Index S

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

Index S

S

S-algebras (FINITELY PRESENTED ALGEBRAS)

S-algebra

S-algebras (FINITELY PRESENTED ALGEBRAS)

S-key

s-key

SchreierSystem

Transversal(G, H) : GrpFP, GrpFP -> {@ GrpFPElt @}, Map
SchreierSystem(G, H) : GrpFP, GrpFP -> {@ GrpFPElt @}, Map

SchreierVector

SchreierVector(G, i) : GrpPerm, RngIntElt -> [RngIntElt]

SchreierVectors

SchreierVectors(G) : GrpPerm -> [ [RngIntElt] ]

Schur

Schur(x, k) : AlgChtrElt, RngIntElt -> FldCycElt

SClass

SClassGroup(S) : SetEnum[PlcFunElt] -> GrpAb, Map
SClassGroupAbelianInvariants(S) : SetEnum[PlcFunElt] -> SeqEnum
SClassGroupExactSequence(S) : SetEnum[PlcFunElt] -> Map, Map, Map
SClassNumber(S) : SetEnum[PlcFunElt] -> RngIntElt

SClassGroup

SClassGroup(S) : SetEnum[PlcFunElt] -> GrpAb, Map

SClassGroupAbelianInvariants

SClassGroupAbelianInvariants(S) : SetEnum[PlcFunElt] -> SeqEnum

SClassGroupExactSequence

SClassGroupExactSequence(S) : SetEnum[PlcFunElt] -> Map, Map, Map

SClassNumber

SClassNumber(S) : SetEnum[PlcFunElt] -> RngIntElt

scope

Scope (MAGMA SEMANTICS)

Scroll

AbsoluteRationalScroll(k,N) : Rng,SeqEnum -> PrjScrl

scroll-map-base-points

Scheme_scroll-map-base-points (Example H81E19)

scrolls

Scrolls and Products (SCHEMES)

sdiff

R sdiff S : SetEnum, SetEnum -> SetEnum

SEA

SEA(H: parameters) : SetPtEll -> RngIntElt
CrvEll_SEA (Example H85E26)

Search

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

SearchEqual(~P: parameters) : Process(Tietze) ->

SearchForDecomposition

SearchForDecomposition(G, S) : GrpMat, [GrpMatElt] -> BoolElt

searching

Searching the Database (THE K3 DATABASE)
Searching with predicates (DATABASES OF GROUPS)

Sec

Sec(c) : FldComElt -> FldComElt
Sec(f) : RngSerElt -> RngSerElt

Secants

AllSecants(P, A) : Plane, { PlanePt } -> { PlaneLn }

Sech

Sech(s) : FldPrElt -> FldPrElt

Second

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

second-affine-patch

Crv_second-affine-patch (Example H82E8)

Secondary

IrreducibleSecondaryInvariants(R) : RngInvar -> [ RngMPolElt ]
R`SecondaryInvariants
SecondaryInvariants(R) : RngInvar -> [ RngMPolElt ]
SecondaryInvariants(R, H) : RngInvar, Grp -> [ RngMPolElt ]

secondary

Secondary Invariants (INVARIANT RINGS OF FINITE GROUPS)

SecondaryInvariants

R`SecondaryInvariants
SecondaryInvariants(R) : RngInvar -> [ RngMPolElt ]
SecondaryInvariants(R, H) : RngInvar, Grp -> [ RngMPolElt ]
RngInvar_SecondaryInvariants (Example H78E7)

Section

AbelianSection(SQP: parameter) : SQProc -> BoolElt, SQProc
ElementaryAbelianSection(SQP: parameter) : SQProc -> BoolElt, SQProc
NonsplitSection(SQP: parameter) : SQProc -> BoolElt, SQProc
NonsplitElementaryAbelianSection(SQP: parameter) : SQProc -> BoolElt, SQProc
PGroupSection(SQP, p: parameter) : SQProc, RngIntElt -> 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

section

Action on an Elementary Abelian Section (MODULES OVER A MATRIX ALGEBRA)

section-actions

Action on an Elementary Abelian Section (MODULES OVER A MATRIX ALGEBRA)

SectionCentraliser

SectionCentralizer(G, H, K) : GrpPerm, GrpPerm, GrpPerm -> GrpPerm
SectionCentraliser(G, H, K) : GrpPerm, GrpPerm, GrpPerm -> GrpPerm

SectionCentralizer

SectionCentralizer(G, H, K) : GrpPerm, GrpPerm, GrpPerm -> GrpPerm
SectionCentraliser(G, H, K) : GrpPerm, GrpPerm, GrpPerm -> GrpPerm

Sections

Sections(L) : LinSys -> SeqEnum

sections

Calculation of Standard Sections (FP GROUPS - ADVANCED FEATURES)

Seed

GetSeed() : -> RngIntElt, RngIntElt
SetSeed(s, c) : RngIntElt ->
SetSeed(s, c) : RngIntElt ->
SetSeed(s, c) : RngIntElt ->

Seek

Seek(F, o, p) : File, RngIntElt, RngIntElt ->

select

Expression (OVERVIEW)
The select expression (OVERVIEW)

Self

IsSelfOrthogonal(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) : GrpPC, GrpPC -> BoolElt
IsSelfNormalizing(G, H) : GrpPerm, GrpPerm -> BoolElt
IsSelfNormalizing(G, H) : GrpFP, GrpFP -> BoolElt
IsWeaklySelfDual(C) : Code -> BoolElt
IsWeaklySelfDual(C) : Code -> BoolElt
Self(n) : RngIntElt -> Elt
SelfIntersections(g) : GrphRes -> SeqEnum
Seq_Self (Example H8E5)

SelfDual

CodeFld_SelfDual (Example H97E17)

SelfDualZ4

CodeRng_SelfDualZ4 (Example H98E7)

Selfintersection

ModifySelfintersection(~v,n) : GrphResVert,RngIntElt ->

SelfIntersections

SelfIntersections(g) : GrphRes -> SeqEnum

Selmer

TwoSelmerGroupData(J: parameters) : JacHyp -> RngIntElt, RngIntElt, Tup, List

selmer

The 2-Selmer Group (HYPERELLIPTIC CURVES)

semantics

MAGMA SEMANTICS

Semi

IsNegativeSemiDefinite(F) : ModMatRngElt -> BoolElt
IsPositiveSemiDefinite(F) : ModMatRngElt -> BoolElt
IsSemiLinear(G) : GrpMat -> BoolElt
SemiLinearGroup(G, S) : GrpMat, FldFin -> GrpMat
SemiSimpleType(L) : AlgLie -> AlgLie

Semigroup

FreeSemigroup(n) : RngIntElt -> SgpFP
Semigroup< generators | relations > : SgpFPElt, ..., SgpFPElt, Rel, ...Rel -> SgpFP

semigroup

Semigroups (OVERVIEW)

semigroups

Semigroups (OVERVIEW)

SemiLinearGroup

SemiLinearGroup(G, S) : GrpMat, FldFin -> GrpMat

Semilinearity

GrpMat_Semilinearity (Example H21E32)

semilinearity

Semilinearity (MATRIX GROUPS)

Semiregular

IsSemiregular(G, Y) : GrpPerm, GSet -> BoolElt
IsSemiregular(G, Y, S) : GrpPerm, GSet, SetEnum -> BoolElt

Semisimple

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

semisimple

The Type of a Semisimple Lie Algebra (LIE ALGEBRAS)

semisimple-type

The Type of a Semisimple Lie Algebra (LIE ALGEBRAS)

SemisimpleEFAModuleMaps

SemisimpleEFAModuleMaps(G) : GrpGPC -> [ModGrp]

SemisimpleEFAModules

SemisimpleEFAModules(G) : GrpGPC -> [ModGrp]

SemisimpleEFASeries

SemisimpleEFASeries(G) : GrpGPC -> [GrpGPC]

SemisimpleRank

SemisimpleRank( G ) : GrpLie -> RngIntElt

SemiSimpleType

SemiSimpleType(L) : AlgLie -> AlgLie
AlgLie_SemiSimpleType (Example H75E8)

Separable

IsMDS(C) : Code -> BoolElt
IsMaximumDistanceSeparable(C) : Code -> BoolElt
IsSeparable(G) : Grph -> BoolElt
IsSeparable(f) : RngUPolElt -> BoolElt

Separating

IsSeparating(x) : FldFunGElt -> BoolElt
SeparatingElement(F) : FldFunG -> FldFunGElt

SeparatingElement

SeparatingElement(F) : FldFunG -> FldFunGElt

Seq

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

Seqelt(s, F) : [ FldFinElt ] -> FldFinElt
SequenceToElement(s, F) : [ FldFinElt ] -> FldFinElt

SeqEnum

Sequences (OVERVIEW)

SeqFact

SequenceToFactorization(s) : SeqEnum -> RngIntEltFact
SeqFact(s) : SeqEnum -> RngIntEltFact

Seqint

Seqint(s, b) : [RngIntElt], RngIntElt -> RngIntElt
SequenceToInteger(s, b) : [RngIntElt], RngIntElt -> RngIntElt

Seqlist

Seqlist(Q) : SeqEnum -> List
SequenceToList(Q) : SeqEnum -> List

Seqset

SequenceToSet(S) : SeqEnum -> SetEnum
Seqset(S) : SeqEnum -> SetEnum

Sequence

sequence

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 (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)

Sequences

LongestIncreasingSequences(w, k) : SeqEnum,RngIntElt -> RngIntElt

sequences

PSEUDO-RANDOM BIT SEQUENCES

SequenceToElement

Seqelt(s, F) : [ FldFinElt ] -> FldFinElt
SequenceToElement(s, F) : [ FldFinElt ] -> FldFinElt

SequenceToFactorization

SequenceToFactorization(s) : SeqEnum -> RngIntEltFact
SeqFact(s) : SeqEnum -> RngIntEltFact

SequenceToInteger

Seqint(s, b) : [RngIntElt], RngIntElt -> RngIntElt
SequenceToInteger(s, b) : [RngIntElt], RngIntElt -> RngIntElt

SequenceToList

Seqlist(Q) : SeqEnum -> List
SequenceToList(Q) : SeqEnum -> List

SequenceToMultiset

SequenceToMultiset(Q) : SeqEnum -> SetMulti

SequenceToSet

SequenceToSet(S) : SeqEnum -> SetEnum
Seqset(S) : SeqEnum -> SetEnum

Series

series

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)

series-power-Laurent

POWER, LAURENT AND PUISEUX SERIES

series-print

RngLoc_series-print (Example H59E2)
RngPad_series-print (Example H42E1)

Serre

SerreBound(F) : FldFun -> RngIntElt

SerreBound

SerreBound(F) : FldFun -> RngIntElt

Set

set

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 WHOSE ELEMENTS ARE 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)

Set-Get

GetViMode() : -> BoolElt
Set and Get (ENVIRONMENT AND OPTIONS)

set-ops

Set Operations (FINITE SOLUBLE GROUPS)

set_ops

GrpPC_set_ops (Example H25E10)

SetAFR

SetAFR(~DB) : SeqEnum ->

SetAllInvariantsOfDegree

SetAllInvariantsOfDegree(R, d, Q) : RngInvar, RngIntElt, [ RngMPolElt ] ->

SetAssertions

GetAssertions() : -> BoolElt
SetAssertions(b) : BoolElt ->

SetAttribute

SetAttribute(A, s, v) : GrpAuto, MonStgElt, . ->
HasAttribute(A, s) : GrpAuto, MonStgElt -> BoolElt, .

SetAutoColumns

GetAutoColumns() : -> BoolElt
SetAutoColumns(b) : BoolElt ->

SetAutoCompact

GetAutoCompact() : -> BoolElt
SetAutoCompact(b) : BoolElt ->

SetBeep

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

SetBufferSize

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

SetColumns

GetColumns() : -> RngIntElt
SetColumns(n) : RngIntElt ->

SetDefaultRealField

SetDefaultRealField(R) : FldRe ->

SetDisplayLevel

SetDisplayLevel(~P, Level) : Process(pQuot), RngIntElt ->

SetEchoInput

SetEchoInput(b) : BoolElt ->
SetEchoInput(b) : BoolElt ->

SetEnum

Sets (OVERVIEW)

SetExtraspecialSigns

SetExtraspecialSigns( RD, s ) : RootDtm, . ->

SetFormal

Sets (OVERVIEW)

SetGlobalTCParameters

SetGlobalTCParameters(: parameters) : ->

SetHeckeBound

SetHeckeBound(M, n) : ModSym, RngIntElt -> RngIntElt

SetHelpExternalBrowser

SetHelpExternalBrowser(S, T) : MonStgElt, MonStgElt ->

SetHelpExternalSystem

SetHelpExternalSystem(s) : MonStgElt ->

SetHelpUseExternalBrowser

SetHelpUseExternalBrowser(b) : BoolElt ->

SetHelpUseExternalSystem

SetHelpUseExternalSystem(b) : BoolElt ->

SetHistorySize

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

SetIgnorePrompt

GetIgnorePrompt() : -> BoolElt
SetIgnorePrompt(b) : BoolElt ->

SetIgnoreSpaces

GetIgnoreSpaces() : -> BoolElt
SetIgnoreSpaces(b) : BoolElt ->

SetIndent

GetIndent() : -> RngIntElt
SetIndent(n) : RngIntElt ->

SetIndx

Sets (OVERVIEW)

SetIntegerSolutionVariables

SetIntegerSolutionVariables(L, I, m) : LP, SeqEnum[RngIntElt], BoolElt ->

SetKantPrecision

SetKantPrecision(O, n) : RngOrd, RngIntElt ->

SetKantPrinting

SetKantPrinting(f) : BoolElt -> BoolElt

SetLibraries

GetLibraries() : -> MonStgElt
SetLibraries(s) : MonStgElt ->

SetLibraryRoot

GetLibraryRoot() : -> MonStgElt
SetLibraryRoot(s) : MonStgElt ->

SetLineEditor

GetLineEditor() : BoolElt ->
SetLineEditor(b) : BoolElt ->

SetLogFile

SetLogFile(F) : MonStgElt ->
SetLogFile(F) : MonStgElt ->

SetLowerBound

SetLowerBound(L, n, b) : LP, RngIntElt, RngElt ->

SetMaximiseFunction

SetMaximiseFunction(L, m) : LP, BoolElt ->

SetMemoryLimit

GetMemoryLimit() : -> RngIntElt
SetMemoryLimit(n) : RngIntElt ->

SetNormalising

SetNormalizing( G, Normalising ) : GrpLie, BoolElt -> .
SetNormalising( G, Normalising ) : GrpLie, BoolElt -> .

SetNormalizing

SetNormalizing( G, Normalising ) : GrpLie, BoolElt -> .
SetNormalising( G, Normalising ) : GrpLie, BoolElt -> .

SetObjectiveFunction

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

SetOperations

GrpPerm_SetOperations (Example H20E10)
Grp_SetOperations (Example H19E13)

SetOptions

SetOptions(~P : parameters) : Process(Tietze) ->

SetOrderMaximal

SetOrderMaximal(O, b) : RngOrd, BoolElt ->

SetOrderTorsionUnit

SetOrderTorsionUnit(O, e, r) : RngOrd, RngOrdElt, RngIntElt ->

SetOrderUnitsAreFundamental

SetOrderUnitsAreFundamental(O) : RngOrd ->

SetOutputFile

UnsetOutputFile() : ->
SetOutputFile(F) : MonStgElt ->
SetOutputFile(F) : MonStgElt ->

SetPath

GetPath() : -> MonStgElt
SetPath(s) : MonStgElt ->

SetPowerPrinting

AssertAttribute(F, "PowerPrinting", l) : FldFin, MonStgElt, BoolElt ->
SetPowerPrinting(F, l) : FldFin, BoolElt ->

SetPrecision

SetPrecision(M, prec) : ModFrm, RngIntElt ->

SetPreviousSize

SetPreviousSize(n) : RngIntElt ->

SetPrimitiveElement

SetPrimitiveElement(F, x) : FldFin, FldFinElt ->

SetPrintLevel

GetPrintLevel() : -> MonStgElt
SetPrintLevel(l) : MonStgElt ->

SetProcessParameters

SetProcessParameters(~P: parameters) : GrpFPCosetEnumProc ->

SetPrompt

GetPrompt() : -> MonStgElt
SetPrompt(s) : MonStgElt ->

SetQuitOnError

SetQuitOnError(b) : BoolElt ->

SetRows

GetRows() : -> RngIntElt
SetRows(n) : RngIntElt ->

Sets

AllInformationSets(C) : Code -> [ [ RngIntElt ] ]

sets

G-Sets (PERMUTATION GROUPS)
Places (PLANE ALGEBRAIC CURVES)
Sets (OVERVIEW)
Sets of Places (PLANE ALGEBRAIC CURVES)

SetSeed

SetSeed(s, c) : RngIntElt ->
SetSeed(s, c) : RngIntElt ->

Setseq

SetToSequence(S) : SetEnum -> SeqEnum
Setseq(S) : SetEnum -> SeqEnum

setting

Setting Properties of Orders (ORDERS AND ALGEBRAIC FIELDS)

SetToIndexedSet

SetToIndexedSet(E) : SetEnum -> SetIndx

SetToMultiset

SetToMultiset(E) : SetEnum -> SetMulti

SetToSequence

SetToSequence(S) : SetEnum -> SeqEnum
Setseq(S) : SetEnum -> SeqEnum

SetTraceback

GetTraceback() : -> BoolElt
SetTraceback(n) : BoolElt ->

SetUpperBound

SetUpperBound(L, n, b) : LP, RngIntElt, RngElt ->

SetVerbose

SetViMode

GetViMode() : -> BoolElt
SetViMode(b) : BoolElt ->

Seysen

Seysen(L) : Lat -> Lat, AlgMatElt
Seysen(X) : ModMatRngElt -> ModMatRngElt, AlgMatElt
SeysenGram(F) : ModMatRngElt -> ModMatRngElt, AlgMatElt, RngIntElt
Lat_Seysen (Example H66E13)

seysen

Seysen Reduction (LATTICES)

SeysenGram

SeysenGram(F) : ModMatRngElt -> ModMatRngElt, AlgMatElt, RngIntElt

sg-process

GrpData_sg-process (Example H34E12)
GrpData_sg-process (Example H34E2)

sgdb

Database of Almost-Simple Groups (DATABASES OF GROUPS)
GrpData_sgdb (Example H34E10)

SgpFP

Semigroups (OVERVIEW)

Shape

OuterShape(t) : Tableau -> SeqEnum
Shape(t) : Tableau -> SeqEnum
SkewShape(t) : Tableau -> SeqEnum

Sharply

IsSharplyTransitive(G, Y, k) : GrpPerm, GSet, RngIntElt -> BoolElt

shell

Performing shell commands from Magma (OVERVIEW)

shell-escape

Performing shell commands from Magma (OVERVIEW)

Shephard

ShephardTodd(n) : RngIntElt -> GrpMat, Fld

ShephardTodd

ShephardTodd(n) : RngIntElt -> GrpMat, Fld

Shift

Shift(C, n) : ModCpx, RngIntElt -> ModCpx
ShiftToDegreeZero(C) : ModCpx -> ModCpx

ShiftToDegreeZero

ShiftToDegreeZero(C) : ModCpx -> ModCpx

Short

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

Short and Close Vectors (LATTICES)

short-close

Short and Close Vectors (LATTICES)

ShortBasis

ShortBasis(D : parameters) : DivFunElt -> [RngElt], [RngIntElt]

ShortCuts

Mat_ShortCuts (Example H62E2)

Shortcuts

Mat_Shortcuts (Example H62E3)

shortcuts

Shortcuts (MATRICES)

Shorten

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

ShortenCode(C, i) : Code, RngIntElt -> Code
ShortenCode(C, i) : Code, RngIntElt -> Code
ShortenCode(C, S) : Code, { RngIntElt } -> Code
ShortenCode(C, S) : Code, { RngIntElt } -> Code

Shortest

ShortestVectors(L) : Lat -> [ LatElt ], RngElt
ShortestVectorsMatrix(L) : Lat -> ModMatRngElt

shortest

Shortest and Closest Vectors (LATTICES)

shortest-closest

Shortest and Closest Vectors (LATTICES)

ShortestVectors

ShortestVectors(L) : Lat -> [ LatElt ], RngElt

ShortestVectorsMatrix

ShortestVectorsMatrix(L) : Lat -> ModMatRngElt

ShortVectors

ShortVectors(L, u) : Lat, RngElt -> [ <LatElt, RngElt> ]

ShortVectorsMatrix

ShortVectorsMatrix(L, u) : Lat, RngElt -> ModMatRngElt

ShortVectorsProcess

ShortVectorsProcess(L, u) : Lat, RngElt -> LatEnumProc

Show

ShowIdentifiers() : ->
ShowMemoryUsage() : ->
ShowOptions(~P : parameters) : Process(Tietze) ->
ShowPrevious() : ->
ShowPrevious(i) : RngIntElt ->
ShowValues() : ->

ShowIdentifiers

ShowIdentifiers() : ->

ShowMemoryUsage

ShowMemoryUsage() : ->

ShowOptions

ShowOptions(~P : parameters) : Process(Tietze) ->

ShowPrevious

ShowPrevious() : ->
ShowPrevious(i) : RngIntElt ->

ShowValues

ShowValues() : ->

Shrikhande

ShrikhandeGraph() : -> GrphUnd
GewirtzGraph() : -> GrphUnd
ClebschGraph() : -> GrphUnd

ShrikhandeGraph

ShrikhandeGraph() : -> GrphUnd
GewirtzGraph() : -> GrphUnd
ClebschGraph() : -> GrphUnd

Shrinking

ShrinkingGenerator(C1, S1, C2, S2, t) : RngUPolElt, SeqEnum, RngUPolElt,SeqEnum, RngIntElt -> SeqEnum

ShrinkingGenerator

ShrinkingGenerator(C1, S1, C2, S2, t) : RngUPolElt, SeqEnum, RngUPolElt,SeqEnum, RngIntElt -> SeqEnum

Shub

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

Side

RootSide(v) : GrphVert -> GrphVert

Sided

TwoSidedIdealClasses(S) : AlgQuatOrd -> [AlgQuatOrd]

Sieve

PolynomialSieve( T ) : Tup -> SeqEnum

Sigma

ASigmaL(arguments)
AffineSigmaLinearGroup(arguments)
DivisorSigma(i, n) : RngIntElt, RngIntElt -> RngIntElt
ProjectiveSigmaLinearGroup(arguments)
ProjectiveSigmaSymplecticGroup(arguments)
ProjectiveSigmaUnitaryGroup(arguments)

Sign

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

sign

Absolute Value and Sign (RATIONAL FIELD)

Signature

Signature(Q) : FldRat -> RngIntElt, RngIntElt
Signature(Z) : RngInt -> RngIntElt, RngIntElt
Signature(O) : RngOrd -> RngIntElt, RngIntElt

signature

Signature (OVERVIEW)

Signatures

ListSignatures(C) : Cat ->

SignDecomposition

SignDecomposition(D) : DivCrvElt -> DivElt,DivElt

Signs

SetExtraspecialSigns( RD, s ) : RootDtm, . ->

Silverman

SilvermanBound(H) : SetPtEll -> FldPrElt

SilvermanBound

SilvermanBound(H) : SetPtEll -> FldPrElt

simgps

Database of Simple Groups: Permutations, Presentations, Conjugacy Classes, Maximal Subgroups and Sylow Subgroups (OVERVIEW)

Similar

IsSimilar(A, B) : AlgMatElt, AlgMatElt -> BoolElt, AlgMatElt
IsSimilar(a, b) : AlgMatElt, AlgMatElt -> BoolElt, AlgMatElt

Simple

simple

Construction of Simple 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

Simple Assignment (STATEMENTS AND EXPRESSIONS)

SimpleCodeChain

CodeFld_SimpleCodeChain (Example H97E4)

SimpleCohomologyDimensions

SimpleCohomologyDimensions(M) : ModAlg -> SeqEnum

SimpleCoreflectionMatrices

SimpleCoreflectionMatrices( RD ) : RootDtm -> []
SimpleReflectionMatrices( RD ) : RootDtm -> []

SimpleCoroots

SimpleCoroots( W ) : GrpCox -> Mtrx
SimpleRoots( W ) : GrpCox -> Mtrx
SimpleRoots( RD ) : RootDtm -> Mtrx

SimpleExtension

SimpleExtension(F) : FldAlg -> FldAlg

SimpleHomologyDimensions

SimpleHomologyDimensions(M) : ModAlg -> SeqEnum

SimpleLieAlgebra

SimpleLieAlgebra(X, n, F) : MonStgElt, RngIntElt, Fld -> AlgLie
AlgLie_SimpleLieAlgebra (Example H75E1)

SimpleModule

SimpleModule(B, i) : AlgBas, RngIntElt -> ModAlg
IrreducibleModule(B, i) : AlgBas, RngIntElt -> ModAlg

SimpleReflectionMatrices

SimpleCoreflectionMatrices( RD ) : RootDtm -> []
SimpleReflectionMatrices( RD ) : RootDtm -> []

SimpleReflectionPermutations

SimpleReflectionPermutations( RD ) : RootDtm -> []

SimpleRoots

SimpleCoroots( W ) : GrpCox -> Mtrx
SimpleRoots( W ) : GrpCox -> Mtrx
SimpleRoots( RD ) : RootDtm -> Mtrx

SimpleSubgroups

SimpleSubgroups(G: parameters) : GrpFin -> [ rec< Grp, RngIntElt, RngIntElt, GrpFP> ]
SimpleSubgroups(G: parameters) : GrpPerm -> [ rec< GrpPerm, RngIntElt, RngIntElt, GrpFP> ]

Simplex

Simplex(A) : Prj -> SeqEnum
SimplexCode(r) : RngIntElt -> Code
TranslationOfSimplex(P,Q) : Prj, [Pt] -> MapSch

SimplexCode

SimplexCode(r) : RngIntElt -> Code

simplification

Simplification (FINITELY PRESENTED GROUPS)

Simplified

IsSimplifiedModel(E) : CrvEll -> BoolElt
SimplifiedModel(E): CrvEll -> CrvEll, Map, Map
SimplifiedModel(C) : CrvHyp -> CrvHyp, MapCrvHyp

SimplifiedModel

SimplifiedModel(E): CrvEll -> CrvEll, Map, Map
SimplifiedModel(C) : CrvHyp -> CrvHyp, MapCrvHyp

Simplify

Simplify(A) : FldAC ->
Simplify(D) : Inc -> Inc
Simplify(~P : parameters) : Process(Tietze) ->
Simplify(O) : RngOrd -> RngOrd
Simplify(G: parameters) : GrpFP -> GrpFP
SimplifyLength(~P : parameters) : Process(Tietze) ->
SimplifyLength(G: parameters) : GrpFP -> GrpFP

simplify

Simplification (ALGEBRAICALLY CLOSED FIELDS)

Simplify1

GrpFP_1_Simplify1 (Example H22E54)

SimplifyLength

SimplifyLength(~P : parameters) : Process(Tietze) ->
SimplifyLength(G: parameters) : GrpFP -> GrpFP

SimplifyPresentation

SimplifyPresentation(~P : parameters) : Process(Tietze) ->
Simplify(~P : parameters) : Process(Tietze) ->

Simply

IsSimplyConnected( G ) : GrpLie-> BoolElt
IsSimplyConnected( RD ) : RootDtm-> BoolElt
IsSimplyLaced( G ) : GrpLie-> BoolElt
IsSimplyLaced( RD ) : RootDtm-> BoolElt

Simpson

SimpsonQuadrature(f, a, b, n) : Program, FldPrElt, FldPrElt, RngIntElt -> FldPrElt

SimpsonQuadrature

SimpsonQuadrature(f, a, b, n) : Program, FldPrElt, FldPrElt, RngIntElt -> FldPrElt

Sims

SimsSchreier(G: parameters) : GrpPerm : ->

SimsSchreier

SimsSchreier(G: parameters) : GrpPerm : ->

Sin

Sin(c) : FldComElt -> FldComElt
Sin(f) : RngSerElt -> RngSerElt
Sin(f) : RngSerElt -> RngSerElt

since

Release Notes V1.20-1 (8 January 1996) since June 1995 (OVERVIEW)

Sincos

Sincos(s) : FldPrElt -> FldPrElt, FldPrElt
Sincos(f) : RngSerElt -> RngSerElt
Sincos(f) : RngSerElt -> RngSerElt

sing

Singularity Analysis (PLANE ALGEBRAIC CURVES)

sing-test

Singularity Analysis (PLANE ALGEBRAIC CURVES)

Singer

SingerDifferenceSet(n, q) : RngIntElt, RngIntElt -> { RngIntResElt }

SingerDifferenceSet

SingerDifferenceSet(n, q) : RngIntElt, RngIntElt -> { RngIntResElt }

Single

IsSinglePrecision(n) : RngIntElt -> BoolElt

single

The `single use' Rule (MAGMA SEMANTICS)

single-use

The `single use' Rule (MAGMA SEMANTICS)

Singleton

SingletonAsymptoticBound(delta) : FldPrElt -> FldPrElt
SingletonBound(K, n, d) : FldFin, RngIntElt, RngIntElt -> RngIntElt

SingletonAsymptoticBound

SingletonAsymptoticBound(delta) : FldPrElt -> FldPrElt

SingletonBound

SingletonBound(K, n, d) : FldFin, RngIntElt, RngIntElt -> RngIntElt

Singular

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 -> SeqEnum
SingularSubscheme(X) : Sch -> Sch

SingularElements

Lat_SingularElements (Example H66E9)

Singularity

IsOrdinarySingularity(p) : Sch,Pt -> BoolElt
IsOrdinarySingularity(p) : Sch,Pt -> BoolElt

singularity

GrphRes_singularity (Example H83E1)

SingularPoints

SingularPoints(C) : Sch -> SeqEnum

SingularSubscheme

SingularSubscheme(X) : Sch -> Sch

Sinh

Sinh(s) : FldPrElt -> FldPrElt
Sinh(f) : RngSerElt -> RngSerElt
Sinh(f) : RngSerElt -> RngSerElt

SIntegral

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 ]

sintegral

S-integral Points (ELLIPTIC CURVES)

SIntegralDesbovesPoints

SIntegralDesbovesPoints(Q, S) : [ RngIntElt ], [ RngIntElt ] -> [ SeqEnum ]

SIntegralLjunggrenPoints

SIntegralLjunggrenPoints(Q, S) : [ RngIntElt ], [ RngIntElt ] -> [ SeqEnum ]

SIntegralPoints

SIntegralPoints(E, S) : CrvEll, SeqEnum -> [ PtEll ], [ Tup ]
CrvEll_SIntegralPoints (Example H85E22)

SIntegralQuarticPoints

SIntegralQuarticPoints(Q, S) : [ RngIntElt ], [ RngIntElt ] -> [ SeqEnum ]

Size

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

size

Groups (OVERVIEW)
Rings, Fields, and Algebras (OVERVIEW)
Sets (OVERVIEW)

Sizes

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

Skew

ColumnSkewLength(t, j) : Tableau,RngIntElt -> RngIntElt
IsLittleWoodRichardsonSkew(t) : Tableau -> BoolElt
IsSkew(t) : Tableau -> BoolElt
NumberOfSkewRows(t) : Tableau -> RngIntElt
RowSkewLength(t, i) : Tableau,RngIntElt -> RngIntElt
SkewShape(t) : Tableau -> SeqEnum
SkewWeight(t) : Tableau -> RngIntElt

Skewness

OptimalSkewness(F) : RngMPolElt -> FldReElt, FldReElt

SkewShape

SkewShape(t) : Tableau -> SeqEnum

SkewWeight

SkewWeight(t) : Tableau -> RngIntElt

SL

SL(arguments)
SpecialLinearGroup(arguments)

Slope

Slope(l) : PlaneLn -> FldFinElt

SLPGroup

SLPGroup(n) : RngIntElt -> GrpSLP
GrpSLP_SLPGroup (Example H32E1)

Small

Smaller

IsOverSmallerField(G) : GrpMat -> BoolElt, GrpMat
IsOverSmallerField(G, d) : GrpMat, RngIntElt -> BoolElt, GrpMat
WriteOverSmallerField(G, F) : GrpMat, FldFin -> GrpMat, Map

smaller

Comparison (OVERVIEW)

SmallGroup

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

SmallGroupDatabase

SmallGroupDatabase() : -> DB

SmallGroupDatabaseLimit

SmallGroupDatabaseLimit() : -> RngIntElt

SmallGroupIsInsoluble

SmallGroupIsInsoluble(o, n) : RngIntElt, RngIntElt -> Grp

SmallGroupIsSoluble

SmallGroupIsSoluble(o, n) : RngIntElt, RngIntElt -> Grp

SmallGroupProcess

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

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 H34E1)

SmallIdentify

GrpData_SmallIdentify (Example H34E3)

Smith

SmithForm(a) : AlgMatElt -> AlgMatElt, AlgMatElt, AlgMatElt
SmithForm(A) : ModMatRngElt -> ModMatRngElt, ModMatRngElt, ModMatRngElt

SmithForm

SmithForm(a) : AlgMatElt -> AlgMatElt, AlgMatElt, AlgMatElt
SmithForm(A) : ModMatRngElt -> ModMatRngElt, ModMatRngElt, ModMatRngElt

smlgps

The Database of Groups of Order up to 1000 (DATABASES OF GROUPS)

smlgps-database

The Database of Groups of Order up to 1000 (DATABASES OF GROUPS)

Smooth

NumberOfSmoothDivisors(n, m, P) : RngIntElt, RngIntElt, SeqEnum[RngElt] -> RngElt

SO

SO(arguments)
SpecialOrthogonalGroup(arguments)

Socle

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

Socle Series (MODULES OVER A MATRIX ALGEBRA)
The Socle (PERMUTATION GROUPS)

SocleAction

SocleAction(G) : GrpPerm -> Hom, GrpPerm, GrpPerm

SocleFactor

SocleFactor(G) : GrpPerm -> GrpPerm

SocleFactors

SocleFactors(G) : GrpPerm -> [ GrpPerm ]
SocleFactors(M) : ModRng -> [ ModRng ]

SocleImage

SocleImage(G) : GrpPerm -> GrpPerm

SocleKernel

SocleKernel(G) : GrpPerm -> GrpPerm

SocleQuotient

SocleQuotient(G) : GrpPerm -> GrpPerm, Hom, GrpPerm

SocleSeries

SocleSeries(G) : GrpPerm -> [ GrpPerm ]
SocleSeries(M) : ModRng -> [ ModRng ], [ ModRng ], AlgMatElt

solgps

Database of Soluble Groups (OVERVIEW)

Solomon

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

solomon

Mattson--Solomon Transforms (LINEAR CODES OVER FINITE FIELDS)
Reed--Solomon and Justesen Codes (LINEAR CODES OVER FINITE FIELDS)

Solubility

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

SolubilityCertificate

SolubilityCertificate(C) : CrvCon -> SeqEnum

Soluble

IsSolvable(G) : GrpAb -> BoolElt
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) : GrpPerm -> GrpPerm
SmallGroupIsSoluble(o, n) : RngIntElt, RngIntElt -> Grp
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

soluble

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 (PERMUTATION GROUPS)

soluble-matrix-group

Invariants(G) : GrpMat -> [ RngIntElt ]
Soluble Matrix Groups (MATRIX GROUPS)

soluble-quotient

Soluble Quotient (FINITELY PRESENTED GROUPS)

soluble-quotient-process

Soluble Quotient Processes (FP GROUPS - ADVANCED FEATURES)

soluble-quotients

Soluble Quotients (FP GROUPS - ADVANCED FEATURES)

soluble-radical

The Soluble Radical and its Quotient (PERMUTATION GROUPS)

SolubleQuotient

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 H23E13)

SolubleQuotient1

GrpFP_1_SolubleQuotient1 (Example H22E26)

SolubleQuotient2

GrpFP_1_SolubleQuotient2 (Example H22E27)

SolubleQuotientProcess

SolubleQuotientProcess(F : parameters): GrpFP -> SQProc

SolubleRadical

SolubleRadical(G) : GrpPerm -> GrpPerm
SolvableRadical(G) : GrpPerm -> GrpPerm
Radical(G) : GrpPerm -> GrpPerm

SolubleResidual

SolvableResidual(G) : GrpFin -> GrpFin
SolubleResidual(G) : GrpFin -> GrpFin
SolubleResidual(G) : GrpMat -> GrpMat
SolubleResidual(G) : GrpPerm -> GrpPerm

SolubleSchreier

SolvableSchreier(G: parameters) : GrpPerm : ->
SolubleSchreier(G: parameters) : GrpPerm : ->

SolubleSubgroups

SolvableSubgroups(G: parameters) : GrpFin -> [ rec< Grp, RngIntElt, RngIntElt, GrpFP> ]
SolubleSubgroups(G: parameters) : GrpFin -> [ rec< Grp, RngIntElt, RngIntElt, GrpFP> ]

Solution

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
ReducedAffineSolution(C) : CrvCon -> BoolElt, Pt
ReducedProjectiveSolution(C) : CrvCon -> Pt
SetIntegerSolutionVariables(L, I, m) : LP, SeqEnum[RngIntElt], BoolElt ->
Solution(C) : CrvCon -> Pt
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
CrvCon_Solution (Example H84E7)
Mat_Solution (Example H62E8)

solution

Finding Points on Conics (RATIONAL CURVES AND CONICS)
Nullspaces and Solutions of Systems (MATRICES)
Solutions of Systems of Linear Equations (MATRIX ALGEBRAS)

solution-equation

Nullspaces and Solutions of Systems (MATRICES)
Solutions of Systems of Linear Equations (MATRIX ALGEBRAS)

Solutions

Solutions(t, a) : Thue, RngIntElt -> [ [ RngIntElt, RngIntElt ] ]

Solutionspace

DeleteNonsplitSolutionspace (SQP, p, i, k): SQProc, RngIntElt, RngIntElt, RngIntElt ->
DeleteSplitSolutionspace(SQP, p, i, k): SQProc, RngIntElt, RngIntElt, RngIntElt ->

Solvable

IsSolvable(G) : GrpAb -> BoolElt
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) : 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

SolvableRadical

SolubleRadical(G) : GrpPerm -> GrpPerm
SolvableRadical(G) : GrpPerm -> GrpPerm
Radical(G) : GrpPerm -> GrpPerm
SolvableRadical(L) : AlgLie -> AlgLie

SolvableResidual

SolvableResidual(G) : GrpFin -> GrpFin
SolubleResidual(G) : GrpFin -> GrpFin
SolubleResidual(G) : GrpMat -> GrpMat
SolubleResidual(G) : GrpPerm -> GrpPerm

SolvableSchreier

SolvableSchreier(G: parameters) : GrpPerm : ->
SolubleSchreier(G: parameters) : GrpPerm : ->

SolvableSubgroups

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

SOMinus(arguments)
SpecialOrthogonalGroupMinus(arguments)

SOPlus

SOPlus(arguments)
SpecialOrthogonalGroupPlus(arguments)

Sort

Sort(~S) : SeqEnum ->
Sort(~S, C) : SeqEnum, UserProgram ->
SortDecomposition(D) : [ModBrdt] -> SeqEnum
SortDecomposition(D) : [ModSym] -> SeqEnum

SortDecomposition

SortDecomposition(D) : [ModBrdt] -> SeqEnum
SortDecomposition(D) : [ModSym] -> SeqEnum

Sp

PSigmaSp(arguments)
ProjectiveSigmaSymplecticGroup(arguments)
SymplecticGroup(arguments)

sp-vertices-ex

Newton_sp-vertices-ex (Example H58E4)

Space

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
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
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
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, ., . -> .

space

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)
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

SpaceOfDifferentialsFirstKind

SpaceOfHolomorphicDifferentials(C) : Crv -> ModFld, Map
SpaceOfDifferentialsFirstKind(C) : Crv -> ModFld, Map
SpaceOfDifferentialsFirstKind(F) : FldFunG -> ModFld, Map

SpaceOfHolomorphicDifferentials

SpaceOfHolomorphicDifferentials(C) : Crv -> ModFld, Map
SpaceOfDifferentialsFirstKind(C) : Crv -> ModFld, Map
SpaceOfDifferentialsFirstKind(F) : FldFunG -> ModFld, Map

Spaces

NumberOfFixedSpaces (x, s) : GrpMatElt, RngIntElt -> RngIntElt
OrbitsOfSpaces(G, k) : GrpMat, RngIntElt -> SeqEnum
SetIgnoreSpaces(b) : BoolElt ->
StabiliserOfSpaces(Q) : Spaces -> GrpMat, SeqEnum

spaces

Action on a Coset Space (MATRIX GROUPS)
Extension Spaces (FP GROUPS - ADVANCED FEATURES)
Labels (MODULAR SYMBOLS)

Spanning

SpanningForest(G) : Grph -> Grph
SpanningTree(G) : Grph -> Grph

spanning

DFSTree(u) : GrphVert -> Grph
Spanning Trees of a Graph or Digraph (GRAPHS)

spanning-tree

DFSTree(u) : GrphVert -> Grph
Spanning Trees of a Graph or Digraph (GRAPHS)

SpanningForest

SpanningForest(G) : Grph -> Grph

SpanningTree

SpanningTree(G) : Grph -> Grph

sparse

Representation (UNIVARIATE POLYNOMIAL RINGS)

spchyp

Creation (SUBGROUPS OF PSL_2(R))

SPEC

MAGMA_SYSTEM_SPEC
MAGMA_USER_SPEC

Spec

Spec(R) : RngMPol -> Aff
AffineSpace(R) : RngMPol -> Aff
AttachSpec(S) : file ->
DetachSpec(S) : file ->
Spec(R) : AlgAff -> Sch,Prj

spec

Package Specification files (FUNCTIONS, PROCEDURES AND PACKAGES)
User Startup Specification Files (FUNCTIONS, PROCEDURES AND PACKAGES)
Func_spec (Example H2E9)

Special

ASL(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> ]

special

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-ideals

Special Functions for Ideals (QUADRATIC FIELDS)

special-lattices

Special Lattices (LATTICES)

special-presentation

Special Presentations (FINITE SOLUBLE GROUPS)

Speciality

IndexOfSpeciality(D) : DivCrvElt -> RngIntElt
IndexOfSpeciality(D) : DivFunElt -> RngIntElt

SpecialLinearGroup

SL(arguments)
SpecialLinearGroup(arguments)

SpecialOrthogonalGroup

SO(arguments)
SpecialOrthogonalGroup(arguments)

SpecialOrthogonalGroupMinus

SOMinus(arguments)
SpecialOrthogonalGroupMinus(arguments)

SpecialOrthogonalGroupPlus

SOPlus(arguments)
SpecialOrthogonalGroupPlus(arguments)

SpecialPresentation

SpecialPresentation(G) : GrpPC -> GrpPC
GrpPC_SpecialPresentation (Example H25E24)

SpecialQuotient

GrpMat_SpecialQuotient (Example H21E18)
GrpPerm_SpecialQuotient (Example H20E17)

SpecialUnitaryGroup

SU(arguments)
SpecialUnitaryGroup(arguments)

SpecialWeights

SpecialWeights(G) : GrpPC -> [ <RngIntElt, RngIntElt, RngIntElt> ]

specific

Specific Factorization Algorithms (RING OF INTEGERS)

Spectrum

Spectrum(G) : GrphUnd -> SetEnum

Sphere

Sphere(u, n) : GrphVert, RngIntElt -> { GrphVert }
SpherePackingBound(K, n, d) : FldFin, RngIntElt, RngIntElt -> RngIntElt

SpherePackingBound

SpherePackingBound(K, n, d) : FldFin, RngIntElt, RngIntElt -> RngIntElt

Spinor

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

SpinorCharacters(G) : SymGen -> [ GrpDrchElt ]

SpinorGenera

SpinorGenera(G) : SymGen -> [ SymGen ]

SpinorGenerators

SpinorGenerators(G) : SymGen -> [ RngIntElt ]

SpinorGenus

SpinorGenus(L) : Lat -> SymGen

SpinorRepresentatives

SpinorRepresentatives(L) : Lat -> [ Lat ]
Representatives(G) : SymGen -> [ Lat ]
GenusRepresentatives(L) : Lat -> [ Lat ]

Splice

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

Splice Diagrams (RESOLUTION GRAPHS AND SPLICE DIAGRAMS)
Splice Diagrams from Resolution Graphs (RESOLUTION GRAPHS AND SPLICE DIAGRAMS)

splice-diagrams

Splice Diagrams (RESOLUTION GRAPHS AND SPLICE DIAGRAMS)

SpliceDiagram

SpliceDiagram(g) : GrphRes -> GrphSpl
SpliceDiagram(g,v) : GrphRes,GrphResVert -> GrphSpl
SpliceDiagram(v) : GrphSplVert -> GrphSpl
SpliceDiagram(C,p) : Sch,Pt -> GrphSpl

SpliceDiagramVertex

SpliceDiagramVertex(s,i) : GrphSpl,RngIntElt -> GrphSplVert

Split

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(a, O) : RngFunOrdElt, 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 H56E6)
IO_Split (Example H3E2)

SplitAbelianSection

SplitAbelianSection(SQP: parameter) : SQProc -> BoolElt, SQProc

SplitCollector

SplitCollector(SQP, p) : SQProc, RngIntElt ->
NonsplitCollector(SQP, p) : SQProc, RngIntElt ->

SplitElementaryAbelianSection

SplitElementaryAbelianSection(SQP: parameter) : SQProc -> BoolElt, SQProc

SplitExtension

SplitExtension(G, M, F) : GrpFin, ModRng, GrpFinFP -> GrpFinFP
SplitExtension(G, M, F) : GrpPerm, ModRng, GrpFP -> GrpFP

SplitExtensionSpace

NonsplitExtensionSpace (SQP): SQProc -> SeqEnum
SplitExtensionSpace (SQP): SQProc -> SeqEnum

SplitSection

SplitSection(SQP: parameter) : SQProc -> BoolElt, SQProc

Splitting

FactorisationOverSplittingField(f) : RngPolElt(FldFin) -> [<RngPolElt, RngIntElt>], FldFin
FactorizationOverSplittingField(f) : RngPolElt(FldFin) -> [<RngPolElt, RngIntElt>], FldFin
RootsInSplittingField(f) : RngPolElt(FldFin) -> [<RngPolElt, RngIntElt>], FldFin
SplittingField(F) : FldAlg -> FldAlg, SeqEnum
SplittingField(S) : RngPolElt(FldFin) -> FldFin
SplittingField(P) : RngPolElt(FldFin) -> FldFin
SupportOverSplittingField(Z) : Clstr -> SetEnum

splitting

Reducibility (MODULES OVER A MATRIX ALGEBRA)

SplittingField

SplittingField(F) : FldAlg -> FldAlg, SeqEnum
SplittingField(S) : RngPolElt(FldFin) -> FldFin
SplittingField(P) : RngPolElt(FldFin) -> FldFin

SPolynomial

SPolynomial(f, g) : ModMPolElt, ModMPolElt -> ModMPolElt
SPolynomial(f, g) : RngMPolElt, RngMPolElt -> RngMPolElt

SPrincipal

IsSPrincipal(D, S) : DivFunElt, SetEnum[PlcFunElt] -> BoolElt, FldFunElt
SPrincipalDivisorMap(S) : SetEnum[PlcFunElt] -> Map

SPrincipalDivisorMap

SPrincipalDivisorMap(S) : SetEnum[PlcFunElt] -> Map

Sprint

Sprint(x) : Elt -> MonStgElt

sprint

Printing to a String (INPUT AND OUTPUT)

Sprintf

Sprintf(F, ...) : MonStElt, ... -> MonStgElt
IO_Sprintf (Example H3E8)

SQ

SQ_check(SQP) : SQProc -> BoolElt

Sqrt

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(f) : RngSerElt -> RngSerElt

Sqrts

AllSqrts(a) : RngIntResElt -> [ RngIntResElt ]
AllSquareRoots(a) : RngIntResElt -> [ RngIntResElt ]

Square

AllSqrts(a) : RngIntResElt -> [ RngIntResElt ]
AllSquareRoots(a) : RngIntResElt -> [ RngIntResElt ]
ExteriorSquare(a) : AlgMat -> AlgMatElt
ExteriorSquare(L) : Lat -> Lat
ExteriorSquare(M) : ModTupRng -> ModTupRng
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
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(f) : RngSerElt -> RngSerElt
SymmetricSquare(a) : AlgMatElt -> AlgMatElt
SymmetricSquare(L) : Lat -> Lat
SymmetricSquare(M) : ModTupRng -> ModTupRng

square

Sequences (OVERVIEW)
Square Root (POWER, LAURENT AND PUISEUX SERIES)

square-bracket

Sequences (OVERVIEW)

square-root

Sqrt(f) : RngSerElt -> RngSerElt
Square Root (POWER, LAURENT AND PUISEUX SERIES)

Squared

IsogenyMapPsiSquared(I) : Map -> RngUPolElt

Squarefree

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

SquareFreeFactorization(g) : RngUPolElt -> [ < RngUPolElt, RngIntElt > ]
SquareFreeFactorization(g) : RngUPolElt -> [ < RngUPolElt, RngIntElt > ]

SquarefreeFactorization

Squarefree(n) : RngIntElt -> RngIntElt, RngIntElt
SquarefreeFactorization(n) : RngIntElt -> RngIntElt, RngIntElt
SquarefreeFactorization(f) : RngMPolElt -> [ <RngMPolElt, RngIntElt> ]
SquarefreeFactorization(f) : RngUPolElt -> [ <RngUPolElt, RngIntElt> ]

SquarefreePart

SquarefreePart(f) : RngMPolElt -> RngMPolElt

SquarefreePartialFractionDecomposition

SquarefreePartialFractionDecomposition(f) : FldFunRatUElt -> [ <RngUPolElt, RngIntElt, RngUPolElt> ]

SquareLatticeGraph

SquareLatticeGraph(n) : RngIntElt -> GrphUnd

SquareRoot

SQUOFOF

SQUOFOF(n) : RngIntElt -> RngIntEltFact, [ RngIntElt ]

SRegulator

SRegulator(S) : SetEnum[PlcFunElt] -> RngIntElt

Srivastava

GeneralizedSrivastavaCode(A, W, Z, t, S) : [ FldFinElt ], [ FldFinElt ], [ FldFinElt ], RngIntElt, FldFin -> Code
SrivastavaCode(A, W, mu, S) : [ FldFinElt ], [ FldFinElt ], RngIntElt, FldFin -> Code

SrivastavaCode

SrivastavaCode(A, W, mu, S) : [ FldFinElt ], [ FldFinElt ], RngIntElt, FldFin -> Code

Stabiliser

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

StabiliserOfSpaces(Q) : Spaces -> GrpMat, SeqEnum
GrpMat_StabiliserOfSpaces (Example H21E22)

Stabilizer

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

Images, Orbits and Stabilizers (PERMUTATION GROUPS)
Orbit and Stabilizer Functions for Large Groups (MATRIX GROUPS)
Orbits and Stabilizers (MATRIX GROUPS)

Stabilizers

GrpPerm_Stabilizers (Example H20E19)

Standard

IsStandard(t) : Tableau -> BoolElt
IsStandardParabolicSubgroup( W, H ) : GrpCox -> GrpCox
NumberOfStandardTableaux(P) : SeqEnum -> 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
GrpPC_Standard (Example H25E1)

standard

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)

standard-construction

Standard Constructions and Conversions (ABELIAN GROUPS)

standard-digraph

Construction of a Standard Digraph (GRAPHS)

standard-form

The Standard Form (LINEAR CODES OVER FINITE RINGS)

standard-graph

Construction of a Standard Graph (GRAPHS)

standard-group

Construction of Standard Groups (POLYCYCLIC GROUPS)

standard-presentation

Isomorphism testing and Standard Presentations (p-GROUPS)

standard-sections-soluble-quotient-process

Calculation of Standard Sections (FP GROUPS - ADVANCED FEATURES)

StandardAction

StandardAction( W ) : GrpCox -> Map
GrpCox_StandardAction (Example H36E18)

StandardActionGroup

StandardActionGroup( W ) : GrpCox -> GrpPerm, Map

StandardForm

StandardForm(C) : Code -> Code, Map
StandardForm(C) : Code -> Code, Map
CodeFld_StandardForm (Example H97E9)
CodeRng_StandardForm (Example H98E8)

StandardGraph

StandardGraph(G) : Grph -> Grph

StandardGroup

StandardGroup(G) : GrpPerm -> GrpPerm, Map

StandardGroups

GrpFP_1_StandardGroups (Example H22E14)
GrpPerm_StandardGroups (Example H20E7)
Grp_StandardGroups (Example H19E7)

StandardLattice

StandardLattice(n) : RngIntElt -> Lat

StandardParabolicSubgroup

StandardParabolicSubgroup( W, s ) : GrpCox, {} -> GrpCox

StandardPresentation

StandardPresentation(G): GrpPC -> GrpPC, Map
GrpPGp_StandardPresentation (Example H26E4)

StandardRepresentation

StandardRepresentation( G ) : GrpLie -> Map
GrpLie_StandardRepresentation (Example H37E7)

Star

DualStarInvolution(M) : ModSym -> AlgMatElt
StarInvolution(M) : ModSym -> AlgMatElt

StarInvolution

StarInvolution(M) : ModSym -> AlgMatElt

Start

StartEnumeration(~P: parameters) : GrpFPCosetEnumProc ->
StartNewClass (~P: parameters) : Process(pQuot) ->

start

Loading files (OVERVIEW)
Overview (OVERVIEW)

start-up

Loading files (OVERVIEW)

StartEnumeration

StartEnumeration(~P: parameters) : GrpFPCosetEnumProc ->

starting

Starting and Restarting an Enumeration (FP GROUPS - ADVANCED FEATURES)

StartNewClass

StartNewClass (~P: parameters) : Process(pQuot) ->

Startup

Env_Startup (Example H4E1)

startup

Loading files (OVERVIEW)
Starting, Interrupting and Terminating (STATEMENTS AND EXPRESSIONS)
User Startup Specification Files (FUNCTIONS, PROCEDURES AND PACKAGES)

startup-interrupt-quit

Starting, Interrupting and Terminating (STATEMENTS AND EXPRESSIONS)

startup-spec

User Startup Specification Files (FUNCTIONS, PROCEDURES AND PACKAGES)
Func_startup-spec (Example H2E10)

STARTUP_

MAGMA_STARTUP_FILE

statement

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)

statement-expressions

STATEMENTS AND EXPRESSIONS

status

Status and Future Directions (MODULAR FORMS)

Steenrod

SteenrodOperation(f, i) : RngMPolElt, RngIntElt -> RngMPolElt

steenrod

Steenrod Operations (INVARIANT RINGS OF FINITE GROUPS)

SteenrodOperation

SteenrodOperation(f, i) : RngMPolElt, RngIntElt -> RngMPolElt
RngInvar_SteenrodOperation (Example H78E12)

steinberg

The Steinberg presentation (GROUPS OF LIE TYPE)

Steiner

IsSteiner(D, t) : Dsgn -> BoolElt

Steiniz

[Future release] Steiniz(M) : ModOrd -> RngOrdIdl

Step

ReductionStep(f) : QuadBinElt -> QuadBinElt

step

Sequences (OVERVIEW)
Sets (OVERVIEW)
The for statement (OVERVIEW)

Stirling

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

StirlingFirst(m, n) : RngIntElt, RngIntElt -> RngIntElt
StirlingFirst(m, n) : RngIntElt, RngIntElt -> RngIntElt

StirlingSecond

StirlingSecond(m, n) : RngIntElt, RngIntElt -> RngIntElt
StirlingSecond(m, n) : RngIntElt, RngIntElt -> RngIntElt

stop

Control-C key (OVERVIEW)
Quitting (OVERVIEW)

storage

Identifiers and variables (OVERVIEW)

store

Identifiers and variables (OVERVIEW)

stream

A General Facility (GRAPHS)

String

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 ]

string

Character Strings (INPUT AND OUTPUT)
Strings (OVERVIEW)

Strings

IO_Strings (Example H3E1)

StringToCode

StringToCode(s) : MonStgElt -> RngIntElt

StringToInteger

StringToInteger(s) : MonStgElt -> RngIntElt
StringToInteger(s, b) : MonStgElt, MonStgElt -> RngIntElt

StringToIntegerSequence

StringToIntegerSequence(s) : MonStgElt -> [ RngIntElt ]

Strip

Strip(H, x) : GrpPerm, GrpPermElt -> BoolElt, GrpPermElt, RngIntElt
WordStrip(H, x) : GrpPerm, GrpPermElt -> BoolElt, GrpFPElt, RngIntElt

Strong

PGroupStrong(G) : GrpMat -> GrpFP, Hom(Grp)
FPGroupStrong(G) : GrpPerm -> GrpFP, Hom(Grp)
FPGroupStrong(G) : GrpMat :-> 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)

strong

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

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

Strongly

IsStronglyAG(C) : Code -> BoolElt
IsStronglyConnected(G) : GrphDir -> BoolElt
StronglyRegularGraphsDatabase() : -> DB

strongly

Strongly Regular Graphs (GRAPHS)

StronglyRegularGraphs

Graph_StronglyRegularGraphs (Example H93E18)

StronglyRegularGraphsDatabase

StronglyRegularGraphsDatabase() : -> DB

strop

RngLoc_strop (Example H59E5)
RngPad_strop (Example H42E3)

struct

Creation of Structures (ALGEBRAIC FUNCTION FIELDS)
Related Structures (ALGEBRAIC FUNCTION FIELDS)
Structure Predicates (ALGEBRAIC FUNCTION FIELDS)

struct-pred

Structure Predicates (ALGEBRAIC FUNCTION FIELDS)

structural

The Weight Distribution (LINEAR CODES OVER FINITE FIELDS)
The Weight Distribution (LINEAR CODES OVER FINITE RINGS)

Structure

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

structure

structure-of-congruence-groups

Structure of congruence subgroups (SUBGROUPS OF PSL_2(R))

structure-operations

Operations on Structures (LOCAL RINGS AND FIELDS)
Operations on Structures (p-ADIC RINGS AND FIELDS)

structure-predicates

Structure Predicates (ALGEBRAIC FUNCTION FIELDS)
Structure Predicates (ALGEBRAIC FUNCTION FIELDS)
Structure Predicates (ALGEBRAIC FUNCTION FIELDS)
Structure Predicates (ALGEBRAIC FUNCTION FIELDS)

structure_operations

BaseRing(C) : Sch -> Fld
CoefficientRing(C) : Sch -> Fld
Operations on Curves (HYPERELLIPTIC CURVES)

structure_ops

Operations on Structures (QUADRATIC FIELDS)

StructureConstant

StructureConstant(G, i, j, k) : Grp, RngIntElt, RngIntElt, RngIntElt -> RngIntElt

StructureConstants

StructureConstants( RD ) : RootDtm -> RngIntElt

Structures

Associated Structures (BRANDT MODULES)

structures

Type(L) : Lat -> Cat
Associated Structures (LATTICES)
Related structures (ROOT DATA FOR LIE THEORY)

SU

SU(arguments)
SpecialUnitaryGroup(arguments)

Sub

SubOrder(O) : RngOrd -> RngOrd

sub

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 | 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 | L> : ModMPol, List -> ModMPol
sub<M | m> : ModOrd, SeqEnum[ModOrdElt] -> ModOrd, Map
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
sub< G | L > : GrpFP, List -> GrpFP
sub<G | L> : GrpGPC, List -> GrpGPC, Map
Plane_sub (Example H95E4)
Plane_sub (Example H95E5)

sub-predicates

GrpPC_sub-predicates (Example H25E16)

sub-quo

Creation of Submodules and Quotient Modules (MODULES OVER AFFINE ALGEBRAS)
Subcomplexes and Quotient Complexes (CHAIN COMPLEXES)
ModOrd_sub-quo (Example H65E2)

sub-super-quo

Sublattices, Superlattices and Quotients (LATTICES)

sub_creation

GrpPC_sub_creation (Example H25E13)

SubAlgebra

AlgMat_SubAlgebra (Example H72E4)

Subalgebra

CartanSubalgebra(L) : AlgLie -> AlgLie
HasLeviSubalgebra(L) : AlgLie -> BoolElt

subalgebra

Construction of a Subalgebra (FINITELY PRESENTED ALGEBRAS)
Elementary Operations on Subalgebras and Ideals (MATRIX ALGEBRAS)
Operations on Subalgebras of Group Algebras (GROUP ALGEBRAS)

subalgebra-ideal

Elementary Operations on Subalgebras and Ideals (MATRIX ALGEBRAS)

Subcode

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

subcode

Construction of Subcodes of Linear Codes (LINEAR CODES OVER FINITE RINGS)
Subcodes (LINEAR CODES OVER FINITE FIELDS)

SubcodeBetweenCode

SubcodeBetweenCode(C1, C2, k) : Code,Code,RngIntElt -> Code
CodeFld_SubcodeBetweenCode (Example H97E14)

SubcodeWordsOfWeight

SubcodeWordsOfWeight(C, S) : Code,RngIntElt -> Code

Subcomplex

RandomSubcomplex(C,Q) : ModCpx, SeqEnum -> ModCpx, MapChn

Subdatum

RootSubdatum( RD, s ) : RootDtm, SeqEnum -> RootDtm
RootSubdatum( RD, a ) : RootDtm, SetEnum -> RootDtm

Subfield

IsSubfield(F, L) : FldAlg, FldAlg -> BoolElt, Map
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

subfield

The Subfield Lattice (ORDERS AND ALGEBRAIC FIELDS)

subfield-lattice

The Subfield Lattice (ORDERS AND ALGEBRAIC FIELDS)

SubfieldCode

SubfieldCode(C, S) : Code, FldFin -> Code

SubfieldLattice

SubfieldLattice(K) : FldNum -> SubFldLat
RngOrd_SubfieldLattice (Example H53E23)

SubfieldRepresentationCode

SubfieldRepresentationCode(C, S) : Code, FldFin -> Code

SubfieldRepresentationParityCode

SubfieldRepresentationParityCode(C, K) : Code, FldFin -> Code

Subfields

MaximalSubfields(e) : SubFldLatElt -> [ SubFldLatElt ]
Subfields(K) : FldAlg -> [ < FldAlg, Hom > ]
Subfields(K, n) : FldAlg -> [ < FldAlg, Hom > ]
Subfields(F) : FldFun -> SeqEnum[FldFun]
FldFunG_Subfields (Example H57E6)

subfields

Subfields (ORDERS AND ALGEBRAIC FIELDS)

SubfieldSubcode

RestrictField(C, S) : Code, FldFin -> Code, Map
SubfieldSubcode(C, S) : Code, FldFin -> Code, Map

SubfieldSubplane

SubfieldSubplane(P, F) : Plane, FldFin -> Plane, PlanePtSet, PlaneLnSet

subgraph

Subgraphs, Quotient Graphs, and Super-graphs (GRAPHS)
The Graph of a Map (MAPPINGS)

subgraph-graph

The Graph of a Map (MAPPINGS)

subgraph-supergraph-quotient

Subgraphs, Quotient Graphs, and Super-graphs (GRAPHS)

Subgroup

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) : GrpMat -> GrpMat
DerivedSubgroup(G) : GrpPerm -> GrpPerm
ElementaryAbelianNormalSubgroup(G) : GrpPerm -> GrpPerm
FittingSubgroup(G) : GrpGPC -> GrpGPC
FittingSubgroup(G) : GrpAb -> GrpAb
FittingSubgroup(G) : GrpFin -> GrpFin
[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 H24E3)
Grp_Subgroup (Example H19E5)

subgroup

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)

subgroup-Boolean

General Properties of Subgroups (ABELIAN GROUPS)

subgroup-boolean

General Properties of Subgroups (POLYCYCLIC GROUPS)

subgroup-boolean-nilpotent

Properties of Subgroups Requiring a Nil-po-tent Covering Group (POLYCYCLIC GROUPS)

subgroup-classes

Conjugacy Classes of Subgroups (FINITE SOLUBLE GROUPS)
Conjugacy Classes of Subgroups (GROUPS)

subgroup-constructions

Standard Subgroups (MATRIX GROUPS)
GrpPC_subgroup-constructions (Example H25E15)

subgroup-poset

The Poset of Subgroup Classes (GROUPS)

subgroup-predicates

Predicates for Subgroups (FINITE SOLUBLE GROUPS)

subgroup-presentation

Constructing a Presentation for a Subgroup (FINITELY PRESENTED GROUPS)

subgroup-properties

Elementary Properties of Subgroups (MATRIX GROUPS)
Properties of Subgroups (FINITE SOLUBLE GROUPS)

subgroup-quotient

Construction of Subgroups and Quotient Groups (ABELIAN GROUPS)

subgroup-quotient-homomorphism-extension

Subgroups, Quotient Groups, Homomorphisms and Extensions (POLYCYCLIC GROUPS)

subgroup-series

subgroup-structure

Subgroup Structure (ABELIAN GROUPS)
The Subgroup Structure (ABELIAN GROUPS)
The Subgroup Structure (POLYCYCLIC GROUPS)

subgroup_creation

Construction of Subgroups (GENERIC ABELIAN GROUPS)

subgroup_schemes

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)

subgroup_schemes-category

Associated Structures (ELLIPTIC CURVES)

subgroup_schemes-creation

Creation of Subgroup Schemes (ELLIPTIC CURVES)

subgroup_schemes-points

Points of Subgroup Schemes (ELLIPTIC CURVES)

subgroup_schemes-predicates

Predicates on Subgroup Schemes (ELLIPTIC CURVES)

SubgroupClasses

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 H25E18)

SubgroupConstructions

GrpFP_1_SubgroupConstructions (Example H22E41)
GrpPerm_SubgroupConstructions (Example H20E13)

SubgroupCreation

GrpAbGen_SubgroupCreation (Example H27E4)

SubgroupLattice

SubgroupLattice(G) : GrpFin -> SubGrpLat
SubgroupLattice(G) : GrpPC -> SubGrpLat

SubgroupOfTorus

SubgroupOfTorus(M, x) : ModSym, ModSymElt -> RngIntElt
SubgroupOfTorus(M, s) : ModSym, SeqEnum -> GrpAb

SubgroupOps

GrpFP_1_SubgroupOps (Example H22E43)

Subgroups

subgroups

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)

subgroups-conditional

Classes of Subgroups Satisfying a Condition (PERMUTATION GROUPS)

Subgroups1

GrpFP_1_Subgroups1 (Example H22E28)

Subgroups2

GrpFP_1_Subgroups2 (Example H22E29)

subgroupsabelianpgroups

GrpPGp_subgroupsabelianpgroups (Example H26E7)

SubgroupScheme

SubgroupScheme(E,P) : CrvEll, Pt -> CrvEllSubgroup
SubgroupScheme(G, f) : SchGrpEll, RngUPolElt -> SchGrpEll

SubgroupSchemes

CrvEll_SubgroupSchemes (Example H85E8)

SubgroupsLift

SubgroupsLift(G, A, B, Q: parameters) : GrpPerm, GrpPerm, GrpPerm, SeqEnum -> SeqEnum

SubgroupsQuotientsTransfer

GrpGPC_SubgroupsQuotientsTransfer (Example H24E6)

SubgroupStructure

GrpGPC_SubgroupStructure (Example H24E9)

SubgroupStructure2

GrpGPC_SubgroupStructure2 (Example H24E10)

sublattice

G-invariant Sublattices (LATTICES)

Sublattices

Sublattices(G) : GrpMat -> [ AlgMatElt ]
Sublattices(G, p) : GrpMat, RngIntElt -> [ AlgMatElt ]
Sublattices(G, Q) : GrpMat, [ RngIntElt ] -> [ AlgMatElt ]
Lat_Sublattices (Example H66E22)

Submatrix

submatrix

Extracting and Inserting Blocks (MATRIX ALGEBRAS)
Joining Matrices (MATRIX ALGEBRAS)

SubmatrixRange

ExtractBlockRange(A, i, j, r, s) : Mtrx, RngIntElt, RngIntElt, RngIntElt, RngIntElt -> Mtrx
SubmatrixRange(A, i, j, r, s) : Mtrx, RngIntElt, RngIntElt, RngIntElt, RngIntElt -> Mtrx

Submodule

IsSubmodule(M, N) : ModOrd, ModOrd -> 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 H76E13)
ModRng_Submodule (Example H64E4)

submodule

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)

submodule-construction

Construction (MODULES OVER A MATRIX ALGEBRA)

submodule-lattice

Lattice of Submodules (MODULES OVER A MATRIX ALGEBRA)

SubmoduleAction

SubmoduleAction(G, S) : GrpMat -> Map, GrpMat

SubmoduleImage

SubmoduleImage(G, S) : GrpMat -> GrpMat

SubmoduleLattice

SubmoduleLattice(M) : ModRng -> SubModLat, BoolElt

SubmoduleLatticeAbort

SubmoduleLatticeAbort(M, n) : ModRng, RngIntElt -> BoolElt, SubModLat

Submodules

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

Submodules (MODULES OVER A MATRIX ALGEBRA)

Subnormal

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

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

SubOrder(O) : RngOrd -> RngOrd

Subplane

BaerSubplane(P) : PlaneProj -> PlaneProj, PlanePtSet, PlaneLnSet
SubfieldSubplane(P, F) : Plane, FldFin -> Plane, PlanePtSet, PlaneLnSet

subplane

Subplanes (FINITE PLANES)

SubQuo

PMod_SubQuo (Example H52E3)

SubRD

RootDtm_SubRD (Example H35E18)

subring

Construction of Subalgebras, Ideals and Quotient Algebras (GROUP ALGEBRAS)
Construction of Subalgebras, Ideals and Quotient Rings (MATRIX ALGEBRAS)

subring-ideal-quotient

Construction of Subalgebras, Ideals and Quotient Algebras (GROUP ALGEBRAS)
Construction of Subalgebras, Ideals and Quotient Rings (MATRIX ALGEBRAS)

subroutine

Functions, Procedures, and Mappings (OVERVIEW)

subs

Construction of Subalgebras, Ideals and Quotient Algebras (ALGEBRAS)
Subalgebras and Ideals (ALGEBRAS)

subs-quos

Construction of Subalgebras, Ideals and Quotient Algebras (ALGEBRAS)

Subscheme

DefiningSubschemePolynomial(G) : SchGrpEll -> RngUPolElt
SingularSubscheme(X) : Sch -> Sch

subsemigroup

Subsemigroups and Ideals (FINITELY PRESENTED SEMIGROUPS)
Subsemigroups, Ideals and Quotients (FINITELY PRESENTED SEMIGROUPS)

subsemigroup-ideal

Subsemigroups and Ideals (FINITELY PRESENTED SEMIGROUPS)

subsemigroup-ideal-quotient

Subsemigroups, Ideals and Quotients (FINITELY PRESENTED SEMIGROUPS)

Subsequence

IsSubsequence(S, T) : SeqEnum, SeqEnum -> BoolElt

Subsequences

Subsequences(S, k) : SetEnum, RngIntElt -> SetEnum
Subsequences(S, k) : SetEnum, RngIntElt -> SetEnum

subset

Subsets

Subsets(S) : SetEnum -> SetEnum
Subsets(S) : SetEnum -> SetEnum
Subsets(S, k) : SetEnum, RngIntElt -> SetEnum
Subsets(S, k) : SetEnum, RngIntElt -> SetEnum

subsets

Subsets of a Finite Set (ENUMERATIVE COMBINATORICS)

Subspace

CuspidalSubspace(M) : ModBrdt -> ModBrdt
CuspidalSubspace(M) : ModFrm -> ModFrm
CuspidalSubspace(M) : ModSym -> ModSym
EisensteinSubspace(M) : ModBrdt -> ModBrdt
EisensteinSubspace(M) : ModFrm -> ModFrm
EisensteinSubspace(M) : ModSym -> ModSym
NewSubspace(M) : ModFrm-> ModFrm
NewSubspace(M, p) : ModSym, RngIntElt -> ModSym
NewSubspace(M) : ModSym-> ModSym
ZeroSubspace(M) : ModFrm -> ModFrm

subspace

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)

subspace-quotient-homomorphism

Subspaces, Quotient Spaces and Homomorphisms (VECTOR SPACES)

Subspace1

ModFld_Subspace1 (Example H63E8)

Subspace2

ModFld_Subspace2 (Example H63E9)

Subspaces

ModForm_Subspaces (Example H90E11)
ModSym_Subspaces (Example H88E12)

subspaces

Subspaces (ALGEBRAIC FUNCTION FIELDS)
Subspaces (MODULAR FORMS)
Subspaces (MODULAR SYMBOLS)

Substitute

Substitute(u, f, n, v) : GrpFPElt, RngIntElt, RngIntElt, GrpFPElt -> GrpFPElt
Substitute(u, f, n, v) : SgpFPElt, RngIntElt, SgpFPElt, RngIntElt -> SgpFPElt

Substring

Substring(s, n, k) : MonStgElt, RngIntElt, RngIntElt -> MonStgElt

SubSuperQuo

Lat_SubSuperQuo (Example H66E5)

Subsystem

IsSubsystem(L,K) : LinSys,LinSys -> BoolElt
K subset L : LinSys,LinSys -> BoolElt

subsystems

Scheme_subsystems (Example H81E31)

subtraction

Operators (OVERVIEW)

Subword

Subword(u, f, n) : GrpFPElt, RngIntElt, RngIntElt -> GrpFPElt
Subword(u, f, n) : SgpFPElt, RngIntElt, RngIntElt -> SgpFPElt

Successive

SuccessiveMinima(L) : Lat, RngIntElt -> [ RngIntElt ], [ LatElt ]

SuccessiveMinima

SuccessiveMinima(L) : Lat, RngIntElt -> [ RngIntElt ], [ LatElt ]

Suggested

SuggestedPrecision(f) : RngUPolElt -> RngIntElt
SuggestedPrecision(f) : RngUPolElt -> RngIntElt

SuggestedPrecision

SuggestedPrecision(f) : RngUPolElt -> RngIntElt
SuggestedPrecision(f) : RngUPolElt -> RngIntElt

Sum

AlternatingSum(m, i) : Map, RngIntElt -> FldPrElt
DiagonalSum(t1, t2) : Tableau,Tableau -> Tableau
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) : 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) : [ 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(C, D) : 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

sum

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-dual

Sum, Intersection and Dual (LINEAR CODES OVER FINITE FIELDS)
Sum, Intersection and Dual (LINEAR CODES OVER FINITE RINGS)

SumIntersection

CodeFld_SumIntersection (Example H97E15)
CodeRng_SumIntersection (Example H98E5)

Summand

IsDirectSummand(M, S) : ModGrp, ModGrp -> BoolElt, ModGrp
HasComplement(M, S) : ModGrp, ModGrp -> BoolElt, ModGrp

Summands

IndecomposableSummands(M) : ModGrp -> [ ModGrp ]

summation

Summation of Infinite Series (REAL AND COMPLEX FIELDS)

SumNorm

SumNorm(f) : RngMPolElt -> RngIntElt
SumNorm(p) : RngUPolElt -> RngIntElt

SumOfDivisors

SumOfDivisors(n) : RngIntElt -> RngIntElt

SUnit

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

SUnitGroup(I) : RngOrdFracIdl -> GrpAb, Map
SUnitGroup(S) : SetEnum[PlcFunElt] -> GrpAb, Map

super

Sublattices, Superlattices and Quotients (LATTICES)

supergraph

Subgraphs, Quotient Graphs, and Super-graphs (GRAPHS)

Supermodules

MinimalSupermodules(e) : SubModLatElt -> { SubModLatElt }

Supersingular

IsProbablySupersingular(E) : CrvEll -> BoolElt
IsSupersingular(E: parameters) : CrvEll -> BoolElt
SupersingularEllipticCurve(K) : FldFin -> CrvEll

supersingular_predicates

Predicates for Supersingularity (ELLIPTIC CURVES)

SupersingularEllipticCurve

SupersingularEllipticCurve(K) : FldFin -> CrvEll

supp

Plane_supp (Example H95E3)

Supplement

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

Supplements

Supplements(G, M) : GrpPerm, GrpPerm -> [ GrpPerm ]
Supplements(G, M, N) : GrpPerm, GrpPerm, GrpPerm -> [ GrpPerm ]

Support

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(Z) : Clstr -> SetEnum
Support(D) : DivCrvElt -> SeqEnum
Support(D) : DivFunElt -> [ PlcFunElt ]
Support(D) : DivFunElt -> [ PlcFunElt ], [ RngIntElt ]
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(P) : Plane -> { Elt }
Support(P, p) : Plane, PlanePt -> .
Support(l) : PlaneLn -> SetEnum
SupportOverSplittingField(Z) : Clstr -> SetEnum

support

A Pair of Twisted Cubics (SCHEMES)
Operations on the Support (GRAPHS)
The Defining Points of a Plane (FINITE PLANES)
The Support (MATRIX GROUPS)

SupportOverSplittingField

SupportOverSplittingField(Z) : Clstr -> SetEnum

Surface

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,a,b) : Rng,RngIntElt,RngIntElt -> PrjScrl

Surfaces

K3SurfaceFromBasket(DB,B) : SeqEnum,SeqEnum -> SeqEnum
K3SurfacesFromBasket(DB,B) : SeqEnum,SeqEnum -> SeqEnum
K3SurfacesFromWeights(DB,W) : SeqEnum,SeqEnum -> SeqEnum

surfaces

EnriquesForm(X) : VSrfK3 -> SeqEnum
NoetherForm(X) : VSrfK3 -> SeqEnum
K3 Surfaces in the Database (THE K3 DATABASE)
Kummer Surfaces (HYPERELLIPTIC CURVES)

Surjective

IsSurjective(f) : Map -> [ BoolElt ]
IsSurjective(a) : ModMatRngElt -> BoolElt
IsSurjective(f) : MotMatCpxElt -> BoolElt

Suzuki

PSz(arguments)
ProjectiveSuzukiGroup(arguments)
SuzukiGroup(arguments)
GrpMat_Suzuki (Example H21E9)

suzuki

Suzuki Groups (MATRIX GROUPS)

SuzukiGroup

Sz(arguments)
SuzukiGroup(arguments)

SVPermutation

SVPermutation(G, i, a) : GrpPerm, RngIntElt, Elt -> GrpPermElt

SVWord

SVWord(G, i, a) : GrpPerm, RngIntElt, Elt -> GrpFPElt

Swap

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

SwapColumns(~a, i, j) : AlgMatElt, RngIntElt, RngIntElt ->
SwapColumns(A, i, j) : Mtrx, RngIntElt, RngIntElt -> Mtrx

SwapRows

SwapRows(~a, i, j) : AlgMatElt, RngIntElt, RngIntElt ->
SwapRows(A, i, j) : Mtrx, RngIntElt, RngIntElt -> Mtrx

Swinnerton

SwinnertonDyerPolynomial(n) : RngIntElt -> RngUPolElt

swinnerton

Swinnerton-Dyer Polynomials (UNIVARIATE POLYNOMIAL RINGS)

swinnerton-dyer

Swinnerton-Dyer Polynomials (UNIVARIATE POLYNOMIAL RINGS)

SwinnertonDyer

FldAC_SwinnertonDyer (Example H56E2)

SwinnertonDyerPolynomial

SwinnertonDyerPolynomial(n) : RngIntElt -> RngUPolElt
RngPol_SwinnertonDyerPolynomial (Example H44E5)

Switch

Switch(u) : GrphVert -> GrphUnd
Switch(S) : { GrphVert } -> Grph

switching

Constructing Complements, Line Graphs; Contraction, Switching (GRAPHS)

Sylow

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

SylowBasis(G) : GrpPC -> [GrpPC]

SylowSubgroup

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

Sym

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)

Sym_Bi_Linear

RngMPol_Sym_Bi_Linear (Example H45E6)

Symbol

BiquadraticResidueSymbol(a, b) : RngQuadElt, RngQuadElt -> RngQuadElt
ConvertFromManinSymbol(M, x) : ModSym, Tup -> ModSymElt
DisplayFareySymbolDomain(FS,filename) : 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

symbol

MODULAR SYMBOLS

symbolic

DeleteSplitCollector (SQP) : SQProc, RngIntElt ->
DeleteNonsplitCollector (SQP) : SQProc, RngIntElt ->
Symbolic Collector (FP GROUPS - ADVANCED FEATURES)

symbolic-collector

DeleteSplitCollector (SQP) : SQProc, RngIntElt ->
DeleteNonsplitCollector (SQP) : SQProc, RngIntElt ->
Symbolic Collector (FP GROUPS - ADVANCED FEATURES)

Symbols

symbols

Modular Symbols (MODULAR FORMS)
Modular Symbols (MODULAR SYMBOLS)

Symmetric

ElementarySymmetricPolynomial(P, k) : RngMPol, RngIntElt -> RngMPolElt
ElementarySymmetricPolynomial(P, k) : RngMPol, RngIntElt -> RngMPolElt
IsSymmetric(a) : AlgMatElt -> BoolElt
IsSymmetric(D) : Dsgn -> BoolElt
IsSymmetric(G) : GrpPerm -> BoolElt
IsSymmetric(A) : Mtrx -> BoolElt
IsSymmetric(G : parameters) : GrphUnd -> 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) : ModTupRng -> ModTupRng
SymmetricWeightEnumerator(C): Code -> RngMPolElt

symmetric

Construction of Elements (GROUPS)
Creation of a Permutation Group (PERMUTATION GROUPS)
Symmetric Polynomials (IDEAL THEORY AND GRÖBNER BASES)
Symmetric Polynomials (MULTIVARIATE POLYNOMIAL RINGS)

Symmetric1

GrpFP_1_Symmetric1 (Example H22E5)

Symmetric2

GrpFP_1_Symmetric2 (Example H22E6)
GrpGPC_Symmetric2 (Example H24E5)

SymmetricBilinearForm

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

SymmetricComponents

SymmetricComponents(x, n) : AlgChtrElt, RngIntElt -> SetEnum

SymmetricForms

SymmetricForms(G) : GrpMat -> [ AlgMatElt ]
SymmetricForms(G, n) : GrpMat, RngIntElt -> [ AlgMatElt ]

SymmetricGroup

SymmetricMatrix

SymmetricMatrix(R, Q) : Rng, [ RngElt ] -> Mtrx
SymmetricMatrix(Q) : [ RngElt ] -> Mtrx

SymmetricNormaliser

SymmetricNormaliser(G) : GrpPerm -> GrpPerm
SymmetricNormalizer(G) : GrpPerm -> GrpPerm

SymmetricNormalizer

SymmetricNormaliser(G) : GrpPerm -> GrpPerm
SymmetricNormalizer(G) : GrpPerm -> GrpPerm

SymmetricSquare

SymmetricSquare(a) : AlgMatElt -> AlgMatElt
SymmetricSquare(L) : Lat -> Lat
SymmetricSquare(M) : ModTupRng -> ModTupRng

SymmetricWeightEnumerator

SymmetricWeightEnumerator(C): Code -> RngMPolElt

Symmetrization

Symmetrization(x, p) : AlgChtrElt, [ RngIntElt ] -> AlgChtrElt

symmetrization

Symmetrization (CHARACTERS OF FINITE GROUPS)

symmetry

Symmetry and Regularity Properties of Graphs (GRAPHS)
Transitivity Properties (FINITE PLANES)

symmetry-regularity

Symmetry and Regularity Properties of Graphs (GRAPHS)
Transitivity Properties (FINITE PLANES)

Symplectic

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)

symplectic

Sp(arguments)
Symplectic Groups (MATRIX GROUPS)

SymplecticComponent

SymplecticComponent(x, p) : AlgChtrElt, [ RngIntElt ] -> AlgChtrElt

SymplecticComponents

SymplecticComponents(x, n) : AlgChtrElt, RngIntElt -> SetEnum

SymplecticForm

SymplecticForm(G) : GrpMat -> AlgMatElt

SymplecticGroup

Sp(arguments)
SymplecticGroup(arguments)

Syndrome

Syndrome(w, C) : ModTupFldElt, Code -> ModTupFldElt
SyndromeSpace(C) : Code -> ModTupFld

syndrome

The Syndrome Space (LINEAR CODES OVER FINITE FIELDS)

syndrome-space

The Syndrome Space (LINEAR CODES OVER FINITE FIELDS)

SyndromeSpace

SyndromeSpace(C) : Code -> ModTupFld

System

system

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)

system-calls

Memory Usage (INPUT AND OUTPUT)
System Calls (INPUT AND OUTPUT)

SYSTEM_

MAGMA_SYSTEM_SPEC

SystemAttributes

Func_SystemAttributes (Example H2E11)

SystemNormaliser

SystemNormaliser(G) : GrpPC -> GrpPC
SystemNormalizer(G) : GrpPC -> GrpPC

SystemNormalizer

SystemNormaliser(G) : GrpPC -> GrpPC
SystemNormalizer(G) : GrpPC -> GrpPC

SystemOfEigenvalues

SystemOfEigenvalues(M, prec) : ModSym, RngIntElt -> SeqEnum

systems

Root Systems (REFLECTION GROUPS)

Syzygy

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

Syzygy Modules (IDEAL THEORY AND GRÖBNER BASES)
Syzygy Modules (MODULES OVER AFFINE ALGEBRAS)

syzygy-module

Syzygy Modules (IDEAL THEORY AND GRÖBNER BASES)

SyzygyMatrix

SyzygyMatrix(Q) : [ RngMPolElt ] -> ModMatRngElt

SyzygyModule

SyzygyModule(M, n) : ModAlg, RngIntElt -> ModAlg
SyzygyModule(M) : ModMPol -> [ ModMPolElt ]
SyzygyModule(Q) : [ RngMPolElt ] -> ModTupRng
GB_SyzygyModule (Example H50E24)

Sz

Sz(arguments)
SuzukiGroup(arguments)

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