffinePlane(k) : Rng -> Aff
AffineSpace(k,2) : Rng, RngIntElt -> Aff
AffineSpace(k,n) : Rng,RngIntElt -> Aff
AffineSpace(R) : RngMPol -> Aff
Ambient(L) : LinSys -> Prj
AmbientSpace(C) : Code -> ModTupRng
AmbientSpace(C) : Code -> ModTupRng
AmbientSpace(L) : Lat -> ModTupFld, Map
AmbientSpace(C) : Sch -> Sch
AmbientSpace(X) : Sch -> Sch
AssociatedNewSpace(M) : ModSym -> ModSym
[Future release] CircuitSpace(G) : GrphUnd -> ModTup
ClassFunctionSpace(G) : Grp -> AlgChtr
CoefficientSpace(L) : LinSys -> ModTupFld
CoordinateSpace(L) : Lat -> ModTupFld, Map
CosetSpace(P) : GrpFPCosetEnumProc -> GrpFPCos
CosetSpace(G, H: parameters) : GrpFP, GrpFP: -> GrpFPCos
DifferentialSpace(C) : Crv -> DiffFun
DifferentialSpace(D) : DivCrvElt -> ModTup,Map
DifferentialSpace(D) : DivFunElt -> ModFld, Map
DifferentialSpace(D) : DivFunElt -> ModFld, Map
DifferentialSpace(F) : FldFun -> DiffFun
DifferentialSpace(F) : FldFunG -> DiffFun
DualVectorSpace(M) : ModSym -> ModTupFld
Image(a) : AlgMatElt -> ModTup
InformationSpace(C) : Code -> ModTupFld
IsAffineSpace(X) : Sch -> BoolElt
IsAmbientSpace(M) : ModFrm -> BoolElt
IsAmbientSpace(M) : ModSS -> BoolElt
IsLinearSpace(D) : Inc -> BoolElt
IsNearLinearSpace(D) : Inc -> BoolElt
IsOrdinaryProjectiveSpace(X) : Sch -> BoolElt
IsProjectiveSpace(X) : Sch -> BoolElt
KMatrixSpace(K, m, n) : Fld, RngIntElt, RngIntElt -> ModMat
KMatrixSpaceWithBasis(Q) : [ ModMatRngElt ] -> ModMatRng
Kernel(a) : AlgMatElt -> ModTup
Kernel(a) : ModMatElt -> ModTupFld
Kernel(a) : ModMatRngElt -> ModTupRng
LinearSpace(I) : Inc -> IncLsp
LinearSpace< v | X : parameters > : RngIntElt, List -> IncLsp
MinkowskiSpace(F) : FldAlg -> Lat, Map
MinkowskiSpace(K) : FldNum -> KModTup, Map
NearLinearSpace(I) : Inc -> IncNsp
NearLinearSpace< v | X : parameters > : RngIntElt, List -> IncNsp
NonsplitExtensionSpace(SQP): SQProc -> SeqEnum
NormSpace(A) : AlgQuat -> ModTupFld
ProductProjectiveSpace(k,N) : Rng,SeqEnum -> PrjScrl
ProjectiveSpace(k,2) : Rng,RngIntElt -> Prj
ProjectiveSpace(k,n) : Rng,RngIntElt -> Prj
ProjectiveSpace(R) : RngMPol -> Prj
RMatrixSpace(R, m, n) : Rng, RngIntElt, RngIntElt -> ModMatRng
RMatrixSpace(R, m, n) : Rng, RngIntElt, RngIntElt -> ModMatRng
RMatrixSpaceWithBasis(Q) : [ ModMatRngElt ] -> ModMatRng
RMatrixSpaceWithBasis(Q) : [ModTupRngElt] -> ModMatRng
RSpace(C) : Code -> ModTupRng
RiemannRochSpace(D) : DivCrvElt -> ModTupFld,Map
RiemannRochSpace(D) : DivFunElt -> ModFld, Map
RightCosetSpace(P) : GrpFPCosetEnumProc -> GrpFPCos
RightCosetSpace(G, H: parameters) : GrpFP, GrpFP -> GrpFPCos
RootSpace( W ) : GrpCox -> .
RootSpace( RD ) : RootDtm -> .
RowNullSpace(a) : AlgMatElt -> ModTup
ShadowSpace(D,I) : IncGeom, Set -> Inc
SpaceOfDifferentialsFirstKind(C) : Crv -> ModFld, Map
SpaceOfDifferentialsFirstKind(F) : FldFunG -> ModFld, Map
SplitExtensionSpace(SQP): SQProc -> SeqEnum
SyndromeSpace(C) : Code -> ModTupFld
TangentSpace(p) : Sch,Pt -> Sch
VectorSpace(B) : AlgBas -> ModTupFld
VectorSpace(K, n) : Fld, RngIntElt -> ModTupFld
VectorSpace(K, n, F) : Fld, RngIntElt, Mtrx -> ModTupFld
VectorSpace(K, J) : FldCyc, Fld -> ModTupFld, Map
VectorSpace(F, E) : FldFin, FldFin -> ModTupFld, Map
VectorSpace(F, E, B) : FldFin, FldFin, [ FldFinElt ] -> ModTupFld, Map
VectorSpace(G) : GrpMat -> ModTupFld
VectorSpace(M) : ModSym -> ModTupFld, Map, Map
VectorSpace(V, F) : ModTupFld, Fld -> ModTupFld, Map
KMatrixSpace(V, F) : ModTupFld, Fld -> ModTupFld, Map
VectorSpace(M) : ModTupRng -> ModTupRng
VectorSpace(P) : Plane -> ModTupFld
VectorSpace(Q) : RngMPolRes -> ModTupFld, Map
VectorSpaceWithBasis(B) : [ModTupFldElt] -> ModTupFld
KModuleWithBasis(B) : [ModTupFldElt] -> ModTupFld
WordOnRootSpace( W, v, w ) : GrpCox, ., . -> .
Action on a Coset Space (GROUPS)
Coset Spaces (ABELIAN GROUPS)
Coset Spaces (POLYCYCLIC GROUPS)
Coset Spaces and Tables (FINITELY PRESENTED GROUPS)
Coset Spaces: Construction (FINITELY PRESENTED GROUPS)
Curves in Space (SCHEMES)
Differential Space (PLANE ALGEBRAIC CURVES)
Matrices and Vector Spaces Associated with a Graph or Digraph (GRAPHS)
Modules (OVERVIEW)
Norm Spaces and Basis Reduction (QUATERNION ALGEBRAS)
Shadow Spaces (INCIDENCE GEOMETRY)
The Ambient Space and Alphabet (LINEAR CODES OVER FINITE FIELDS)
The Dual Space (LINEAR CODES OVER FINITE FIELDS)
The Syndrome Space (LINEAR CODES OVER FINITE FIELDS)
The Underlying Vector Space (MODULES OVER A MATRIX ALGEBRA)
VECTOR SPACES
SpaceOfHolomorphicDifferentials(C) : Crv -> ModFld, Map
SpaceOfDifferentialsFirstKind(C) : Crv -> ModFld, Map
SpaceOfDifferentialsFirstKind(F) : FldFunG -> ModFld, Map
SpaceOfHolomorphicDifferentials(C) : Crv -> ModFld, Map
SpaceOfDifferentialsFirstKind(C) : Crv -> ModFld, Map
SpaceOfDifferentialsFirstKind(F) : FldFunG -> ModFld, Map
NumberOfFixedSpaces(x, s) : GrpMatElt, RngIntElt -> RngIntElt
OrbitsOfSpaces(G, k) : GrpMat, RngIntElt -> SeqEnum
SetIgnoreSpaces(b) : BoolElt ->
StabiliserOfSpaces(Q) : Spaces -> GrpMat, SeqEnum
Action on a Coset Space (MATRIX GROUPS)
Associated Spaces ({THE MODULE OF}{SUPERSINGULAR POINTS})
Extension Spaces (FP GROUPS - ADVANCED FEATURES)
Labels (MODULAR SYMBOLS)
SpanningForest(G) : Grph -> Grph
SpanningTree(G) : GrphUnd -> Grph
DFSTree(u) : GrphVert -> Grph
Spanning Trees of a Graph or Digraph (GRAPHS)
DFSTree(u) : GrphVert -> Grph
Spanning Trees of a Graph or Digraph (GRAPHS)
SpanningForest(G) : Grph -> Grph
SpanningTree(G) : GrphUnd -> Grph
SparseMatrix(R, A) : Ring, MtrxSprs -> MtrxSprs
ChangeRing(A, R) : MtrxSprs, Ring -> MtrxSprs
HasSparseRep(G) : Grph -> BoolElt
HasSparseRepOnly(G) : Grph -> BoolElt
HasDenseRepOnly(G) : Grph -> BoolElt
SparseMatrix(A) : Mtrx -> MtrxSprs
SparseMatrix(R) : Rng -> MtrxSprs
SparseMatrix(R, m, n) : Rng, RngIntElt, RngIntElt -> MtrxSprs
SparseMatrix(R, m, n, Q) : Rng, RngIntElt, RngIntElt, [ <RngIntElt, RngIntElt, RngElt> ] -> MtrxSprs
SparseMatrix(m, n) : RngIntElt, RngIntElt -> MtrxSprs
Representation (UNIVARIATE POLYNOMIAL RINGS)
Sparse Graphs (GRAPHS)
Sparse Graphs (GRAPHS)
SparseMatrix(R, A) : Ring, MtrxSprs -> MtrxSprs
ChangeRing(A, R) : MtrxSprs, Ring -> MtrxSprs
SparseMatrix(A) : Mtrx -> MtrxSprs
SparseMatrix(R) : Rng -> MtrxSprs
SparseMatrix(R, m, n) : Rng, RngIntElt, RngIntElt -> MtrxSprs
SparseMatrix(R, m, n, Q) : Rng, RngIntElt, RngIntElt, [ <RngIntElt, RngIntElt, RngElt> ] -> MtrxSprs
SparseMatrix(m, n) : RngIntElt, RngIntElt -> MtrxSprs
Graph_SparseReps (Example H97E6)
Creation (SUBGROUPS OF PSL_2(R))
MAGMA_SYSTEM_SPEC
MAGMA_USER_SPEC
Spec(R) : RngMPol -> Aff
AffineSpace(R) : RngMPol -> Aff
AttachSpec(S) : file ->
DetachSpec(S) : file ->
Spec(R) : RngMPolRes -> Sch,Aff
Package Specification files (FUNCTIONS, PROCEDURES AND PACKAGES)
User Startup Specification Files (FUNCTIONS, PROCEDURES AND PACKAGES)
Func_spec (Example H2E9)
ASL(arguments)
AffineSpecialLinearGroup(arguments)
AffineSpecialLinearGroup(arguments)
AffineSpecialLinearGroup(arguments)
ExtraSpecialGroup(G) : GrpMat -> GrpMat
ExtraSpecialGroup(C, p, n : parameters) : Cat, RngIntElt, RngIntElt -> GrpFin
ExtraSpecialGroup(GrpFP, p, n : parameters) : Cat, RngIntElt, RngIntElt -> GrpFP
ExtraSpecialGroup(GrpGPC, p, n : parameters) : Cat, RngIntElt, RngIntElt -> GrpGPC
ExtraSpecialGroup(GrpPC, p, n : parameters) : Cat, RngIntElt, RngIntElt -> GrpPC
ExtraSpecialGroup(GrpPerm, p, n : parameters) : Cat, RngIntElt, RngIntElt -> GrpPerm
ExtraSpecialParameters(G) : GrpMat -> [RngIntElt, RngIntElt]
IsExtraSpecial(G) : GrpFin -> BoolElt
IsExtraSpecial(G) : GrpMat -> BoolElt
IsExtraSpecial(G) : GrpPC -> BoolElt
IsExtraSpecial(G) : GrpPerm -> BoolElt
IsExtraSpecialNormalise(G) : GrpMat -> BoolElt
IsSpecial(D) : DivCrvElt -> BoolElt
IsSpecial(G) : GrpFin -> BoolElt
IsSpecial(G) : GrpMat -> BoolElt
IsSpecial(G) : GrpPC -> BoolElt
IsSpecial(G) : GrpPerm -> BoolElt
PSO(arguments)
PSOMinus(arguments)
PSOPlus(arguments)
ProjectiveSpecialLinearGroup(arguments)
ProjectiveSpecialUnitaryGroup(arguments)
SpecialLinearGroup(arguments)
SpecialOrthogonalGroup(arguments)
SpecialOrthogonalGroupMinus(arguments)
SpecialOrthogonalGroupPlus(arguments)
SpecialPresentation(G) : GrpPC -> GrpPC
SpecialUnitaryGroup(arguments)
SpecialWeights(G) : GrpPC -> [ <RngIntElt, RngIntElt, RngIntElt> ]
Abelian and p-Quotients (FINITE SOLUBLE GROUPS)
Abelian, Nilpotent and Soluble Quotients (MATRIX GROUPS)
Abelian, Nilpotent and Soluble Quotients (PERMUTATION GROUPS)
Other Element Functions (RING OF INTEGERS)
Other Special Functions (REAL AND COMPLEX FIELDS)
Special forms of Curves (PLANE ALGEBRAIC CURVES)
Special Functions for Ideals (QUADRATIC FIELDS)
Special Lattices (LATTICES)
Special Matrix Constructions (MATRICES)
Special Options (REAL AND COMPLEX FIELDS)
Special Presentations (FINITE SOLUBLE GROUPS)
Special Functions for Ideals (QUADRATIC FIELDS)
Special Lattices (LATTICES)
Special Presentations (FINITE SOLUBLE GROUPS)
IndexOfSpeciality(D) : DivCrvElt -> RngIntElt
IndexOfSpeciality(D) : DivFunElt -> RngIntElt
SL(arguments)
SpecialLinearGroup(arguments)
SO(arguments)
SpecialOrthogonalGroup(arguments)
SOMinus(arguments)
SpecialOrthogonalGroupMinus(arguments)
SOPlus(arguments)
SpecialOrthogonalGroupPlus(arguments)
SpecialPresentation(G) : GrpPC -> GrpPC
GrpPC_SpecialPresentation (Example H24E24)
GrpMat_SpecialQuotient (Example H21E18)
GrpPerm_SpecialQuotient (Example H20E17)
SU(arguments)
SpecialUnitaryGroup(arguments)
SpecialWeights(G) : GrpPC -> [ <RngIntElt, RngIntElt, RngIntElt> ]
Specific Factorization Algorithms (RING OF INTEGERS)
Tools for the calculation of specific normal series (FP GROUPS - ADVANCED FEATURES)
Spectrum(G) : GrphUnd -> SetEnum
Sphere(u, n) : GrphVert, RngIntElt -> { GrphVert }
SpherePackingBound(K, n, d) : FldFin, RngIntElt, RngIntElt -> RngIntElt
SpherePackingBound(K, n, d) : FldFin, RngIntElt, RngIntElt -> RngIntElt
SpinorRepresentatives(L) : Lat -> [ Lat ]
Representatives(G) : SymGen -> [ Lat ]
GenusRepresentatives(L) : Lat -> [ Lat ]
IsSpinorGenus(G) : SymGen -> BoolElt
IsSpinorNorm(G,p) : SymGen, RngIntElt -> RngIntElt
SpinorCharacters(G) : SymGen -> [ GrpDrchElt ]
SpinorGenera(G) : SymGen -> [ SymGen ]
SpinorGenerators(G) : SymGen -> [ RngIntElt ]
SpinorGenus(L) : Lat -> SymGen
SpinorCharacters(G) : SymGen -> [ GrpDrchElt ]
SpinorGenera(G) : SymGen -> [ SymGen ]
SpinorGenerators(G) : SymGen -> [ RngIntElt ]
SpinorGenus(L) : Lat -> SymGen
SpinorRepresentatives(L) : Lat -> [ Lat ]
Representatives(G) : SymGen -> [ Lat ]
GenusRepresentatives(L) : Lat -> [ Lat ]
CoefficientsNonSpiral(s, n) : RngPowLazElt, [RngIntElt] -> SeqEnum
MakeSpliceDiagram(g,e,a) : GrphDir,SeqEnum,SeqEnum -> GrphSpl
MakeSpliceDiagram(e,l,a) : SeqEnum,SeqEnum,SeqEnum -> GrphSpl
RegularSpliceDiagram(P) : PnclJac -> GrphSpl
Splice(C, D) : ModCpx, ModCpx -> ModCpx
Splice(C, D, f) : ModCpx, ModCpx, ModMatFldElt -> ModCpx
SpliceDiagram(g) : GrphRes -> GrphSpl
SpliceDiagram(g,v) : GrphRes,GrphResVert -> GrphSpl
SpliceDiagram(v) : GrphSplVert -> GrphSpl
SpliceDiagram(C,p) : Sch,Pt -> GrphSpl
SpliceDiagramVertex(s,i) : GrphSpl,RngIntElt -> GrphSplVert
Splice Diagrams (RESOLUTION GRAPHS AND SPLICE DIAGRAMS)
Splice Diagrams from Resolution Graphs (RESOLUTION GRAPHS AND SPLICE DIAGRAMS)
Splice Diagrams (RESOLUTION GRAPHS AND SPLICE DIAGRAMS)
SpliceDiagram(g) : GrphRes -> GrphSpl
SpliceDiagram(g,v) : GrphRes,GrphResVert -> GrphSpl
SpliceDiagram(v) : GrphSplVert -> GrphSpl
SpliceDiagram(C,p) : Sch,Pt -> GrphSpl
SpliceDiagramVertex(s,i) : GrphSpl,RngIntElt -> GrphSplVert
DeleteSplitCollector(SQP) : SQProc, RngIntElt ->
DeleteNonsplitCollector(SQP) : SQProc, RngIntElt ->
DeleteCollector(SQP) : SQProc, RngIntElt ->
DeleteCollector(SQP, p) : SQProc, RngIntElt ->
DeleteSplitSolutionspace(SQP, p, i, k): SQProc, RngIntElt, RngIntElt, RngIntElt ->
IntegralSplit(a, O) : FldFunElt, RngFunOrd -> RngFunOrdElt, RngElt
IntegralSplit(I) : RngFunOrdIdl -> RngFunOrdIdl, RngElt
IsSplit(P) : RngOrdIdl -> BoolElt
IsSplit(P, O) : RngOrdIdl, RngOrd -> BoolElt
IsTotallySplit(P) : RngOrdIdl -> BoolElt
IsTotallySplit(P, O) : RngOrdIdl, RngOrd -> BoolElt
KeepSplit(SQG, SQH) : SQProc, SQProc -> SeqEnum
KeepSplitAbelian(SQG, SQH) : SQProc, SQProc -> SeqEnum
KeepSplitElementaryAbelian(SQG, SQH) : SQProc, SQProc -> SeqEnum
LiftSplitExtension(SQP, p, i, k : parameters) : SQProc, RngIntElt, RngIntElt, RngIntElt -> RngIntElt, SQProc
LiftSplitExtensionRow(SQP): SQProc -> RngIntElt, SQProc
NonsplitCollector(SQP, p) : SQProc, RngIntElt ->
Split(S, D) : MonStgElt, MonStgElt -> [ MonStgElt ]
SplitAbelianSection(SQP: parameter) : SQProc -> BoolElt, SQProc
SplitElementaryAbelianSection(SQP: parameter) : SQProc -> BoolElt, SQProc
SplitExtension(G, M, F) : GrpFin, ModRng, GrpFinFP -> GrpFinFP
SplitExtension(G, M, F) : GrpPerm, ModRng, GrpFP -> GrpFP
SplitExtensionSpace(SQP): SQProc -> SeqEnum
SplitSection(SQP: parameter) : SQProc -> BoolElt, SQProc
FldAC_Split (Example H52E6)
IO_Split (Example H3E2)
SplitAbelianSection(SQP: parameter) : SQProc -> BoolElt, SQProc
SplitCollector(SQP, p) : SQProc, RngIntElt ->
NonsplitCollector(SQP, p) : SQProc, RngIntElt ->
SplitElementaryAbelianSection(SQP: parameter) : SQProc -> BoolElt, SQProc
SplitExtension(G, M, F) : GrpFin, ModRng, GrpFinFP -> GrpFinFP
SplitExtension(G, M, F) : GrpPerm, ModRng, GrpFP -> GrpFP
SplitExtensionSpace(SQP): SQProc -> SeqEnum
SplitSection(SQP: parameter) : SQProc -> BoolElt, SQProc
FactorisationOverSplittingField(f) : RngPolElt(FldFin) -> [<RngPolElt, RngIntElt>], FldFin
FactorizationOverSplittingField(f) : RngPolElt(FldFin) -> [<RngPolElt, RngIntElt>], FldFin
PointsOverSplittingField(Z) : Clstr -> SetEnum
RootsInSplittingField(f) : RngPolElt(FldFin) -> [<RngPolElt, RngIntElt>], FldFin
SplittingField(F) : FldAlg -> FldAlg, SeqEnum
SplittingField(S) : RngPolElt(FldFin) -> FldFin
SplittingField(P) : RngPolElt(FldFin) -> FldFin
SplittingField(f) : RngUPolElt -> FldAlg
Reducibility (MODULES OVER A MATRIX ALGEBRA)
SplittingField(F) : FldAlg -> FldAlg, SeqEnum
SplittingField(S) : RngPolElt(FldFin) -> FldFin
SplittingField(P) : RngPolElt(FldFin) -> FldFin
SplittingField(f) : RngUPolElt -> FldAlg
SPolynomial(f, g) : ModMPolElt, ModMPolElt -> ModMPolElt
SPolynomial(f, g) : RngMPolElt, RngMPolElt -> RngMPolElt
IsSPrincipal(D, S) : DivFunElt, SetEnum[PlcFunElt] -> BoolElt, FldFunElt
SPrincipalDivisorMap(S) : SetEnum[PlcFunElt] -> Map
SPrincipalDivisorMap(S) : SetEnum[PlcFunElt] -> Map
Sprint(x) : Elt -> MonStgElt
Printing to a String (INPUT AND OUTPUT)
Sprintf(F, ...) : MonStElt, ... -> MonStgElt
IO_Sprintf (Example H3E8)
SQ_check(SQP) : SQProc -> BoolElt
Checking the soluble quotient (FP GROUPS - ADVANCED FEATURES)
SquareRoot(a) : RngIntResElt -> RngIntResElt
Sqrt(a) : RngIntResElt -> RngIntResElt
Sqrt(a) : RngOrdElt -> RngOrdElt
SquareRoot(a) : FldACElt -> FldACElt
SquareRoot(c) : FldComElt -> FldComElt
SquareRoot(a) : FldFinElt -> FldFinElt
SquareRoot(x) : RngLocElt -> RngLocElt
SquareRoot(I) : RngOrdFracIdl -> RngOrdFracIdl
SquareRoot(s) : RngPowLazElt -> RngPowLazElt
SquareRoot(f) : RngSerElt -> RngSerElt
AllSqrts(a) : RngIntResElt -> [ RngIntResElt ]
AllSquareRoots(a) : RngIntResElt -> [ RngIntResElt ]
AllSqrts(a) : RngIntResElt -> [ RngIntResElt ]
AllSquareRoots(a) : RngIntResElt -> [ RngIntResElt ]
ExteriorSquare(a) : AlgMat -> AlgMatElt
ExteriorSquare(L) : Lat -> Lat
ExteriorSquare(M) : ModGrp -> ModGrp
IsPower(a, k) : FldAlgElt, RngIntElt -> BoolElt, FldAlgElt
IsSquare(a) : FldACElt -> BoolElt
IsSquare(a) : FldFinElt -> BoolElt
IsSquare(n) : RngIntElt -> BoolElt, RngIntElt
IsSquare(n) : RngIntResElt -> BoolElt, RngIntResElt
IsSquare(x) : RngLocElt -> BoolElt
IsSquare(I) : RngOrdFracIdl -> BoolElt, RngOrdFracIdl
IsSquare(s) : RngPowLazElt -> BoolElt, RngPowLazElt
Sqrt(a) : RngIntResElt -> RngIntResElt
Sqrt(a) : RngOrdElt -> RngOrdElt
SquareFreeFactorization(g) : RngUPolElt -> [ < RngUPolElt, RngIntElt > ]
SquareFreeFactorization(g) : RngUPolElt -> [ < RngUPolElt, RngIntElt > ]
SquareLatticeGraph(n) : RngIntElt -> GrphUnd
SquareRoot(a) : FldACElt -> FldACElt
SquareRoot(c) : FldComElt -> FldComElt
SquareRoot(a) : FldFinElt -> FldFinElt
SquareRoot(x) : RngLocElt -> RngLocElt
SquareRoot(I) : RngOrdFracIdl -> RngOrdFracIdl
SquareRoot(s) : RngPowLazElt -> RngPowLazElt
SquareRoot(f) : RngSerElt -> RngSerElt
SymmetricSquare(a) : AlgMatElt -> AlgMatElt
SymmetricSquare(L) : Lat -> Lat
SymmetricSquare(M) : ModGrp -> ModGrp
Sequences (OVERVIEW)
Square Root (POWER, LAURENT AND PUISEUX SERIES)
Sequences (OVERVIEW)
Sqrt(f) : RngSerElt -> RngSerElt
Square Root (POWER, LAURENT AND PUISEUX SERIES)
IsogenyMapPsiSquared(I) : Map -> RngUPolElt
IsSquarefree(n) : RngIntElt -> BoolElt
SquarefreeFactorization(n) : RngIntElt -> RngIntElt, RngIntElt
SquarefreeFactorization(f) : RngMPolElt -> [ <RngMPolElt, RngIntElt> ]
SquarefreeFactorization(f) : RngUPolElt -> [ <RngUPolElt, RngIntElt> ]
SquarefreePart(f) : RngMPolElt -> RngMPolElt
SquarefreePartialFractionDecomposition(f) : FldFunRatUElt -> [ <RngUPolElt, RngIntElt, RngUPolElt> ]
SquareFreeFactorization(g) : RngUPolElt -> [ < RngUPolElt, RngIntElt > ]
SquareFreeFactorization(g) : RngUPolElt -> [ < RngUPolElt, RngIntElt > ]
Squarefree(n) : RngIntElt -> RngIntElt, RngIntElt
SquarefreeFactorization(n) : RngIntElt -> RngIntElt, RngIntElt
SquarefreeFactorization(f) : RngMPolElt -> [ <RngMPolElt, RngIntElt> ]
SquarefreeFactorization(f) : RngUPolElt -> [ <RngUPolElt, RngIntElt> ]
SquarefreePart(f) : RngMPolElt -> RngMPolElt
SquarefreePartialFractionDecomposition(f) : FldFunRatUElt -> [ <RngUPolElt, RngIntElt, RngUPolElt> ]
SquareLatticeGraph(n) : RngIntElt -> GrphUnd
SquareRoot(a) : RngIntResElt -> RngIntResElt
Sqrt(a) : RngIntResElt -> RngIntResElt
Sqrt(a) : RngOrdElt -> RngOrdElt
SquareRoot(a) : FldACElt -> FldACElt
SquareRoot(c) : FldComElt -> FldComElt
SquareRoot(a) : FldFinElt -> FldFinElt
SquareRoot(x) : RngLocElt -> RngLocElt
SquareRoot(I) : RngOrdFracIdl -> RngOrdFracIdl
SquareRoot(s) : RngPowLazElt -> RngPowLazElt
SquareRoot(f) : RngSerElt -> RngSerElt
SQUOFOF(n) : RngIntElt -> RngIntEltFact, [ RngIntElt ]
SRegulator(S) : SetEnum[PlcFunElt] -> RngIntElt
GeneralizedSrivastavaCode(A, W, Z, t, S) : [ FldFinElt ], [ FldFinElt ], [ FldFinElt ], RngIntElt, FldFin -> Code
SrivastavaCode(A, W, mu, S) : [ FldFinElt ], [ FldFinElt ], RngIntElt, FldFin -> Code
SrivastavaCode(A, W, mu, S) : [ FldFinElt ], [ FldFinElt ], RngIntElt, FldFin -> Code
ApproximateStabiliser(G, A, U: parameters) : GrpMat, GrpMat, ModTupFld -> GrpMat, GrpMat, RngIntElt, RngIntElt, RngIntElt
BasicStabilizer(G, i) : GrpMat, RngIntElt -> GrpMat
BasicStabilizer(G, i) : GrpPerm, RngIntElt -> GrpPerm
BasicStabilizerChain(G) : GrpMat -> [GrpMat]
BasicStabilizerChain(G) : GrpPerm -> [GrpPerm]
StabiliserOfSpaces(Q) : Spaces -> GrpMat, SeqEnum
Stabilizer(G, Y, y) : GrpPerm, GSet, Elt -> GrpPerm
UnipotentStabiliser(G, U: parameters) : Grp, ModTupFld -> GrpMat, ModTupFld, GrpMatElt
StabiliserOfSpaces(Q) : Spaces -> GrpMat, SeqEnum
GrpMat_StabiliserOfSpaces (Example H21E22)
MonomialGroupStabilizer(C, k) : Code, RngIntElt -> GrpPerm, PowMap, Map
AutomorphismGroupStabilizer(C, k) : Code, RngIntElt -> GrpPerm, PowMap, Map
AutomorphismGroupStabilizer(D, k) : Inc, RngIntElt -> GrpPerm, PowMap, Map
BasicStabilizer(G, i) : GrpMat, RngIntElt -> GrpMat
BasicStabilizer(G, i) : GrpPerm, RngIntElt -> GrpPerm
BasicStabilizerChain(G) : GrpMat -> [GrpMat]
BasicStabilizerChain(G) : GrpPerm -> [GrpPerm]
CollineationGroupStabilizer(P, k) : Plane, RngIntElt -> GrpPerm, GSet, GSet, PowMap, Map
Stabilizer(G, y) : GrpMat, Elt -> GrpMat
Stabilizer(A, Y, y) : GrpPerm, Elt -> GrpPerm
Stabilizer(G, Y, y) : GrpPerm, Elt -> GrpPerm
Stabilizer(G, Y, y) : GrpPerm, Elt -> GrpPerm
Stabilizer(G, Y, y) : GrpPerm, GSet, Elt -> GrpPerm
Stabilizer(a,G) : SpcHypElt, GrpPSL2 -> GrpPSL2Elt
Images, Orbits and Stabilizers (PERMUTATION GROUPS)
Orbit and Stabilizer Functions for Large Groups (MATRIX GROUPS)
Orbits and Stabilizers (MATRIX GROUPS)
GrpPerm_Stabilizers (Example H20E19)
IsStandard(t) : Tbl -> BoolElt
IsStandardParabolicSubgroup( W, H ) : GrpCox -> GrpCox
NumberOfStandardTableaux(P) : SeqEnum -> RngIntElt
NumberOfStandardTableauxOnWeight(n) : RngIntElt -> RngIntElt
StandardAction( W ) : GrpCox -> Map
StandardActionGroup( W ) : GrpCox -> GrpPerm, Map
StandardForm(C) : Code -> Code, Map
StandardForm(C) : Code -> Code, Map
StandardGraph(G) : Grph -> Grph
StandardGroup(G) : GrpPerm -> GrpPerm, Map
StandardLattice(n) : RngIntElt -> Lat
StandardParabolicSubgroup( W, s ) : GrpCox, { } -> GrpCox
StandardPresentation(G): GrpPC -> GrpPC, Map
StandardRepresentation( G ) : GrpLie -> Map
StandardTableaux(P) : SeqEnum[RngIntElt] -> SetEnum
StandardTableauxOfWeight(n) : RngIntElt -> SetEnum
GrpPC_Standard (Example H24E1)
Affine and Projective Spaces (SCHEMES)
Calculation of Standard Sections (FP GROUPS - ADVANCED FEATURES)
Construction of a Standard Digraph (GRAPHS)
Construction of a Standard Graph (GRAPHS)
Construction of a Standard Group (FINITELY PRESENTED GROUPS)
Construction of a Standard Group (GROUPS)
Construction of Standard Groups (POLYCYCLIC GROUPS)
Isomorphism testing and Standard Presentations (p-GROUPS)
Some Basic Families of Codes (LINEAR CODES OVER FINITE FIELDS)
Some Standard Permutation Groups (PERMUTATION GROUPS)
Standard Constructions (LINEAR CODES OVER FINITE FIELDS)
Standard Constructions (LINEAR CODES OVER FINITE RINGS)
Standard Constructions and Conversions (ABELIAN GROUPS)
Standard Groups and Extensions (GROUPS)
Standard Matrix Groups (MATRIX GROUPS)
Standard Subgroups (PERMUTATION GROUPS)
The Standard Action (COXETER GROUPS)
The Standard Form (LINEAR CODES OVER FINITE RINGS)
CrvMod_Standard class polynomials (Example H89E5)
Standard Constructions and Conversions (ABELIAN GROUPS)
Construction of a Standard Digraph (GRAPHS)
The Standard Form (LINEAR CODES OVER FINITE RINGS)
Construction of a Standard Graph (GRAPHS)
Construction of Standard Groups (POLYCYCLIC GROUPS)
Isomorphism testing and Standard Presentations (p-GROUPS)
Calculation of Standard Sections (FP GROUPS - ADVANCED FEATURES)
StandardAction( W ) : GrpCox -> Map
GrpCox_StandardAction (Example H34E18)
StandardActionGroup( W ) : GrpCox -> GrpPerm, Map
StandardForm(C) : Code -> Code, Map
StandardForm(C) : Code -> Code, Map
CodeFld_StandardForm (Example H101E9)
CodeRng_StandardForm (Example H102E8)
StandardGraph(G) : Grph -> Grph
StandardGroup(G) : GrpPerm -> GrpPerm, Map
GrpFP_1_StandardGroups (Example H19E14)
GrpPerm_StandardGroups (Example H20E7)
Grp_StandardGroups (Example H16E7)
StandardLattice(n) : RngIntElt -> Lat
StandardParabolicSubgroup( W, s ) : GrpCox, { } -> GrpCox
StandardPresentation(G): GrpPC -> GrpPC, Map
GrpPGp_StandardPresentation (Example H25E4)
StandardRepresentation( G ) : GrpLie -> Map
GrpLie_StandardRepresentation (Example H35E7)
StandardTableaux(P) : SeqEnum[RngIntElt] -> SetEnum
StandardTableauxOfWeight(n) : RngIntElt -> SetEnum
DualStarInvolution(M) : ModSym -> AlgMatElt
StarInvolution(M) : ModSym -> AlgMatElt
StarInvolution(M) : ModSym -> AlgMatElt
StartEnumeration(~P: parameters) : GrpFPCosetEnumProc ->
StartNewClass(~P: parameters) : Process(pQuot) ->
Loading files (OVERVIEW)
Overview (OVERVIEW)
Loading files (OVERVIEW)
StartEnumeration(~P: parameters) : GrpFPCosetEnumProc ->
Starting and Restarting an Enumeration (FP GROUPS - ADVANCED FEATURES)
StartNewClass(~P: parameters) : Process(pQuot) ->
Env_Startup (Example H4E1)
Loading files (OVERVIEW)
Starting, Interrupting and Terminating (STATEMENTS AND EXPRESSIONS)
User Startup Specification Files (FUNCTIONS, PROCEDURES AND PACKAGES)
Starting, Interrupting and Terminating (STATEMENTS AND EXPRESSIONS)
User Startup Specification Files (FUNCTIONS, PROCEDURES AND PACKAGES)
Func_startup-spec (Example H2E10)
MAGMA_STARTUP_FILE
Definite Iteration (STATEMENTS AND EXPRESSIONS)
Indefinite Iteration (STATEMENTS AND EXPRESSIONS)
Statements (OVERVIEW)
STATEMENTS AND EXPRESSIONS
The Case Statement (STATEMENTS AND EXPRESSIONS)
The Simple Conditional Statement (STATEMENTS AND EXPRESSIONS)
STATEMENTS AND EXPRESSIONS
Status and Future Directions (MODULAR FORMS)
SteenrodOperation(f, i) : RngMPolElt, RngIntElt -> RngMPolElt
Steenrod Operations (INVARIANT RINGS OF FINITE GROUPS)
SteenrodOperation(f, i) : RngMPolElt, RngIntElt -> RngMPolElt
RngInvar_SteenrodOperation (Example H80E12)
The Steinberg Presentation (GROUPS OF LIE TYPE)
IsSteiner(D, t) : Dsgn -> BoolElt
SteinitzClass(M) : ModDed -> RngOrdIdl
SteinitzForm(M) : ModDed -> ModDed
SteinitzClass(M) : ModDed -> RngOrdIdl
SteinitzForm(M) : ModDed -> ModDed
ReductionStep(f) : QuadBinElt -> QuadBinElt
Sequences (OVERVIEW)
Sets (OVERVIEW)
The for statement (OVERVIEW)
StirlingFirst(m, n) : RngIntElt, RngIntElt -> RngIntElt
StirlingFirst(m, n) : RngIntElt, RngIntElt -> RngIntElt
StirlingSecond(m, n) : RngIntElt, RngIntElt -> RngIntElt
StirlingSecond(m, n) : RngIntElt, RngIntElt -> RngIntElt
StirlingFirst(m, n) : RngIntElt, RngIntElt -> RngIntElt
StirlingFirst(m, n) : RngIntElt, RngIntElt -> RngIntElt
StirlingSecond(m, n) : RngIntElt, RngIntElt -> RngIntElt
StirlingSecond(m, n) : RngIntElt, RngIntElt -> RngIntElt
Control-C key (OVERVIEW)
Quitting (OVERVIEW)
Identifiers and variables (OVERVIEW)
Identifiers and variables (OVERVIEW)
A General Facility (GRAPHS)
CodeToString(n) : RngIntElt -> MonStgElt
IntegerToString(n) : RngIntElt -> ModStgElt
IntegerToString(n) : RngIntElt -> MonStgElt
IntegerToString(n, b) : RngIntElt, RngIntElt -> MonStgElt
LeftString( RD, r, s ) : RootDtm, RngIntElt, RngIntElt -> RngIntElt
LeftStringLength( RD, r, s ) : RootDtm, RngIntElt, RngIntElt -> RngIntElt
RightString( RD, r, s ) : RootDtm, RngIntElt, RngIntElt -> RngIntElt
RightStringLength( RD, r, s ) : RootDtm, RngIntElt, RngIntElt -> RngIntElt
StringToCode(s) : MonStgElt -> RngIntElt
StringToInteger(s) : MonStgElt -> RngIntElt
StringToInteger(s, b) : MonStgElt, MonStgElt -> RngIntElt
StringToIntegerSequence(s) : MonStgElt -> [ RngIntElt ]
Character Strings (INPUT AND OUTPUT)
Strings (OVERVIEW)
IO_Strings (Example H3E1)
StringToCode(s) : MonStgElt -> RngIntElt
StringToInteger(s) : MonStgElt -> RngIntElt
StringToInteger(s, b) : MonStgElt, MonStgElt -> RngIntElt
StringToIntegerSequence(s) : MonStgElt -> [ RngIntElt ]
Strip(H, x) : GrpPerm, GrpPermElt -> BoolElt, GrpPermElt, RngIntElt
WordStrip(H, x) : GrpPerm, GrpPermElt -> BoolElt, GrpFPElt, RngIntElt
FPGroupStrong(G) : GrpMat :-> GrpFP, Hom(Grp)
FPGroupStrong(G) : GrpPerm -> GrpFP, Hom(Grp)
FPGroupStrong(G, N) : GrpPerm, GrpPerm -> GrpFP, Hom(Grp)
FPGroupStrong(G: parameters) : GrpPerm :-> GrpFP, Hom(Grp)
NumberOfStrongGenerators(G) : GrpMat -> RngIntElt
NumberOfStrongGenerators(G) : GrpPerm -> RngIntElt
NumberOfStrongGenerators(G, i) : GrpPerm, RngIntElt -> RngIntElt
StrongGenerators(G) : GrpMat -> SetIndx(GrpMat)
StrongGenerators(G) : GrpPerm -> SetIndx(GrpPermElt)
StrongGenerators(G, i) : GrpPerm, RngIntElt -> SetIndx(GrpPermElt)
Base and Strong Generating Set (MATRIX GROUPS)
Base and Strong Generating Set (PERMUTATION GROUPS)
Construction of a Base and Strong Generating Set (PERMUTATION GROUPS)
StrongGenerators(G) : GrpMat -> SetIndx(GrpMat)
StrongGenerators(G) : GrpPerm -> SetIndx(GrpPermElt)
StrongGenerators(G, i) : GrpPerm, RngIntElt -> SetIndx(GrpPermElt)
IsStronglyAG(C) : Code -> BoolElt
IsStronglyConnected(G) : GrphDir -> BoolElt
StronglyConnectedComponents(G) : GrphUnd -> [GrphDir]
StronglyRegularGraphsDatabase() : -> DB
Strongly Regular Graphs (GRAPHS)
StronglyConnectedComponents(G) : GrphUnd -> [GrphDir]
Graph_StronglyRegularGraphs (Example H97E20)
StronglyRegularGraphsDatabase() : -> DB
RngLoc_strop (Example H55E5)
RngPad_strop (Example H40E3)
Creation of Structures (ALGEBRAIC FUNCTION FIELDS)
Related Structures (ALGEBRAIC FUNCTION FIELDS)
Structure Predicates (ALGEBRAIC FUNCTION FIELDS)
Structure Predicates (ALGEBRAIC FUNCTION FIELDS)
The Weight Distribution (LINEAR CODES OVER FINITE FIELDS)
The Weight Distribution (LINEAR CODES OVER FINITE RINGS)
ClassGroupStructure(Q: parameters) : QuadBin -> [ RngIntElt ]
CoveringStructure(S, T) : Str, Str -> Str
CycleStructure(g) : GrpPermElt -> [ <RngIntElt, RngIntElt> ]
ExistsCoveringStructure(S, T) : Str, Str -> BoolElt, Str
GeneratorStructure(P) : Process(pQuot) ->
IncidenceStructure(G) : Grph -> Inc
IncidenceStructure(I) : Inc -> Inc
IncidenceStructure< v | X > : RngIntElt, List -> Inc
StructureConstant(G, i, j, k) : Grp, RngIntElt, RngIntElt, RngIntElt -> RngIntElt
StructureConstants( RD ) : RootDtm -> RngIntElt
Characteristic Subgroups and Normal Structure (GROUPS)
Creation of Coproducts (COPRODUCTS)
Creation of Structures (ALGEBRAIC FUNCTION FIELDS)
Creation of Structures (ALGEBRAIC FUNCTION FIELDS)
Creation of Structures (ALGEBRAICALLY CLOSED FIELDS)
Creation of Structures (BINARY QUADRATIC FORMS)
Creation of Structures (FINITE FIELDS)
Creation of Structures (GALOIS RINGS)
Creation of Structures (POWER, LAURENT AND PUISEUX SERIES)
Creation of Structures (RATIONAL FUNCTION FIELDS)
Creation of Structures (RING OF INTEGERS)
Creation of Structures (VALUATION RINGS)
Galois Module Structure (CLASS FIELD THEORY)
General Structure Invariants (ALGEBRAIC FUNCTION FIELDS)
INCIDENCE STRUCTURES AND DESIGNS
Magmas (or Structures) (OVERVIEW)
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)
Operations on Structures (LOCAL RINGS AND FIELDS)
Operations on Structures (p-ADIC RINGS AND FIELDS)
Other Related Structures (ALGEBRAIC FUNCTION FIELDS)
Parent and Category (ALGEBRAIC FUNCTION FIELDS)
Related Structures (ALGEBRAIC FUNCTION FIELDS)
Related Structures (ALGEBRAIC FUNCTION FIELDS)
Related Structures (ALGEBRAIC FUNCTION FIELDS)
Structure of a Module (MODULES OVER A MATRIX ALGEBRA)
Structure of congruence subgroups (SUBGROUPS OF PSL_2(R))
Structure Operations (CYCLOTOMIC FIELDS)
Structure Operations (POWER, LAURENT AND PUISEUX SERIES)
Structure Operations (REAL AND COMPLEX FIELDS)
Structure Operations (VALUATION RINGS)
Structure Predicates (ALGEBRAIC FUNCTION FIELDS)
Structure Predicates (ALGEBRAIC FUNCTION FIELDS)
Structure Predicates (ALGEBRAIC FUNCTION FIELDS)
Subgroup Structure (ABELIAN GROUPS)
The Abelian Quotient Structure of a Group (POLYCYCLIC GROUPS)
The Abstract Structure of a Group (GROUPS)
The Subgroup Structure (ABELIAN GROUPS)
The Subgroup Structure (POLYCYCLIC GROUPS)
General Structure Invariants (ALGEBRAIC FUNCTION FIELDS)
Structure of congruence subgroups (SUBGROUPS OF PSL_2(R))
Operations on Structures (LOCAL RINGS AND FIELDS)
Operations on Structures (p-ADIC RINGS AND FIELDS)
Structure Predicates (ALGEBRAIC FUNCTION FIELDS)
Structure Predicates (ALGEBRAIC FUNCTION FIELDS)
Structure Predicates (ALGEBRAIC FUNCTION FIELDS)
Related Structures (ALGEBRAIC FUNCTION FIELDS)
Other Related Structures (ALGEBRAIC FUNCTION FIELDS)
Parent and Category (ALGEBRAIC FUNCTION FIELDS)
BaseRing(C) : Sch -> Fld
CoefficientRing(C) : Sch -> Fld
Operations on Curves (HYPERELLIPTIC CURVES)
Operations on Structures (QUADRATIC FIELDS)
StructureConstant(G, i, j, k) : Grp, RngIntElt, RngIntElt, RngIntElt -> RngIntElt
StructureConstants( RD ) : RootDtm -> RngIntElt
Associated Structures (BRANDT MODULES)
Type(L) : Lat -> Cat
Associated Structures (LATTICES)
Related Structures (ROOT DATA FOR LIE THEORY)
SU(arguments)
SpecialUnitaryGroup(arguments)
SubOrder(O) : RngOrd -> RngOrd
Constructor (OVERVIEW)
Creation of Submodules and Quotient Modules (MODULES OVER AFFINE ALGEBRAS)
Subcomplexes and Quotient Complexes (CHAIN COMPLEXES)
Sublattices, Superlattices and Quotients (LATTICES)
sub< cat : A | L> : Cat, AlgGrp, List -> AlgGrp, Map
sub<A | L_1, ..., L_r> : AlgFP, AlgFPElt, ..., AlgFPElt -> AlgFP
sub< A | L > : AlgGen, List -> AlgGen, Map
sub<R | L> : AlgMat, List -> AlgMat, Hom(Alg)
sub<C | L> : Code, List -> Code
sub<C | L> : Code, List -> Code
sub< F | e_1, ..., e_n > : FldAlg, FldAlgElt, ..., FldAlgElt -> FldAlg, Map
sub<F | d> : FldFin, RngIntElt -> FldFin, Map
sub<F | f> : FldFin, RngPolElt(FldFin) -> FldFin, Map
sub<G | L> : Grp, List -> Grp
sub<A | L> : GrpAb, List -> GrpAb, Map
sub< G | f > : GrpFP, Hom(Grp) -> GrpFP
sub< G | L > : GrpFP, List -> GrpFP
sub<G | L> : GrpGPC, List -> GrpGPC, Map
sub< G | e_1, ..., e_r > : Grph, List(Edge) -> Grph, GrphVertSet, GrphEdgeSet
sub< G | v_1, ..., v_r > : Grph, List(Vert) -> Grph, GrphVertSet, GrphEdgeSet
sub<G | L> : GrpMat, List -> GrpMat
sub<G | L> : GrpPC, List -> GrpPC, Map
sub<G | L> : GrpPerm, List -> GrpPerm
sub<L | S> : Lat, List -> Lat
sub< C | Q > : ModCpx, SeqEnum[ModAlg] -> ModCpx, MapChn
sub<M | m> : ModDed, SeqEnum[ModDedElt] -> ModDed, Map
sub<M | L> : ModMPol, List -> ModMPol
sub<V | L> : ModTupFld, List -> ModTupFld
sub<M | L> : ModTupRng, List -> ModTupRng
sub<M | L> : ModTupRng, List -> ModTupRng
sub<A | L: parameters> : GrpAbGen, List -> GrpAbGen
sub<P | L> : Plane, List -> Plane
sub< Z | n > : RngInt, RngIntElt -> RngInt
sub< R | n > : RngIntRes, RngIntResElt -> RngIntRes
sub< O | a_1, ..., a_r > : RngOrd, RngOrdElt, ..., RngOrdElt -> RngOrd
sub< O | f > : RngQuad, RngIntElt ->
sub<S | L_1, ..., L_r> : SgpFP, SgpFPElt, ..., SgpFPElt -> SgpFP
Plane_sub (Example H99E4)
Plane_sub (Example H99E5)
GrpPC_sub-predicates (Example H24E16)
Creation of Submodules and Quotient Modules (MODULES OVER AFFINE ALGEBRAS)
Subcomplexes and Quotient Complexes (CHAIN COMPLEXES)
ModDed_sub-quo (Example H63E2)
Sublattices, Superlattices and Quotients (LATTICES)
GrpPC_sub_creation (Example H24E13)
AlgMat_SubAlgebra (Example H73E4)
CartanSubalgebra(L) : AlgLie -> AlgLie
HasLeviSubalgebra(L) : AlgLie -> BoolElt
Construction of a Subalgebra (FINITELY PRESENTED ALGEBRAS)
Elementary Operations on Subalgebras and Ideals (MATRIX ALGEBRAS)
Operations on Subalgebras of Group Algebras (GROUP ALGEBRAS)
Elementary Operations on Subalgebras and Ideals (MATRIX ALGEBRAS)
Subcode(C, S) : Code, RngIntElt -> Code
Subcode(C, k) : Code,RngIntElt -> Code
Subcode(C, k) : Code,RngIntElt -> Code
Subcode(C, S) : Code,RngIntElt -> Code
SubcodeBetweenCode(C1, C2, k) : Code,Code,RngIntElt -> Code
SubcodeWordsOfWeight(C, S) : Code,RngIntElt -> Code
SubfieldSubcode(C, S) : Code, FldFin -> Code, Map
Construction of Subcodes of Linear Codes (LINEAR CODES OVER FINITE RINGS)
Subcodes (LINEAR CODES OVER FINITE FIELDS)
SubcodeBetweenCode(C1, C2, k) : Code,Code,RngIntElt -> Code
CodeFld_SubcodeBetweenCode (Example H101E14)
SubcodeWordsOfWeight(C, S) : Code,RngIntElt -> Code
RandomSubcomplex(C,Q) : ModCpx, SeqEnum -> ModCpx, MapChn
RootSubdatum( RD, s ) : RootDtm, SeqEnum -> RootDtm
RootSubdatum( RD, a ) : RootDtm, SetEnum -> RootDtm
IsRealisableOverSubfield(M, F) : ModGrp, FldFin -> BoolElt, ModGrp
IsSubfield(F, L) : FldAlg, FldAlg -> BoolElt, Map
MaximalAbelianSubfield(M) : RngOrd -> FldAb
SubfieldCode(C, S) : Code, FldFin -> Code
SubfieldLattice(K) : FldNum -> SubFldLat
SubfieldRepresentationCode(C, S) : Code, FldFin -> Code
SubfieldRepresentationParityCode(C, K) : Code, FldFin -> Code
SubfieldSubcode(C, S) : Code, FldFin -> Code, Map
SubfieldSubplane(P, F) : Plane, FldFin -> Plane, PlanePtSet, PlaneLnSet
The Subfield Lattice (ORDERS AND ALGEBRAIC FIELDS)
The Subfield Lattice (ORDERS AND ALGEBRAIC FIELDS)
SubfieldCode(C, S) : Code, FldFin -> Code
SubfieldLattice(K) : FldNum -> SubFldLat
RngOrd_SubfieldLattice (Example H48E23)
SubfieldRepresentationCode(C, S) : Code, FldFin -> Code
SubfieldRepresentationParityCode(C, K) : Code, FldFin -> Code
MaximalSubfields(e) : SubFldLatElt -> [ SubFldLatElt ]
Subfields(K) : FldAlg -> [ < FldAlg, Hom > ]
Subfields(K, n) : FldAlg -> [ < FldAlg, Hom > ]
Subfields(F) : FldFun -> SeqEnum[FldFun]
FldFunG_Subfields (Example H53E9)
Subfields (ORDERS AND ALGEBRAIC FIELDS)
RestrictField(C, S) : Code, FldFin -> Code, Map
SubfieldSubcode(C, S) : Code, FldFin -> Code, Map
SubfieldSubplane(P, F) : Plane, FldFin -> Plane, PlanePtSet, PlaneLnSet
IsSubgraph(G, H) : Grph, Grph -> BoolElt
Graph_Subgraph (Example H97E10)
Subgraphs, Quotient Graphs, and Super-graphs (GRAPHS)
The Graph of a Map (MAPPINGS)
The Graph of a Map (MAPPINGS)
Subgraphs, Quotient Graphs, and Super-graphs (GRAPHS)
TorsionSubgroup(H) : SetPtEll -> GrpAb, Map
AbelianGroup(H) : SetPtEll -> GrpAb, Map
AbelianNormalSubgroup(G) : GrpPerm -> GrpPerm
AddSubgroupGenerator(~P, w) : GrpFPCosetEnumProc, GrpFPElt ->
AutomorphismSubgroup(C) : Code -> GrpPerm, PowMap, Map
AutomorphismSubgroup(D) : Inc -> GrpPerm, PowMap, Map
Borel(C) : CosetGeom -> GrpPerm
CentralizerOfNormalSubgroup(G, H) : GrpPerm, GrpPerm -> GrpPerm
CollineationSubgroup(P) : Plane -> GrpPerm, GSet, GSet, PowMap, Map
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
DerivedGroup(G) : GrpPC -> GrpPC
CommutatorSubgroup(G, H, K) : GrpPC, GrpPC, GrpPC -> GrpPC
CommutatorSubgroup(G, H, K) : GrpPerm, GrpPerm, GrpPerm -> GrpPerm
CongruenceSubgroup(N) : RngIntElt -> GrpPSL2
CongruenceSubgroup(i,N) : RngIntElt, RngIntElt -> GrpPSL2
CongruenceSubgroup([N,M,P]) : SeqEnum -> GrpPSL2
DerivedSubgroup(G) : GrpAb -> GrpAb
DerivedSubgroup(G) : GrpFin -> GrpFin
DerivedSubgroup(G) : GrpGPC -> GrpGPC
DerivedSubgroup(G) : GrpGPC -> GrpGPC
DerivedSubgroup(G) : GrpMat -> GrpMat
DerivedSubgroup(G) : GrpPerm -> GrpPerm
ElementaryAbelianNormalSubgroup(G) : GrpPerm -> GrpPerm
FittingSubgroup(G) : GrpAb -> GrpAb
FittingSubgroup(G) : GrpFin -> GrpFin
FittingSubgroup(G) : GrpGPC -> GrpGPC
[Future release] FittingSubgroup(G) : GrpMat -> GrpMat
FittingSubgroup(G) : GrpPC -> GrpPC
FittingSubgroup(G) : GrpPerm -> GrpPerm
FrattiniSubgroup(G) : GrpAb -> GrpAb
FrattiniSubgroup(G) : GrpFin -> GrpFin
FrattiniSubgroup(G) : GrpMat -> GrpMat
FrattiniSubgroup(G) : GrpPC -> GrpPC
FrattiniSubgroup(G) : GrpPerm -> GrpPerm
HallSubgroup(G, S) : GrpPC, { RngIntElt } -> GrpPC
IsReflectionSubgroup( W, H ) : GrpCox -> GrpCox
IsStandardParabolicSubgroup( W, H ) : GrpCox -> GrpCox
IsSubgroup(G,H) : GrpPSL2, GrpPSL2 -> BoolElt
MaximalNormalSubgroup(G) : GrpPerm -> GrpPerm
MinimalNormalSubgroup(G) : GrpPC -> GrpPC
MinimalNormalSubgroup(G, N) : GrpPC -> GrpPC
NextSubgroup(~P) : Process(Lix) ->
ReflectionSubgroup( W, s ) : GrpCox, [] -> GrpCox
ReflectionSubgroup( W, a ) : GrpCox, { } -> GrpCox
StandardParabolicSubgroup( W, s ) : GrpCox, { } -> GrpCox
Subgroup(V) : GrpFPCos -> GrpFP
Subgroup(P) : GrpFPCosetEnumProc -> GrpFP
SubgroupClasses(G) : GrpPC -> SeqEnum
SubgroupClasses(G: parameters) : GrpFin -> [ rec< Grp, RngIntElt, RngIntElt, GrpFP> ]
SubgroupClasses(G: parameters) : GrpPerm -> [ rec< GrpPerm, RngIntElt, RngIntElt, GrpFP> ]
SubgroupLattice(G) : GrpFin -> SubGrpLat
SubgroupLattice(G) : GrpPC -> SubGrpLat
SubgroupOfTorus(M, x) : ModSym, ModSymElt -> RngIntElt
SubgroupOfTorus(M, s) : ModSym, SeqEnum -> GrpAb
SubgroupScheme(E,P) : CrvEll, Pt -> CrvEllSubgroup
SubgroupScheme(G, f) : SchGrpEll, RngUPolElt -> SchGrpEll
SylowSubgroup(G, p) : GrpAb, RngIntElt -> GrpAb
SylowSubgroup(G, p) : GrpFin, RngIntElt -> GrpFin
SylowSubgroup(G, p) : GrpMat, RngIntElt -> GrpMat
SylowSubgroup(G, p) : GrpPC, RngIntElt -> GrpPC
SylowSubgroup(G, p) : GrpPerm, RngIntElt -> GrpPerm
TorsionFreeSubgroup(A) : GrpAb -> GrpAb
TorsionSubgroup(A) : GrpAb -> GrpAb
TorsionSubgroup(J) : JacHyp -> GrpAb, Map
TorsionSubgroup(H) : SetPtEll -> GrpAb, Map
TorsionSubgroupScheme(G, n) : SchGrpEll, RngIntElt -> SchGrpEll
TwoTorsionSubgroup(J) : JacHyp -> GrpAb, Map
TwoTorsionSubgroup(Q) : QuadBin -> GrpAb, Map
pElementaryAbelianNormalSubgroup(G, p) : GrpPerm, RngIntElt -> GrpPerm
GrpGPC_Subgroup (Example H23E3)
Grp_Subgroup (Example H16E5)
Characteristic Subgroups and Normal Series (PERMUTATION GROUPS)
Characteristic Subgroups and Normal Structure (GROUPS)
Characteristic Subgroups and Subgroup Series (ABELIAN GROUPS)
Characteristic Subgroups and Subgroup Series (GROUPS)
Characteristic Subgroups and Subgroup Series (MATRIX GROUPS)
Characteristic Subgroups and Subgroup Series (POLYCYCLIC GROUPS)
Conjugacy Classes of Subgroups (FINITE SOLUBLE GROUPS)
Conjugacy Classes of Subgroups (GROUPS)
Conjugacy Classes of Subgroups (GROUPS)
Constructing a Presentation for a Subgroup (FINITELY PRESENTED GROUPS)
Construction of a Subgroup (PERMUTATION GROUPS)
Construction of Subgroups (ABELIAN GROUPS)
Construction of Subgroups (GROUPS)
Construction of Subgroups (MATRIX GROUPS)
Construction of Subgroups (POLYCYCLIC GROUPS)
Construction of Subgroups and Quotient Groups (ABELIAN GROUPS)
Elementary Properties of a Subgroup (PERMUTATION GROUPS)
Elementary Properties of Subgroups (MATRIX GROUPS)
General Properties of Subgroups (ABELIAN GROUPS)
General Properties of Subgroups (POLYCYCLIC GROUPS)
General Subgroup Constructions (POLYCYCLIC GROUPS)
Low Index Subgroups (FINITELY PRESENTED 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)
Predicates for Subgroups (FINITE SOLUBLE GROUPS)
Properties of Subgroups (FINITE SOLUBLE GROUPS)
Properties of Subgroups Requiring a Nil-po-tent Covering Group (POLYCYCLIC GROUPS)
Standard Subgroup Constructions (GROUPS)
Standard Subgroups (MATRIX GROUPS)
Standard Subgroups (PERMUTATION GROUPS)
Subgroup Constructions (FINITELY PRESENTED GROUPS)
Subgroup Constructions Requiring a Nil-po-tent Covering Group (POLYCYCLIC GROUPS)
Subgroup Series (FINITE SOLUBLE GROUPS)
Subgroup Structure (ABELIAN GROUPS)
Subgroups (FINITELY PRESENTED GROUPS)
Subgroups (PERMUTATION GROUPS)
Subgroups of Finite Index (FINITELY PRESENTED GROUPS)
Subgroups, Quotient Groups, Homomorphisms and Extensions (POLYCYCLIC GROUPS)
The Poset of Subgroup Classes (GROUPS)
The Subgroup Structure (ABELIAN GROUPS)
The Subgroup Structure (POLYCYCLIC GROUPS)
General Properties of Subgroups (ABELIAN GROUPS)
General Properties of Subgroups (POLYCYCLIC GROUPS)
Properties of Subgroups Requiring a Nil-po-tent Covering Group (POLYCYCLIC GROUPS)
Conjugacy Classes of Subgroups (FINITE SOLUBLE GROUPS)
Conjugacy Classes of Subgroups (GROUPS)
Standard Subgroups (MATRIX GROUPS)
GrpPC_subgroup-constructions (Example H24E15)
The Poset of Subgroup Classes (GROUPS)
Predicates for Subgroups (FINITE SOLUBLE GROUPS)
Constructing a Presentation for a Subgroup (FINITELY PRESENTED GROUPS)
Elementary Properties of Subgroups (MATRIX GROUPS)
Properties of Subgroups (FINITE SOLUBLE GROUPS)
Construction of Subgroups and Quotient Groups (ABELIAN GROUPS)
Subgroups, Quotient Groups, Homomorphisms and Extensions (POLYCYCLIC GROUPS)
Characteristic Subgroups and Normal Series (PERMUTATION GROUPS)
Characteristic Subgroups and Subgroup Series (ABELIAN GROUPS)
Characteristic Subgroups and Subgroup Series (GROUPS)
Characteristic Subgroups and Subgroup Series (MATRIX GROUPS)
Characteristic Subgroups and Subgroup Series (POLYCYCLIC GROUPS)
Subgroup Series (FINITE SOLUBLE GROUPS)
Subgroup Structure (ABELIAN GROUPS)
The Subgroup Structure (ABELIAN GROUPS)
The Subgroup Structure (POLYCYCLIC GROUPS)
Construction of Subgroups (GENERIC ABELIAN GROUPS)
Associated Structures (ELLIPTIC CURVES)
Creation of Subgroup Schemes (ELLIPTIC CURVES)
Points of Subgroup Schemes (ELLIPTIC CURVES)
Predicates on Subgroup Schemes (ELLIPTIC CURVES)
Subgroup Schemes (ELLIPTIC CURVES)
Associated Structures (ELLIPTIC CURVES)
Creation of Subgroup Schemes (ELLIPTIC CURVES)
Points of Subgroup Schemes (ELLIPTIC CURVES)
Predicates on Subgroup Schemes (ELLIPTIC CURVES)
Subgroups(G) : GrpPC -> SeqEnum
SubgroupClasses(G) : GrpPC -> SeqEnum
SubgroupClasses(G: parameters) : GrpFin -> [ rec< Grp, RngIntElt, RngIntElt, GrpFP> ]
SubgroupClasses(G: parameters) : GrpPerm -> [ rec< GrpPerm, RngIntElt, RngIntElt, GrpFP> ]
GrpPC_SubgroupClasses (Example H24E18)
GrpFP_1_SubgroupConstructions (Example H19E41)
GrpPerm_SubgroupConstructions (Example H20E13)
GrpAbGen_SubgroupCreation (Example H17E4)
SubgroupLattice(G) : GrpFin -> SubGrpLat
SubgroupLattice(G) : GrpPC -> SubGrpLat
SubgroupOfTorus(M, x) : ModSym, ModSymElt -> RngIntElt
SubgroupOfTorus(M, s) : ModSym, SeqEnum -> GrpAb
GrpFP_1_SubgroupOps (Example H19E43)
CyclicSubgroups(G) : GrpPC -> SeqEnum
ElementaryAbelianSubgroups(G) : GrpPC -> SeqEnum
NilpotentSubgroups(G) : GrpPC -> SeqEnum
AbelianSubgroups(G) : GrpPC -> SeqEnum
ElementaryAbelianSubgroups(G) : GrpPC -> SeqEnum
NilpotentSubgroups(G) : GrpPC -> SeqEnum
AbelianSubgroups(G: parameters) : GrpFin -> [ rec< Grp, RngIntElt, RngIntElt, GrpFP> ]
AbelianSubgroups(G: parameters) : GrpPerm -> [ rec< GrpPerm, RngIntElt, RngIntElt, GrpFP> ]
CyclicSubgroups(G: parameters) : GrpFin -> [ rec< Grp, RngIntElt, RngIntElt, GrpFP> ]
CyclicSubgroups(G: parameters) : GrpPerm -> [ rec< GrpPerm, RngIntElt, RngIntElt, GrpFP> ]
ElementaryAbelianSubgroups(G: parameters) : GrpFin -> [ rec< Grp, RngIntElt, RngIntElt, GrpFP> ]
ElementaryAbelianSubgroups(G: parameters) : GrpPerm -> [ rec< GrpPerm, RngIntElt, RngIntElt, GrpFP> ]
LowIndexSubgroups(G, R : parameters) : GrpFP, RngIntElt -> [ GrpFP ]
LowIndexSubgroups(G, R : parameters) : GrpMat, RngIntElt -> [ GrpMat ]
LowIndexSubgroups(G, n: parameters) : GrpPerm, RngIntElt -> SeqEnum
MaximalSubgroups(G) : GrpAb -> [GrpAb]
MaximalSubgroups(G) : GrpPC -> [GrpPC]
MaximalSubgroups(G: parameters) : GrpPerm -> [ rec< GrpPerm, RngIntElt, RngIntElt, GrpFP> ]
MaximalSubgroups(e) : SubGrpLatElt -> { SubGrpLatElt }
MinimalNormalSubgroups(G) : GrpPerm -> [ GrpPerm ]
NilpotentSubgroups(G: parameters) : GrpFin -> [ rec< Grp, RngIntElt, RngIntElt, GrpFP> ]
NilpotentSubgroups(G: parameters) : GrpPerm -> [ rec< GrpPerm, RngIntElt, RngIntElt, GrpFP> ]
NonsolvableSubgroups(G: parameters) : GrpFin -> [ rec< Grp, RngIntElt, RngIntElt, GrpFP> ]
NonsolvableSubgroups(G: parameters) : GrpPerm -> [ rec< GrpPerm, RngIntElt, RngIntElt, GrpFP> ]
NormalSubgroups(G) : GrpFin -> [ Rec ]
NormalSubgroups(G) : GrpPC -> SeqEnum
NormalSubgroups(G) : GrpPerm -> [ Rec ]
NormalSubgroups(G: parameters) : GrpPerm -> [ rec< GrpPerm, RngIntElt, RngIntElt, GrpFP> ]
NumberOfSubgroupsAbelianPGroup (A) : SeqEnum -> SeqEnum
PerfectSubgroups(G: parameters) : GrpFin -> [ rec< Grp, RngIntElt, RngIntElt, GrpFP> ]
PerfectSubgroups(G: parameters) : GrpPerm -> [ rec< GrpPerm, RngIntElt, RngIntElt, GrpFP> ]
RegularSubgroups(G: parameters) : GrpFin -> [ rec< Grp, RngIntElt, RngIntElt, GrpFP> ]
SimpleSubgroups(G: parameters) : GrpFin -> [ rec< Grp, RngIntElt, RngIntElt, GrpFP> ]
SimpleSubgroups(G: parameters) : GrpPerm -> [ rec< GrpPerm, RngIntElt, RngIntElt, GrpFP> ]
SolubleSubgroups(G: parameters) : GrpFin -> [ rec< Grp, RngIntElt, RngIntElt, GrpFP> ]
SolvableSubgroups(G: parameters) : GrpPerm -> [ rec< GrpPerm, RngIntElt, RngIntElt, GrpFP> ]
SubgroupClasses(G) : GrpPC -> SeqEnum
SubgroupClasses(G: parameters) : GrpFin -> [ rec< Grp, RngIntElt, RngIntElt, GrpFP> ]
SubgroupClasses(G: parameters) : GrpPerm -> [ rec< GrpPerm, RngIntElt, RngIntElt, GrpFP> ]
Subgroups(G:parameters) : GrpAb -> [Rec]
SubgroupsLift(G, A, B, Q: parameters) : GrpPerm, GrpPerm, GrpPerm, SeqEnum -> SeqEnum
GrpAb_Subgroups (Example H18E4)
GrpMat_Subgroups (Example H21E15)
GrpPerm_Subgroups (Example H20E15)
Grp_Subgroups (Example H16E15)
Abelian Normal Subgroups (PERMUTATION GROUPS)
Characteristic Subgroups (FINITE SOLUBLE GROUPS)
Classes of Subgroups Satisfying a Condition (PERMUTATION GROUPS)
Congruence Subgroups (SUBGROUPS OF PSL_2(R))
Lattice of Normal Subgroups (PERMUTATION GROUPS)
Maximal and Minimal Normal Subgroups (PERMUTATION GROUPS)
Subgroups (FINITE SOLUBLE GROUPS)
Subgroups (GENERIC ABELIAN GROUPS)
Subgroups (MATRIX GROUPS)
Subgroups and Subgroup Series (p-GROUPS)
Subgroups and Transversals (COXETER GROUPS)
Classes of Subgroups Satisfying a Condition (PERMUTATION GROUPS)
GrpFP_1_Subgroups1 (Example H19E28)
GrpFP_1_Subgroups2 (Example H19E29)
GrpPGp_subgroupsabelianpgroups (Example H25E7)
SubgroupScheme(E,P) : CrvEll, Pt -> CrvEllSubgroup
SubgroupScheme(G, f) : SchGrpEll, RngUPolElt -> SchGrpEll
CrvEll_SubgroupSchemes (Example H87E9)
SubgroupsLift(G, A, B, Q: parameters) : GrpPerm, GrpPerm, GrpPerm, SeqEnum -> SeqEnum
GrpGPC_SubgroupsQuotientsTransfer (Example H23E6)
GrpGPC_SubgroupStructure (Example H23E9)
GrpGPC_SubgroupStructure2 (Example H23E10)
G-invariant Sublattices (LATTICES)
Sublattices(G) : GrpMat -> [ AlgMatElt ]
Sublattices(G, p) : GrpMat, RngIntElt -> [ AlgMatElt ]
Sublattices(G, Q) : GrpMat, [ RngIntElt ] -> [ AlgMatElt ]
Lat_Sublattices (Example H64E22)
ColumnSubmatrix(A, i) : Mtrx, RngIntElt -> Mtrx
ColumnSubmatrix(A, i, k) : Mtrx, RngIntElt, RngIntElt -> Mtrx
ColumnSubmatrixRange(A, i, j) : Mtrx, RngIntElt, RngIntElt -> Mtrx
RowSubmatrix(A, i) : Mtrx, RngIntElt -> Mtrx
RowSubmatrix(A, i, k) : Mtrx, RngIntElt, RngIntElt -> Mtrx
RowSubmatrixRange(A, i, j) : Mtrx, RngIntElt, RngIntElt -> Mtrx
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
Mat_Submatrix (Example H59E5)
Extracting and Inserting Blocks (MATRIX ALGEBRAS)
Joining Matrices (MATRIX ALGEBRAS)
ExtractBlockRange(A, i, j, r, s) : Mtrx, RngIntElt, RngIntElt, RngIntElt, RngIntElt -> Mtrx
SubmatrixRange(A, i, j, r, s) : Mtrx, RngIntElt, RngIntElt, RngIntElt, RngIntElt -> Mtrx
IsSubmodule(M, N) : ModDed, ModDed -> BoolElt, Map
MinimalSubmodule(M) : ModRng -> ModRng
SubmoduleAction(G, S) : GrpMat -> Map, GrpMat
SubmoduleImage(G, S) : GrpMat -> GrpMat
SubmoduleLattice(M) : ModRng -> SubModLat, BoolElt
SubmoduleLatticeAbort(M, n) : ModRng, RngIntElt -> BoolElt, SubModLat
TwistedWindingSubmodule(M, j, eps) : ModSym, RngIntElt, GrpDrchElt -> ModTupFld
WindingSubmodule(M, j : parameters) : ModSym, RngIntElt -> ModTupFld
ModAlg_Submodule (Example H77E3)
ModRng_Submodule (Example H62E4)
Construction (MODULES OVER A MATRIX ALGEBRA)
Construction of Submodules (FREE MODULES)
Lattice of Submodules (MODULES OVER A MATRIX ALGEBRA)
Operations on Submodules (FREE MODULES)
Socle Series (MODULES OVER A MATRIX ALGEBRA)
Submodules (FREE MODULES)
Construction (MODULES OVER A MATRIX ALGEBRA)
Lattice of Submodules (MODULES OVER A MATRIX ALGEBRA)
SubmoduleAction(G, S) : GrpMat -> Map, GrpMat
SubmoduleImage(G, S) : GrpMat -> GrpMat
SubmoduleLattice(M) : ModRng -> SubModLat, BoolElt
SubmoduleLatticeAbort(M, n) : ModRng, RngIntElt -> BoolElt, SubModLat
MaximalSubmodules(M) : ModRng -> [ ModRng ], BoolElt
MaximalSubmodules(e) : SubModLatElt -> { SubModLatElt }
MinimalSubmodules(M) : ModRng -> [ ModRng ], BoolElt
MinimalSubmodules(M, F) : ModRng, ModRng -> [ ModRng ], BoolElt
Submodules(M) : ModRng -> [ModRng]
Submodules (MODULES OVER A MATRIX ALGEBRA)
IsSubnormal(G, H) : GrpAb, GrpAb -> BoolElt
IsSubnormal(G, H) : GrpFin, GrpFin -> BoolElt
IsSubnormal(G, H) : GrpMat, GrpMat -> BoolElt
IsSubnormal(G, H) : GrpPC, GrpPC -> BoolElt
IsSubnormal(G, H) : GrpPerm, GrpPerm -> BoolElt
SubnormalSeries(G, H) : GrpAb, GrpAb -> [GrpAb]
SubnormalSeries(G, H) : GrpFin, GrpFin -> [ GrpFin ]
SubnormalSeries(G, H) : GrpMat, GrpMat -> [ GrpMat ]
SubnormalSeries(G, H) : GrpPC, GrpPC -> [GrpPC]
SubnormalSeries(G, H) : GrpPerm, GrpPerm -> [ GrpPerm ]
SubnormalSeries(G, H) : GrpAb, GrpAb -> [GrpAb]
SubnormalSeries(G, H) : GrpFin, GrpFin -> [ GrpFin ]
SubnormalSeries(G, H) : GrpMat, GrpMat -> [ GrpMat ]
SubnormalSeries(G, H) : GrpPC, GrpPC -> [GrpPC]
SubnormalSeries(G, H) : GrpPerm, GrpPerm -> [ GrpPerm ]
SubOrder(O) : RngOrd -> RngOrd
BaerSubplane(P) : PlaneProj -> PlaneProj, PlanePtSet, PlaneLnSet
SubfieldSubplane(P, F) : Plane, FldFin -> Plane, PlanePtSet, PlaneLnSet
Subplanes (FINITE PLANES)
PMod_SubQuo (Example H68E3)
RootDtm_SubRD (Example H33E18)
Construction of Subalgebras, Ideals and Quotient Algebras (GROUP ALGEBRAS)
Construction of Subalgebras, Ideals and Quotient Rings (MATRIX ALGEBRAS)
Construction of Subalgebras, Ideals and Quotient Algebras (GROUP ALGEBRAS)
Construction of Subalgebras, Ideals and Quotient Rings (MATRIX ALGEBRAS)
Functions, Procedures, and Mappings (OVERVIEW)
Construction of Subalgebras, Ideals and Quotient Algebras (ALGEBRAS)
Subalgebras and Ideals (ALGEBRAS)
Construction of Subalgebras, Ideals and Quotient Algebras (ALGEBRAS)
DefiningSubschemePolynomial(G) : SchGrpEll -> RngUPolElt
EmptySubscheme(X) : Sch -> Sch, MapSch
ReducedSubscheme(X) : Sch -> Sch, MapSch
SingularSubscheme(X) : Sch -> Sch
Access Functions (RATIONAL CURVES AND CONICS)
Automorphisms of Conics (RATIONAL CURVES AND CONICS)
Automorphisms of Rational Curves (RATIONAL CURVES AND CONICS)
Rational Curve and Conic Creation (RATIONAL CURVES AND CONICS)
Isomorphisms of Conics (RATIONAL CURVES AND CONICS)
Isomorphisms of Rational Curves (RATIONAL CURVES AND CONICS)
Isomorphisms with Standard Models (RATIONAL CURVES AND CONICS)
Subsemigroups and Ideals (FINITELY PRESENTED SEMIGROUPS)
Subsemigroups, Ideals and Quotients (FINITELY PRESENTED SEMIGROUPS)
Subsemigroups and Ideals (FINITELY PRESENTED SEMIGROUPS)
Subsemigroups, Ideals and Quotients (FINITELY PRESENTED SEMIGROUPS)
IsSubsequence(S, T) : SeqEnum, SeqEnum -> BoolElt
Subsequences(S, k) : SetEnum, RngIntElt -> SetEnum
Subsequences(S, k) : SetEnum, RngIntElt -> SetEnum
X subset R : { AlgMatElt } , AlgMat -> BoolElt
x in R : AlgMatElt, AlgMat -> BoolElt
e le f : SubGrpLatElt, SubGrpLatElt -> BoolElt
A subset B : AlgGen, AlgGen -> BoolElt
C subset D : Code, Code -> BoolElt
C subset D : Code, Code -> BoolElt
H subset G : GrpAb, GrpAb -> BoolElt
H subset A : GrpAbGen, GrpAbGen -> BoolElt
H subset G : GrpFin, GrpFin -> BoolElt
H subset K : GrpFP, GrpFP -> BoolElt
H subset G : GrpGPC, GrpGPC -> BoolElt
H subset G : GrpMat, GrpMat -> BoolElt
H subset G : GrpPC, GrpPC -> BoolElt
H subset G : GrpPerm, GrpPerm -> BoolElt
K subset L : LinSys,LinSys -> BoolElt
M1 subset M2 : ModBrdt, ModBrdt -> BoolElt
M subset N : ModDed, ModDed -> BoolElt
M subset N : ModMPol, ModMPol -> BoolElt
M1 subset M2 : ModSS, ModSS -> BoolElt
U subset V : ModTupFld, ModTupFld -> BoolElt
N subset M : ModTupRng, ModTupRng -> BoolElt
N subset M : ModTupRng, ModTupRng -> BoolElt
P subset Q : Plane, Plane -> BoolElt
I subset J : RngIdl, RngIdl -> BoolElt
I subset J : RngMPol, RngMPol -> BoolElt
I subset J : RngMPolRes, RngMPolRes -> BoolElt
I subset J : RngUPol, RngUPol -> BoolElt
C subset D : Sch,Sch -> BoolElt
X subset Y : Sch,Sch -> BoolElt
R subset S : SetEnum, Set -> BoolElt
S subset X : Setq,Sch -> BoolElt
e subset f : SubFldLatElt, SubFldLatElt -> BoolElt
e subset f : SubModLatElt, SubModLatElt -> SubModLatElt
S subset G : { GrpAbElt } , GrpAb -> BoolElt
S subset A : { GrpAbGenElt } , GrpAbGen -> BoolElt
S subset G : { GrpAtcElt }, GrpAtc -> BoolElt
S subset G : { GrpFinElt }, GrpFin -> BoolElt
S subset G : { GrpGPCElt } , GrpGPC -> BoolElt
S subset G : { GrpMatElt }, GrpMat -> BoolElt
S subset G : { GrpPCElt } , GrpPC -> BoolElt
S subset G : { GrpPermElt }, GrpPerm -> BoolElt
S subset G : { GrpRWSElt }, GrpRWS -> BoolElt
S subset G : { GrpSLPElt } , GrpSLP -> BoolElt
S subset B : { IncPt }, IncBlk -> BoolElt
S subset M : { MonRWSElt }, MonRWS -> BoolElt
S subset l : { PlanePt }, PlaneLn -> BoolElt
Subsets(S) : SetEnum -> SetEnum
Subsets(S) : SetEnum -> SetEnum
Subsets(S, k) : SetEnum, RngIntElt -> SetEnum
Subsets(S, k) : SetEnum, RngIntElt -> SetEnum
Subsets of a Finite Set (ENUMERATIVE COMBINATORICS)
CuspidalSubspace(M) : ModBrdt -> ModBrdt
CuspidalSubspace(M) : ModFrm -> ModFrm
CuspidalSubspace(M) : ModSS -> ModSS
CuspidalSubspace(M) : ModSym -> ModSym
EisensteinSubspace(M) : ModBrdt -> ModBrdt
EisensteinSubspace(M) : ModFrm -> ModFrm
EisensteinSubspace(M) : ModSS -> ModSS
EisensteinSubspace(M) : ModSym -> ModSym
NewSubspace(M) : ModFrm-> ModFrm
NewSubspace(M, p) : ModSym, RngIntElt -> ModSym
NewSubspace(M) : ModSym-> ModSym
ZeroSubspace(M) : ModFrm -> ModFrm
Construction of Subspaces (VECTOR SPACES)
Operations on Subspaces (VECTOR SPACES)
Subspaces, Quotient Spaces and Homomorphisms (VECTOR SPACES)
The Code Space (LINEAR CODES OVER FINITE FIELDS)
Subspaces, Quotient Spaces and Homomorphisms (VECTOR SPACES)
ModFld_Subspace1 (Example H61E8)
ModFld_Subspace2 (Example H61E9)
ModForm_Subspaces (Example H93E12)
ModSym_Subspaces (Example H90E12)
Subspaces (ALGEBRAIC FUNCTION FIELDS)
Subspaces (MODULAR FORMS)
Subspaces (MODULAR SYMBOLS)
Subspaces ({THE MODULE OF}{SUPERSINGULAR POINTS})
Substitute(u, f, n, v) : GrpFPElt, RngIntElt, RngIntElt, GrpFPElt -> GrpFPElt
Substitute(u, f, n, v) : SgpFPElt, RngIntElt, SgpFPElt, RngIntElt -> SgpFPElt
Substring(s, n, k) : MonStgElt, RngIntElt, RngIntElt -> MonStgElt
Lat_SubSuperQuo (Example H64E5)
IsSubsystem(L,K) : LinSys,LinSys -> BoolElt
K subset L : LinSys,LinSys -> BoolElt
Scheme_subsystems (Example H83E31)
Operators (OVERVIEW)
Subword(u, f, n) : GrpFPElt, RngIntElt, RngIntElt -> GrpFPElt
Subword(u, f, n) : SgpFPElt, RngIntElt, RngIntElt -> SgpFPElt
SuccessiveMinima(L) : Lat, RngIntElt -> [ RngIntElt ], [ LatElt ]
SuccessiveMinima(L) : Lat, RngIntElt -> [ RngIntElt ], [ LatElt ]
SuggestedPrecision(f) : RngUPolElt -> RngIntElt
SuggestedPrecision(f) : RngUPolElt -> RngIntElt
SuggestedPrecision(f) : RngUPolElt -> RngIntElt
SuggestedPrecision(f) : RngUPolElt -> RngIntElt
AlternatingSum(m, i) : Map, RngIntElt -> FldPrElt
DiagonalSum(t1, t2) : Tbl,Tbl -> Tbl
DirectSum(A, B) : AlgGen, AlgGen -> AlgGen
DirectSum(R, T) : AlgMat, AlgMat -> AlgMat
DirectSum(a, b) : AlgMatElt, AlgMatElt -> AlgMatElt
DirectSum(C, D) : Code, Code -> Code
DirectSum(C, D) : Code, Code -> Code
DirectSum(A, B) : GrpAb, GrpAb -> GrpAb
DirectSum(L, M) : Lat, Lat -> Lat
DirectSum(C, D) : ModCpx, ModCpx -> ModCpx
DirectSum(M, N) : ModGrp, ModGrp -> ModGrp, Map, Map, Map, Map
DirectSum(M, N) : ModRng, ModRng -> ModRng, Map, Map, Map, Map
DirectSum(M, N) : ModRng, ModRng -> ModRng, Map, Map, Map, Map
DirectSum( RD1, RD2 ) : RootDtm, RootDtm -> RootDtm
DirectSum(Q) : [ ModGrp ] -> [ ModGrp ], [ Map ], [ Map ]
DirectSum(Q) : [ ModRng ] -> [ ModRng ], [ Map ], [ Map ]
DirectSum(Q) : [ ModRng ] -> [ ModRng ], [ Map ], [ Map ]
DirectSum(Q) : [Code] -> Code
DirectSumDecomposition(L) : AlgLie -> [ AlgLie ]
DirectSumDecomposition( RD ) : RootDtm -> []
ExponentSum(w, x) : GrpFPElt, GrpFPElt -> RngIntElt
InfiniteSum(m, i) : Map, RngIntElt -> FldPrElt
PlotkinSum(C, D) : Code, Code -> Code
PlotkinSum(C1, C2) : Code, Code -> Code
PlotkinSum(C1, C2, C3: parameters) : Code, Code, Code -> Code
PositiveSum(m, i) : Map, RngIntElt -> FldPrElt
Sum( RD, r, s ) : RootDtm, RngIntElt, RngIntElt -> RngIntElt
Sum(Q) : [ Inc ] -> Inc
SumNorm(f) : RngMPolElt -> RngIntElt
SumNorm(p) : RngUPolElt -> RngIntElt
SumOfDivisors(n) : RngIntElt -> RngIntElt
ZeroSumCode(R, n) : FldFin, RngIntElt -> Code
ZeroSumCode(R, n) : Rng, RngIntElt -> Code
Direct Sum (K[G]-MODULES AND GROUP REPRESENTATIONS)
Direct Sum (MODULES OVER A MATRIX ALGEBRA)
Sum, Intersection and Dual (LINEAR CODES OVER FINITE FIELDS)
Sum, Intersection and Dual (LINEAR CODES OVER FINITE RINGS)
Sum, Intersection and Dual (LINEAR CODES OVER FINITE FIELDS)
Sum, Intersection and Dual (LINEAR CODES OVER FINITE RINGS)
CodeFld_SumIntersection (Example H101E15)
CodeRng_SumIntersection (Example H102E5)
IsDirectSummand(M, S) : ModGrp, ModGrp -> BoolElt, ModGrp
HasComplement(M, S) : ModGrp, ModGrp -> BoolElt, ModGrp
IndecomposableSummands(M) : ModGrp -> [ ModGrp ]
Summation of Infinite Series (REAL AND COMPLEX FIELDS)
SumNorm(f) : RngMPolElt -> RngIntElt
SumNorm(p) : RngUPolElt -> RngIntElt
SumOfDivisors(n) : RngIntElt -> RngIntElt
IsSUnit(a, S) : FldFunElt, SetEnum[PlcFunElt] -> BoolElt
IsSUnitWithPreimage(a, S) : FldFunElt, SetEnum[PlcFunElt] -> BoolElt, GrpAbElt
SUnitGroup(I) : RngOrdFracIdl -> GrpAb, Map
SUnitGroup(S) : SetEnum[PlcFunElt] -> GrpAb, Map
SUnitGroup(I) : RngOrdFracIdl -> GrpAb, Map
SUnitGroup(S) : SetEnum[PlcFunElt] -> GrpAb, Map
Sublattices, Superlattices and Quotients (LATTICES)
Subgraphs, Quotient Graphs, and Super-graphs (GRAPHS)
MinimalSupermodules(e) : SubModLatElt -> { SubModLatElt }
IsProbablySupersingular(E) : CrvEll -> BoolElt
IsSupersingular(E: parameters) : CrvEll -> BoolElt
SupersingularEllipticCurve(K) : FldFin -> CrvEll
SupersingularModule(p : parameters) : RngIntElt -> ModSS
{THE MODULE OF}{SUPERSINGULAR POINTS}
Predicates for Supersingularity (ELLIPTIC CURVES)
SupersingularEllipticCurve(K) : FldFin -> CrvEll
SupersingularModule(p : parameters) : RngIntElt -> ModSS
Plane_supp (Example H99E3)
HasSupplement(G, M) : GrpPerm, GrpPerm -> BoolElt, GrpPerm
Supplements(G, M) : GrpPerm, GrpPerm -> [ GrpPerm ]
Supplements(G, M, N) : GrpPerm, GrpPerm, GrpPerm -> [ GrpPerm ]
ChangeSupport(~G, S) : Grph, SetIndx ->
ChangeSupport(G, S) : Grph, SetIndx -> Grph, GrphVertSet, GrphEdgeSet
GeometricSupport(C) : Code -> DivCrvElt
Support(u) : AlgFPElt -> [ MonElt ]
Support(a) : AlgGenElt -> SetEnum
Support(a) : AlgGrpElt -> SeqEnum
Support(D) : DivCrvElt -> SeqEnum, SeqEnum
Support(D) : DivFunElt -> [ PlcFunElt ]
Support(D) : DivFunElt -> [ PlcFunElt ], [ RngIntElt ]
Support(D) : DivNumElt -> SeqEnum, SeqEnum
Support(G) : Grph -> SetIndx
Support(G, Y) : GrpPerm, GSet -> { Elt }
Support(g, Y) : GrpPermElt, GSet -> { Elt }
Support(D) : Inc -> { Elt }
Support(B) : IncBlk -> { Elt }
Support(u) : ModTupFldElt -> { RngElt }
Support(u) : ModTupRngElt -> { RngElt }
Support(u) : ModTupRngElt -> { RngElt }
Support(w) : ModTupRngElt -> { RngIntElt }
Support(w) : ModTupRngElt -> { RngIntElt }
Support(A, i) : MtrxSprs, RngIntElt -> [RngIntElt]
Support(P) : Plane -> { Elt }
Support(P, p) : Plane, PlanePt -> .
Support(l) : PlaneLn -> SetEnum
A Pair of Twisted Cubics (SCHEMES)
Operations on the Support (GRAPHS)
The Defining Points of a Plane (FINITE PLANES)
The Support (MATRIX GROUPS)
K3Surface(g,B) : RngIntElt,SeqEnum -> VSrfK3
K3Surface(DB,i) : SeqEnum,RngIntElt -> VSrfK3
K3SurfaceFromAFR(DB,c,n) : SeqEnum,RngIntElt,RngIntElt -> VSrfK3
K3SurfacesFromBasket(DB,B) : SeqEnum,SeqEnum -> SeqEnum
K3SurfacesFromWeights(DB,W) : SeqEnum,SeqEnum -> SeqEnum
KummerSurface(J) : JacHyp -> SrfKum
RuledSurface(k,n) : Rng,RngIntElt -> PrjScrl
RuledSurface(k,n) : Rng,RngIntElt -> PrjScrl
RuledSurface(k,n) : Rng,RngIntElt -> PrjScrl
RuledSurface(k,a,b) : Rng,RngIntElt,RngIntElt -> PrjScrl
K3SurfaceFromBasket(DB,B) : SeqEnum,SeqEnum -> SeqEnum
K3SurfacesFromBasket(DB,B) : SeqEnum,SeqEnum -> SeqEnum
K3SurfacesFromWeights(DB,W) : SeqEnum,SeqEnum -> SeqEnum
EnriquesForm(X) : VSrfK3 -> SeqEnum
NoetherForm(X) : VSrfK3 -> SeqEnum
K3 Surfaces in the Database (THE K3 DATABASE)
Kummer Surfaces (HYPERELLIPTIC CURVES)
IsSurjective(f) : Map -> [ BoolElt ]
IsSurjective(a) : ModMatRngElt -> BoolElt
IsSurjective(f) : MotMatCpxElt -> BoolElt
PSz(arguments)
ProjectiveSuzukiGroup(arguments)
SuzukiGroup(arguments)
GrpMat_Suzuki (Example H21E9)
Suzuki Groups (MATRIX GROUPS)
Sz(arguments)
SuzukiGroup(arguments)
SVPermutation(G, i, a) : GrpPerm, RngIntElt, Elt -> GrpPermElt
SVWord(G, i, a) : GrpPerm, RngIntElt, Elt -> GrpFPElt
SwapColumns(~a, i, j) : AlgMatElt, RngIntElt, RngIntElt ->
SwapColumns(A, i, j) : Mtrx, RngIntElt, RngIntElt -> Mtrx
SwapRows(~a, i, j) : AlgMatElt, RngIntElt, RngIntElt ->
SwapRows(A, i, j) : Mtrx, RngIntElt, RngIntElt -> Mtrx
SwapColumns(~a, i, j) : AlgMatElt, RngIntElt, RngIntElt ->
SwapColumns(A, i, j) : Mtrx, RngIntElt, RngIntElt -> Mtrx
SwapRows(~a, i, j) : AlgMatElt, RngIntElt, RngIntElt ->
SwapRows(A, i, j) : Mtrx, RngIntElt, RngIntElt -> Mtrx
SwinnertonDyerPolynomial(n) : RngIntElt -> RngUPolElt
Swinnerton-Dyer Polynomials (UNIVARIATE POLYNOMIAL RINGS)
Swinnerton-Dyer Polynomials (UNIVARIATE POLYNOMIAL RINGS)
FldAC_SwinnertonDyer (Example H52E2)
SwinnertonDyerPolynomial(n) : RngIntElt -> RngUPolElt
RngPol_SwinnertonDyerPolynomial (Example H42E5)
Switch(u) : GrphVert -> GrphUnd
Switch(S) : { GrphVert } -> Grph
Constructing Complements, Line Graphs; Contraction, Switching (GRAPHS)
Hall pi-Subgroups and Sylow Systems (FINITE SOLUBLE GROUPS)
Sylow(J, p) : JacHyp, RngIntElt) -> GrpAb, Map, Eseq
Sylow(A, p: parameters) : GrpAbGen, RngInt -> GrpAbGen
SylowBasis(G) : GrpPC -> [GrpPC]
SylowSubgroup(G, p) : GrpAb, RngIntElt -> GrpAb
SylowSubgroup(G, p) : GrpFin, RngIntElt -> GrpFin
SylowSubgroup(G, p) : GrpMat, RngIntElt -> GrpMat
SylowSubgroup(G, p) : GrpPC, RngIntElt -> GrpPC
SylowSubgroup(G, p) : GrpPerm, RngIntElt -> GrpPerm
SylowBasis(G) : GrpPC -> [GrpPC]
Sylow(G, p) : GrpAb, RngIntElt -> GrpAb
SylowSubgroup(G, p) : GrpAb, RngIntElt -> GrpAb
SylowSubgroup(G, p) : GrpFin, RngIntElt -> GrpFin
SylowSubgroup(G, p) : GrpMat, RngIntElt -> GrpMat
SylowSubgroup(G, p) : GrpPC, RngIntElt -> GrpPC
SylowSubgroup(G, p) : GrpPerm, RngIntElt -> GrpPerm
SymmetricGroup(GrpPerm, n) : Cat, RngIntElt -> GrpPerm
Sym(GrpPerm, n) : Cat, RngIntElt -> GrpPerm
Sym(n) : RngIntElt -> GrpPerm
Sym(X) : Set -> GrpPerm
SymmetricGroup(C, n) : Cat, RngIntElt -> GrpFin
SymmetricGroup(GrpFP, n) : Cat, RngIntElt -> GrpFP
GrpPerm_Sym (Example H20E1)
RngMPol_Sym_Bi_Linear (Example H43E6)
BiquadraticResidueSymbol(a, b) : RngQuadElt, RngQuadElt -> RngQuadElt
ConvertFromManinSymbol(M, x) : ModSym, Tup -> ModSymElt
DisplayFareySymbolDomain(FS,file) : SymFry, MonStgElt -> SeqEnum
FareySymbol(G) : GrpPSL2 -> SymFry
JacobiSymbol(n, m) : RngIntElt, RngIntElt -> RngIntElt
KodairaSymbol(E, p) : CrvEll, RngIntElt -> SymKod
KodairaSymbol(s) : MonStgElt -> SymKod
KroneckerSymbol(n, m) : RngIntElt, RngIntElt -> RngIntElt
LegendreSymbol(n, m) : RngIntElt, RngIntElt -> RngIntElt
ManinSymbol(x) : ModSymElt -> SeqEnum
NormResidueSymbol(a,b,p) : FldRatElt, FldRatElt, RngIntElt -> RngIntElt
MODULAR SYMBOLS
DeleteSplitCollector(SQP) : SQProc, RngIntElt ->
DeleteNonsplitCollector(SQP) : SQProc, RngIntElt ->
Symbolic Collector (FP GROUPS - ADVANCED FEATURES)
DeleteSplitCollector(SQP) : SQProc, RngIntElt ->
DeleteNonsplitCollector(SQP) : SQProc, RngIntElt ->
Symbolic Collector (FP GROUPS - ADVANCED FEATURES)
Farey Symbols and Fundamental domains (SUBGROUPS OF PSL_2(R))
KodairaSymbols(E) : CrvEll -> [ SymKod ]
ModularSymbols(E) : CurveEll -> ModSym
ModularSymbols(eps, k) : GrpDrchElt, RngIntElt -> ModSym
ModularSymbols(eps, k, sign) : GrpDrchElt, RngIntElt, RngIntElt -> ModSym
ModularSymbols(M) : ModFrm -> SeqEnum
ModularSymbols(M, sign) : ModFrm, RngIntElt -> ModSym
ModularSymbols(M, N') : ModSym, RngIntElt -> ModSym
ModularSymbols(s, sign) : MonStgElt, RngIntElt -> ModSym
ModularSymbols(M : parameters) : ModSS -> ModSym
ModularSymbols(M, sign : parameters) : ModSS, RngIntElt -> ModSym
ModularSymbols(N) : RngIntElt -> ModSym
ModularSymbols(N, k) : RngIntElt, RngIntElt -> ModSym
ModularSymbols(N, k, F) : RngIntElt, RngIntElt, Fld -> ModSym
ModularSymbols(N, k, F, sign) : RngIntElt, RngIntElt, Fld, RngIntElt -> ModSym
ModularSymbols(N, k, sign) : RngIntElt, RngIntElt, RngIntElt -> ModSym
Modular Symbols (MODULAR FORMS)
Modular Symbols (MODULAR SYMBOLS)
ElementarySymmetricPolynomial(P, k) : RngMPol, RngIntElt -> RngMPolElt
ElementarySymmetricPolynomial(P, k) : RngMPol, RngIntElt -> RngMPolElt
IsSymmetric(a) : AlgMatElt -> BoolElt
IsSymmetric(D) : Dsgn -> BoolElt
IsSymmetric(G) : GrphUnd -> BoolElt
IsSymmetric(G) : GrpPerm -> BoolElt
IsSymmetric(A) : Mtrx -> BoolElt
IsSymmetric(f) : RngMPolElt -> BoolElt, RngMPolElt
IsSymmetric(f) : RngMPolElt -> BoolElt, RngMPolElt
NumberOfSymmetricForms(G) : GrpMat -> RngIntElt
ScalarsSymmetricBilinearForm(G) : GrpMat -> SeqEnum
Sym(GrpPerm, n) : Cat, RngIntElt -> GrpPerm
Sym(n) : RngIntElt -> GrpPerm
Sym(X) : Set -> GrpPerm
SymmetricBilinearForm(G) : GrpMat -> AlgMatElt
SymmetricBilinearForm(f) : RngMPolElt -> ModMatRngElt
SymmetricComponents(x, n) : AlgChtrElt, RngIntElt -> SetEnum
SymmetricForms(G) : GrpMat -> [ AlgMatElt ]
SymmetricForms(G, n) : GrpMat, RngIntElt -> [ AlgMatElt ]
SymmetricGroup(C, n) : Cat, RngIntElt -> GrpFin
SymmetricGroup(GrpFP, n) : Cat, RngIntElt -> GrpFP
SymmetricMatrix(R, Q) : Rng, [ RngElt ] -> Mtrx
SymmetricMatrix(Q) : [ RngElt ] -> Mtrx
SymmetricNormalizer(G) : GrpPerm -> GrpPerm
SymmetricSquare(a) : AlgMatElt -> AlgMatElt
SymmetricSquare(L) : Lat -> Lat
SymmetricSquare(M) : ModGrp -> ModGrp
SymmetricWeightEnumerator(C): Code -> RngMPolElt
Construction of Elements (GROUPS)
Creation of a Permutation Group (PERMUTATION GROUPS)
Symmetric Polynomials (IDEAL THEORY AND GRÖBNER BASES)
Symmetric Polynomials (MULTIVARIATE POLYNOMIAL RINGS)
GrpFP_1_Symmetric1 (Example H19E5)
GrpFP_1_Symmetric2 (Example H19E6)
GrpGPC_Symmetric2 (Example H23E5)
SymmetricBilinearForm(G) : GrpMat -> AlgMatElt
SymmetricBilinearForm(f) : RngMPolElt -> ModMatRngElt
SymmetricComponents(x, n) : AlgChtrElt, RngIntElt -> SetEnum
SymmetricForms(G) : GrpMat -> [ AlgMatElt ]
SymmetricForms(G, n) : GrpMat, RngIntElt -> [ AlgMatElt ]
SymmetricGroup(GrpPerm, n) : Cat, RngIntElt -> GrpPerm
Sym(GrpPerm, n) : Cat, RngIntElt -> GrpPerm
Sym(n) : RngIntElt -> GrpPerm
Sym(X) : Set -> GrpPerm
SymmetricGroup(C, n) : Cat, RngIntElt -> GrpFin
SymmetricGroup(GrpFP, n) : Cat, RngIntElt -> GrpFP
SymmetricMatrix(R, Q) : Rng, [ RngElt ] -> Mtrx
SymmetricMatrix(Q) : [ RngElt ] -> Mtrx
SymmetricNormaliser(G) : GrpPerm -> GrpPerm
SymmetricNormalizer(G) : GrpPerm -> GrpPerm
SymmetricNormaliser(G) : GrpPerm -> GrpPerm
SymmetricNormalizer(G) : GrpPerm -> GrpPerm
SymmetricSquare(a) : AlgMatElt -> AlgMatElt
SymmetricSquare(L) : Lat -> Lat
SymmetricSquare(M) : ModGrp -> ModGrp
SymmetricWeightEnumerator(C): Code -> RngMPolElt
Symmetrization(x, p) : AlgChtrElt, [ RngIntElt ] -> AlgChtrElt
Symmetrization (CHARACTERS OF FINITE GROUPS)
Symmetry and Regularity Properties of Graphs (GRAPHS)
Transitivity Properties (FINITE PLANES)
Symmetry and Regularity Properties of Graphs (GRAPHS)
Transitivity Properties (FINITE PLANES)
IsSymplecticGroup(G) : GrpMat -> BoolElt
ProjectiveSigmaSymplecticGroup(arguments)
ProjectiveSymplecticGroup(arguments)
ScalarsSymplecticForm(G) : GrpMat -> SeqEnum
SymplecticComponent(x, p) : AlgChtrElt, [ RngIntElt ] -> AlgChtrElt
SymplecticComponents(x, n) : AlgChtrElt, RngIntElt -> SetEnum
SymplecticForm(G) : GrpMat -> AlgMatElt
SymplecticGroup(arguments)
GrpMat_Symplectic (Example H21E8)
Sp(arguments)
Symplectic Groups (MATRIX GROUPS)
SymplecticComponent(x, p) : AlgChtrElt, [ RngIntElt ] -> AlgChtrElt
SymplecticComponents(x, n) : AlgChtrElt, RngIntElt -> SetEnum
SymplecticForm(G) : GrpMat -> AlgMatElt
Sp(arguments)
SymplecticGroup(arguments)
Syndrome(w, C) : ModTupFldElt, Code -> ModTupFldElt
SyndromeSpace(C) : Code -> ModTupFld
The Syndrome Space (LINEAR CODES OVER FINITE FIELDS)
The Syndrome Space (LINEAR CODES OVER FINITE FIELDS)
SyndromeSpace(C) : Code -> ModTupFld
BlockSystem(G) : GrpMat -> Rec
GetHelpExternalSystem() : -> MonStgElt
ImageSystem(f,S,d) : AmbProjMap,SchProj,RngIntElt -> LinSys
LinearSystem(L,V) : LinSys,ModTupFld -> LinSys
LinearSystem(L,p) : LinSys,Pt -> LinSys
LinearSystem(L,p,m) : LinSys,Pt,RngIntElt -> LinSys
LinearSystem(L,X) : LinSys,Sch -> LinSys
LinearSystem(L,F) : LinSys,SeqEnum -> LinSys
LinearSystem(P,d) : Prj,RngIntElt -> LinSys
LinearSystem(P,F) : Prj,SeqEnum -> LinSys
LinearSystemTrace(L,X) : LinearSys,Sch -> LinearSys
RootSystem(L) : AlgLie -> [ AlgLieElt ], [ AlgLieElt ], [ AlgLieElt ], AlgMatElt
RootSystemMatrix(t, n) : MonStgElt, RngIntElt -> AlgMatElt
SchreierSystem(G, H) : GrpFP, GrpFP -> {@ GrpFPElt @}, Map
SetHelpExternalSystem(s) : MonStgElt ->
SetHelpUseExternalSystem(b) : BoolElt ->
System(c)
SystemNormalizer(G) : GrpPC -> GrpPC
SystemOfEigenvalues(M, prec) : ModSym, RngIntElt -> SeqEnum
GROUPS DEFINED BY REWRITE SYSTEMS
Memory Usage (INPUT AND OUTPUT)
MONOIDS GIVEN BY REWRITE SYSTEMS
Predefined System Attributes (FUNCTIONS, PROCEDURES AND PACKAGES)
Root Systems (LIE ALGEBRAS)
System Calls (INPUT AND OUTPUT)
System Features (OVERVIEW)
Memory Usage (INPUT AND OUTPUT)
System Calls (INPUT AND OUTPUT)
MAGMA_SYSTEM_SPEC
Func_SystemAttributes (Example H2E11)
SystemNormaliser(G) : GrpPC -> GrpPC
SystemNormalizer(G) : GrpPC -> GrpPC
SystemNormaliser(G) : GrpPC -> GrpPC
SystemNormalizer(G) : GrpPC -> GrpPC
SystemOfEigenvalues(M, prec) : ModSym, RngIntElt -> SeqEnum
Root Systems (REFLECTION GROUPS)
InjectiveSyzygyModule(M, n) : ModAlg, RngIntElt -> ModAlg
MinimalSyzygyModule(M) : ModMPol -> [ ModMPolElt ]
SyzygyMatrix(Q) : [ RngMPolElt ] -> ModMatRngElt
SyzygyModule(M, n) : ModAlg, RngIntElt -> ModAlg
SyzygyModule(M) : ModMPol -> [ ModMPolElt ]
SyzygyModule(Q) : [ RngMPolElt ] -> ModTupRng
Syzygy Modules (IDEAL THEORY AND GRÖBNER BASES)
Syzygy Modules (MODULES OVER AFFINE ALGEBRAS)
Syzygy Modules (IDEAL THEORY AND GRÖBNER BASES)
SyzygyMatrix(Q) : [ RngMPolElt ] -> ModMatRngElt
SyzygyModule(M, n) : ModAlg, RngIntElt -> ModAlg
SyzygyModule(M) : ModMPol -> [ ModMPolElt ]
SyzygyModule(Q) : [ RngMPolElt ] -> ModTupRng
GB_SyzygyModule (Example H66E24)
Sz(arguments)
SuzukiGroup(arguments)
[____] [____] [_____] [____] [__] [Index] [Root]