Index S

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

Index S

S

S-algebras (FINITELY PRESENTED ALGEBRAS)

S-algebra

S-algebras (FINITELY PRESENTED ALGEBRAS)

S-key

S

s-key

s

save

Saving and restoring Magma states (OVERVIEW)

save "filename";

save-restore

Saving and restoring Magma states (OVERVIEW)

ScalarMatrix

ScalarMatrix(R, t) : AlgMat, RngElt -> AlgMatElt

SchreierGenerators

SchreierGenerators(G, H) : GrpFP, GrpFP -> { GrpFPElt }

SchreierGraph

SchreierGraph(A, B) : Grp, Grp -> GrphUnd

SchreierSystem

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

scope

Scope (MAGMA SEMANTICS)

sdiff

R sdiff S : SetEnum, SetEnum -> SetEnum

Search

Search(~P) : Process(Tietze) ->

Sec

Sec(c) : FldComElt -> FldComElt

Sech

Sech(s) : FldPrElt -> FldPrElt

secondary

Secondary Invariants (INVARIANT RINGS OF FINITE GROUPS)

SecondaryInvariants

SecondaryInvariants(R) : RngInvar -> [ RngMPolElt ]

RngInvar_SecondaryInvariants (Example H30E6)

Seek

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

select

Expression (OVERVIEW)

The select expression (OVERVIEW)

Self

Self(n) : RngIntElt -> Elt

Seq_Self (Example H8E5)

semantics

MAGMA SEMANTICS

Semigroup

Semigroup< generators | relations > : SgpFPElt, ..., SgpFPElt, Rel, ...Rel -> SgpFP

semigroup

Semigroups (OVERVIEW)

semigroups

Semigroups (OVERVIEW)

SemiLinearInfoTup

SemiLinearInfoTup(MGT) : SetCartElt -> SetCartElt

SemiLinearTup

SemiLinearTup(MGT) : SetCartElt -> MonStgElt

Seqelt

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

SeqEnum

Sequences (OVERVIEW)

SeqFact

SeqFact(s) : SeqEnum -> RngIntEltFact

Seqint

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

Seqlist

SequenceToList(Q) : SeqEnum -> List

Seqset

Seqset(S) : SeqEnum -> SetEnum

sequence

Deconstruction of a Matrix (MATRIX GROUPS)

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 (FINITE FIELDS)

Sequence Conversions (LOCAL FIELDS)

Sequences (OVERVIEW)

SequenceToElement

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

SequenceToFactorization

SeqFact(s) : SeqEnum -> RngIntEltFact

SequenceToInteger

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

SequenceToList

SequenceToList(Q) : SeqEnum -> List

SequenceToMultiset

SequenceToMultiset(Q) : SeqEnum -> SetMulti

SequenceToSet

Seqset(S) : SeqEnum -> SetEnum

Series

GrpMat_Series (Example H21E17)

GrpPerm_Series (Example H20E17)

series

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 (PERMUTATION GROUPS)

Characteristic Subgroups and Subgroup Series (SOLUBLE GROUPS)

Composition Series (GENERAL MODULES)

Laurent Series and Power Series (POWER SERIES AND LAURENT SERIES)

Minimal Submodules and Socle Series (GENERAL MODULES)

POWER SERIES AND LAURENT SERIES

Rings, Fields, and Algebras (OVERVIEW)

series-power-Laurent

POWER SERIES AND LAURENT SERIES

Set

Set and Get (ENVIRONMENT AND OPTIONS)

Set(F) : FldFin -> SetEnum

Set(B) : IncBlk -> { IncPt }

Set(l) : PlaneLn -> { PlanePt }

Set(R) : RngIntRes -> SetEnum

Set(M) : Struct -> SetEnum

GrpPC_Set (Example H19E3)

set

G-Sets (PERMUTATION GROUPS)

Independent Sets, Cliques, Colourings (GRAPHS)

Parents of Sets and Sequences (INTRODUCTION [SETS, SEQUENCES, AND MAPPINGS])

Power Sets (SETS)

Set Operations (GROUPS)

Set Operations (MATRIX GROUPS)

Set Operations (PERMUTATION GROUPS)

Set-Theoretic Operations (ABELIAN GROUPS)

Set-Theoretic Operations (BLACKBOX GROUPS)

Set-Theoretic Operations in a Group (SOLUBLE GROUPS)

Sets (OVERVIEW)

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

Set and Get (ENVIRONMENT AND OPTIONS)

SetAssertions

SetAssertions(b) : BoolElt ->

SetAutoColumns

SetAutoColumns(b) : BoolElt ->

SetBeep

SetBeep(b) : BoolElt ->

SetColumns

SetColumns(n) : RngIntElt ->

SetDefaultRealField

SetDefaultRealField(R) : FldRe ->

SetDisplayLevel

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

SetEchoInput

SetEchoInput(b) : BoolElt ->

SetEchoInput(b) : BoolElt ->

SetEnum

Sets (OVERVIEW)

SetFormal

Sets (OVERVIEW)

SetHistorySize

SetHistorySize(n) : RngIntElt ->

SetIgnorePrompt

SetIgnorePrompt(b) : BoolElt ->

SetIndent

SetIndent(n) : RngIntElt ->

SetIndx

Sets (OVERVIEW)

SetKantLevel

SetKantLevel(n) : RngIntElt ->

SetKantPrecision

SetKantPrecision(n) : RngIntElt ->

SetKantVerbose

SetKantVerbose(s, n) : MonStgElt, RngIntElt ->

SetLibraries

SetLibraries(s) : MonStgElt ->

SetLibraryRoot

SetLibraryRoot(s) : MonStgElt ->

SetLineEditor

SetLineEditor(b) : BoolElt ->

SetLogFile

SetLogFile(F) : MonStgElt ->

SetLogFile(F) : MonStgElt ->

SetMemoryLimit

SetMemoryLimit(n) : RngIntElt ->

SetOperations

GrpPerm_SetOperations (Example H20E11)

Grp_SetOperations (Example H15E12)

SetOutputFile

SetOutputFile(F) : MonStgElt ->

SetOutputFile(F) : MonStgElt ->

SetPath

SetPath(s) : MonStgElt ->

SetPowerPrinting

SetPowerPrinting(F, l) : FldFin, BoolElt ->

SetPreviousSize

SetPreviousSize(n) : RngIntElt ->

SetPrintLevel

SetPrintLevel(l) : MonStgElt ->

SetPrompt

SetPrompt(s) : MonStgElt ->

SetQuitOnError

SetQuitOnError(b) : BoolElt ->

SetRows

SetRows(n) : RngIntElt ->

sets

Sets (OVERVIEW)

SetSeed

SetSeed(s) : RngIntElt ->

Setseq

Setseq(S) : SetEnum -> SetEnum

SetToIndexedSet

SetToIndexedSet(E) : SetEnum -> SetIndx

SetToMultiset

SetToMultiset(E) : SetEnum -> SetMulti

SetToSequence

Setseq(S) : SetEnum -> SetEnum

SetVerbose

SetVerbose("ECM", b) : MonStgElt, Boolean ->

SetVerbose("Decomposition", v) : MonStgElt, RngIntElt ->

SetVerbose("Groebner", v) : MonStgElt, RngIntElt ->

SetVerbose("HilbertGroebner", v) : MonStgElt, RngIntElt ->

SetVerbose("Invariants", v) : MonStgElt, RngIntElt ->

SetVerbose("SubgroupLattice", i) : MonStgElt, RngIntElt ->

SetVerbose("SubmoduleLattice", i) : MonStgElt, RngIntElt ->

SetVerbose(s, i) : MonStgElt, RngIntElt ->

SetViMode

SetViMode(b) : BoolElt ->

SgpFP

Semigroups (OVERVIEW)

shell

Performing shell commands from Magma (OVERVIEW)

shell-escape

Performing shell commands from Magma (OVERVIEW)

ShortenCode

ShortenCode(C, i) : Code, RngIntElt -> Code

ShortPrimitiveElement

[Future release] ShortPrimitiveElement(O) : RngOrd -> RngOrdElt

ShowIdentifiers

ShowIdentifiers() : ->

ShowPrevious

ShowPrevious() : ->

ShowValues

ShowValues() : ->

Sign

Sign(s) : FldPrElt -> RngIntElt

Sign(q) : FldRatElt -> RngIntElt

Sign(n) : RngIntElt -> RngIntElt

Sign(f) : RngMPolElt -> RngIntElt

Sign(p) : RngUPolElt -> RngIntElt

sign

Absolute Value and Sign (RATIONAL FIELD)

Signature

Signature(K) : FldCyc -> RngIntElt

Signature(K) : FldQuad -> RngIntElt

Signature(O) : RngOrd -> RngIntElt, RngIntElt

signature

Signature (OVERVIEW)

SilvermanBound

SilvermanBound(E) : GeomEC -> FldPrElt

simgps

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

simple

Construction of Simple Linear Codes (ERROR-CORRECTING CODES)

Database of Groups of Order Dividing 729 (OVERVIEW)

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

Other Elementary Functions (RING OF INTEGERS)

Simple Assignment (STATEMENTS AND EXPRESSIONS)

Simple Element Functions (REAL AND COMPLEX FIELDS)

simple-assignment

Simple Assignment (STATEMENTS AND EXPRESSIONS)

SimpleSubgroups

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

SimplexCode

SimplexCode(r) : RngIntElt -> Code

simplification

Simplification (FINITELY PRESENTED GROUPS)

Simplify

Simplify(D) : Inc -> Inc

Simplify(G: parameters) : GrpFP -> GrpFP

Simplify(O) : RngOrd -> RngOrd

SimplifyPresentation

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

SimsSchreier

SimsSchreier(G: parameters) : GrpPerm : ->

Sin

Sin(c) : FldComElt -> FldComElt

Sin(f) : RngSerElt -> RngSerElt

since

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

Sincos

Sincos(s) : FldPrElt -> FldPrElt, FldPrElt

SingerDifferenceSet

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

single

The `single use' Rule (MAGMA SEMANTICS)

single-use

The `single use' Rule (MAGMA SEMANTICS)

SingletonAsymptoticBound

SingletonAsymptoticBound(delta) : FldPrElt -> FldPrElt

SingletonBound

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

Sinh

Sinh(s) : FldPrElt -> FldPrElt

Sinh(f) : RngSerElt -> RngSerElt

Size

Size(G) : Grph -> RngIntElt

size

Groups (OVERVIEW)

Rings, Fields, and Algebras (OVERVIEW)

Sets (OVERVIEW)

SL

SpecialLinearGroup(arguments)

Slope

Slope(l) : PlaneLn -> FldFinElt

smaller

Comparison (OVERVIEW)

Smash

Smash(~MGT, ~S, mode) : SetCartElt, [GrpMatElt], MonStgElt ->

Smash1

GrpMat_Smash1 (Example H21E18)

Smash2

GrpMat_Smash2 (Example H21E19)

SmithForm

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

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

SO

SpecialOrthogonalGroup(arguments)

Socle

Socle(G) : GrpPerm -> GrpPerm

Socle(M) : ModRng -> ModRng

socle

Minimal Submodules and Socle Series (GENERAL MODULES)

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

SocleSeries

SocleSeries(G) : GrpPerm -> [ GrpPerm ]

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

solgps

Database of Soluble Groups (OVERVIEW)

solomon

Mattson-Solomon Transforms (ERROR-CORRECTING CODES)

soluble

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

Database of Soluble Groups (OVERVIEW)

Soluble Matrix Groups (MATRIX GROUPS)

soluble-matrix-group

Soluble Matrix Groups (MATRIX GROUPS)

SolubleQuotient

SolvableQuotient(G) : Grp -> GrpPC, Map

SolubleRadical

Radical(G) : GrpPerm -> GrpPerm

SolubleResidual

SolubleResidual(G) : GrpFin -> GrpFin

SolubleResidual(G) : GrpMat -> GrpMat

SolubleResidual(G) : GrpPerm -> GrpPerm

SolubleSchreier

SolubleSchreier(G: parameters) : GrpPerm : ->

SolubleSubgroups

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

Solution

Solution(a, v) : ModMatFldElt, ModTupFld -> ModTupFldElt, ModTupFld

Solution(A, w) : ModMatRngElt, ModTupRng -> ModTupRngElt, ModTupRng

Solution(A, w) : ModMatRngElt, ModTupRng -> ModTupRngElt, ModTupRng

Solution(a, b, m) : RngIntElt, RngIntElt, RngIntElt -> RngIntElt

Solution(a, b) : RngIntResElt, RngIntResElt -> RngIntResElt

solution

Solution of a System of Linear Equations (VECTOR SPACES)

Solutions of Systems of Linear Equations (MATRIX ALGEBRAS)

Solutions of Systems of Linear Equations (THE MODULES Hom_(R)(M, N) AND End(M))

solution-equation

Solution of a System of Linear Equations (VECTOR SPACES)

Solutions of Systems of Linear Equations (MATRIX ALGEBRAS)

Solutions of Systems of Linear Equations (THE MODULES Hom_(R)(M, N) AND End(M))

SolvableQuotient

SolvableQuotient(G) : Grp -> GrpPC, Map

SolvableRadical

Radical(G) : GrpPerm -> GrpPerm

SolvableResidual

SolubleResidual(G) : GrpFin -> GrpFin

SolubleResidual(G) : GrpMat -> GrpMat

SolubleResidual(G) : GrpPerm -> GrpPerm

SolvableSubgroups

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

SOMinus

SpecialOrthogonalGroupMinus(arguments)

SOPlus

SpecialOrthogonalGroupPlus(arguments)

Sort

Sort(~S) : SeqEnum ->

Sp

SymplecticGroup(arguments)

space

Action on a Coset Space (GROUPS)

Action on a Coset Space (MATRIX GROUPS)

Action on a Coset Space (PERMUTATION GROUPS)

Coset Spaces (ABELIAN GROUPS)

Coset Spaces (SOLUBLE GROUPS)

Coset Spaces and Tables (FINITELY PRESENTED GROUPS)

Coset Spaces: Construction (FINITELY PRESENTED GROUPS)

Matrices and Vector Spaces Associated with a Graph or Digraph (GRAPHS)

Modules (OVERVIEW)

Structure of Inner Product Spaces (VECTOR SPACES)

spanning

Spanning Trees of a Graph or Digraph (GRAPHS)

spanning-tree

Spanning Trees of a Graph or Digraph (GRAPHS)

SpanningForest

SpanningForest(G) : Grph -> Grph

SpanningTree

SpanningTree(G) : Grph -> Grph

sparse

Representation (UNIVARIATE POLYNOMIAL RINGS)

spec

Package Specification files (FUNCTIONS AND PROCEDURES)

User Startup Specification Files (FUNCTIONS AND PROCEDURES)

Func_spec (Example H2E8)

special

Other Element Functions (RESIDUE CLASS RINGS)

Other Special Functions (REAL AND COMPLEX FIELDS)

Special Options (REAL AND COMPLEX FIELDS)

SpecialLinearGroup

SpecialLinearGroup(arguments)

SpecialOrthogonalGroup

SpecialOrthogonalGroup(arguments)

SpecialOrthogonalGroupMinus

SpecialOrthogonalGroupMinus(arguments)

SpecialOrthogonalGroupPlus

SpecialOrthogonalGroupPlus(arguments)

SpecialUnitaryGroup

SpecialUnitaryGroup(arguments)

Spectrum

Spectrum(G) : GrphUnd -> SetEnum

Sphere

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

Split

Split(S, D) : MonStgElt, MonStgElt -> [ MonStgElt ]

IO_Split (Example H3E2)

SplitExtension

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

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

splitting

Splitting a Module (GENERAL MODULES)

SplittingField

SplittingField(P) : RngPolElt(FldFin) -> FldFin

SPolynomial

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

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

Sprint

Sprint(x) : Elt -> MonStgElt

IO_Sprint (Example H3E7)

sprint

Printing to a String (INPUT AND OUTPUT)

Sqrt

Sqrt(a) : FldLocElt -> FldLocElt

Sqrt(a) : RngIntResElt -> RngIntResElt

Sqrt(a) : RngOrdElt -> RngOrdElt

SquareRoot(c) : FldComElt -> FldComElt

SquareRoot(a) : FldFinElt -> FldFinElt

SquareRoot(f) : RngPowElt -> RngPowElt

square

Sequences (OVERVIEW)

Square Root (POWER SERIES AND LAURENT SERIES)

square-bracket

Sequences (OVERVIEW)

square-root

Square Root (POWER SERIES AND LAURENT SERIES)

SquareFree

SquareFree(n) : RngIntElt -> RngIntElt, RngIntElt

SquareFreeFactorization

SquareFreeFactorization(f) : RngMPolElt -> [ <RngMPolElt, RngIntElt> ]

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

SquareRoot

Sqrt(a) : RngIntResElt -> RngIntResElt

Sqrt(a) : RngOrdElt -> RngOrdElt

SquareRoot(c) : FldComElt -> FldComElt

SquareRoot(a) : FldFinElt -> FldFinElt

SquareRoot(f) : RngPowElt -> RngPowElt

SrivastavaCode

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

Stab

Plane_Stab (Example H50E7)

Stabiliser

Stabilizer(G, Y, y) : GrpPerm, GSet, Elt -> GrpPerm

Stabilizer

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 (MATRIX GROUPS)

Images, Orbits and Stabilizers (PERMUTATION GROUPS)

Stabilizers

GrpPerm_Stabilizers (Example H20E12)

Standard

GrpPC_Standard (Example H19E2)

standard

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 a Standard Permutation Group (PERMUTATION GROUPS)

Construction of Standard Groups (SOLUBLE GROUPS)

Construction of Standard Linear Codes (ERROR-CORRECTING CODES)

Standard Constructions and Conversions (ABELIAN GROUPS)

Standard Groups (MATRIX GROUPS)

Standard Groups and Extensions (FINITELY PRESENTED GROUPS)

Standard Groups and Extensions (GROUPS)

Standard Groups and Extensions (PERMUTATION GROUPS)

Standard Presentation Algorithm (SOLUBLE GROUPS)

The Standard Form (ERROR-CORRECTING CODES)

standard-construction

Standard Constructions and Conversions (ABELIAN GROUPS)

standard-digraph

Construction of a Standard Digraph (GRAPHS)

standard-form

The Standard Form (ERROR-CORRECTING CODES)

standard-graph

Construction of a Standard Graph (GRAPHS)

standard-group

Construction of Standard Groups (SOLUBLE GROUPS)

standard-presentation

Standard Presentation Algorithm (SOLUBLE GROUPS)

StandardForm

StandardForm(C) : Code -> Code, Map

Code_StandardForm (Example H51E14)

StandardGraph

StandardGraph(G) : Grph -> Grph

StandardGroup

StandardGroup(G) : GrpPerm -> GrpPerm, Map

StandardGroups

GrpPerm_StandardGroups (Example H20E7)

Grp_StandardGroups (Example H15E6)

StandardPresentation

StandardPresentation(F, p, c: parameters): GrpFP, RngIntElt, RngIntElt -> GrpPC, Map, [Map]

GrpPC_StandardPresentation (Example H19E6)

StandardPresentationProcess

StandardPresentationProcess(G, k : parameters): GrpFP, RngIntElt -> StdPresP

StandardPresentationProcess(F, p, k : parameters): GrpFP, RngIntElt, RngIntElt -> StdPresP

start

Loading files (OVERVIEW)

Overview (OVERVIEW)

start-up

Loading files (OVERVIEW)

Startup

Env_Startup (Example H4E1)

startup

Loading files (OVERVIEW)

Starting, Interrupting and Terminating (STATEMENTS AND EXPRESSIONS)

User Startup Specification Files (FUNCTIONS AND PROCEDURES)

startup-interrupt-quit

Starting, Interrupting and Terminating (STATEMENTS AND EXPRESSIONS)

startup-spec

User Startup Specification Files (FUNCTIONS AND PROCEDURES)

Func_startup-spec (Example H2E9)

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

statistics

Statistics for Database of Groups of Order Dividing 256 (OVERVIEW)

step

Sequences (OVERVIEW)

Sets (OVERVIEW)

The for statement (OVERVIEW)

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)

string

Character Strings (INPUT AND OUTPUT)

Strings (OVERVIEW)

Strings

IO_Strings (Example H3E1)

StringToCode

StringToCode(s) : MonStgElt -> RngIntElt

StringToInteger

StringToInteger(s) : MonStgElt -> RngIntElt

StringToIntegerSequence

StringToIntegerSequence(s) : MonStgElt -> [ RngIntElt ]

Strip

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

strong

Base and Strong Generator Functions (MATRIX GROUPS)

Base and Strong Generator Functions (PERMUTATION GROUPS)

StrongGenerators

StrongGenerators(G) : GrpMat -> SetIndx(GrpMat)

StrongGenerators(G) : GrpPerm -> SetIndx(GrpPermElt)

structural

Structural Properties of Codes (ERROR-CORRECTING CODES)

structure

Characteristic Subgroups and Normal Structure (GROUPS)

Characteristic Subgroups and Normal Structure (MATRIX GROUPS)

Characteristic Subgroups and Normal Structure (PERMUTATION GROUPS)

Creation of Coproducts (COPRODUCTS)

Creation of Structures (FINITE FIELDS)

Creation of Structures (POWER SERIES AND LAURENT SERIES)

Creation of Structures (QUADRATIC FIELDS)

Creation of Structures (RATIONAL FUNCTION FIELDS)

Creation of Structures (RESIDUE CLASS RINGS)

Creation of Structures (RING OF INTEGERS)

Creation of Structures (VALUATION RINGS)

INCIDENCE STRUCTURES AND DESIGNS

Magmas (or Structures) (OVERVIEW)

Normal Structure and Characteristic Subgroups (ABELIAN GROUPS)

Normal Structure and Characteristic Subgroups (SOLUBLE GROUPS)

Normal Structure of a Primitive Group (PERMUTATION GROUPS)

Structure of a Module (GENERAL MODULES)

Structure Operations (CYCLOTOMIC FIELDS)

Structure Operations (ELLIPTIC CURVES)

Structure Operations (POWER SERIES AND LAURENT SERIES)

Structure Operations (REAL AND COMPLEX FIELDS)

Structure Operations (VALUATION RINGS)

Subgroup Structure (ABELIAN GROUPS)

Subgroup Structure (SOLUBLE GROUPS)

The Abstract Structure of a Group (GROUPS)

The Abstract Structure of a Group (MATRIX GROUPS)

The Abstract Structure of a Group (PERMUTATION GROUPS)

The Subgroup Structure (ABELIAN GROUPS)

The Subgroup Structure (SOLUBLE GROUPS)

StructureConstant

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

SU

SpecialUnitaryGroup(arguments)

sub

Constructor (OVERVIEW)

Creation of Submodules and Quotient Modules (MODULES OVER K[x_1, ..., x_n])

sub<A | L_1, ..., L_r> : AlgFP, AlgFPElt, ..., AlgFPElt -> AlgFP

sub<R | L> : AlgMat, List -> AlgMat, Hom(Alg)

sub<C | L> : Code, List -> Code

sub<F | d> : FldFin, RngIntElt -> FldFin, Map

sub< K | e > : FldNum, FldNumElt -> FldNum, Map

sub<G | L> : Grp, List -> Grp

sub<A | L> : GrpAb, List -> GrpAb, Map

sub< G | L > : GrpFP, List -> GrpFP

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<M | L> : ModMPol, List -> ModMPol

sub<V | L> : ModTupFld, List -> ModTupFld

sub<M | L> : ModTupRng, List -> ModTupRng

sub<P | L> : Plane, List -> Plane

sub< Z | n > : RngInt, RngIntElt -> RngInt

sub< R | n > : RngIntRes, RngIntResElt -> RngIntRes

sub< O | f > : RngQuad, RngIntElt ->

sub<S | L_1, ..., L_r> : SgpFP, SgpFPElt, ..., SgpFPElt -> SgpFP

Plane_sub (Example H50E3)

sub-quo

Creation of Submodules and Quotient Modules (MODULES OVER K[x_1, ..., x_n])

SubAlgebra

AlgMat_SubAlgebra (Example H44E4)

subalgebra

Construction of a Subalgebra (FINITELY PRESENTED ALGEBRAS)

Elementary Operations on Subalgebras and Ideals (MATRIX ALGEBRAS)

subalgebra-ideal

Elementary Operations on Subalgebras and Ideals (MATRIX ALGEBRAS)

subcode

Construction of Subcodes of Linear Codes (ERROR-CORRECTING CODES)

Subfields

Subfields(K, n) : FldNum -> [ < FldNum, Hom > ]

subfields

Subfields (NUMBER FIELDS AND THEIR ORDERS)

SubfieldSubcode

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

Subgroup(V) : GrpFPCos -> GrpFP

Grp_Subgroup (Example H15E4)

subgroup

Characteristic Subgroups and Normal Structure (GROUPS)

Characteristic Subgroups and Normal Structure (MATRIX GROUPS)

Characteristic Subgroups and Normal Structure (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 (PERMUTATION GROUPS)

Characteristic Subgroups and Subgroup Series (SOLUBLE GROUPS)

Conjugacy Classes of Subgroups (GROUPS)

Conjugacy Classes of Subgroups (GROUPS)

Constructing a Presentation for a Subgroup (FINITELY PRESENTED GROUPS)

Construction of Subgroups (ABELIAN GROUPS)

Construction of Subgroups (GROUPS)

Construction of Subgroups (MATRIX GROUPS)

Construction of Subgroups (PERMUTATION GROUPS)

Construction of Subgroups (SOLUBLE GROUPS)

Construction of Subgroups and Quotient Groups (ABELIAN GROUPS)

General Properties of Subgroups (ABELIAN GROUPS)

General Properties of Subgroups (SOLUBLE GROUPS)

General Subgroup Constructions (SOLUBLE GROUPS)

Low Index Subgroups (FINITELY PRESENTED GROUPS)

Normal Structure and Characteristic Subgroups (ABELIAN GROUPS)

Normal Structure and Characteristic Subgroups (SOLUBLE GROUPS)

Standard Subgroup Constructions (GROUPS)

Standard Subgroup Constructions (MATRIX GROUPS)

Standard Subgroup Constructions (PERMUTATION GROUPS)

Subgroup Constructions (FINITELY PRESENTED GROUPS)

Subgroup Structure (ABELIAN GROUPS)

Subgroup Structure (SOLUBLE GROUPS)

Subgroups (FINITELY PRESENTED GROUPS)

Subgroups, Quotient Groups and Extensions (SOLUBLE GROUPS)

The Poset of Subgroup Classes (GROUPS)

The Subgroup Structure (ABELIAN GROUPS)

The Subgroup Structure (SOLUBLE GROUPS)

subgroup-Boolean

General Properties of Subgroups (ABELIAN GROUPS)

General Properties of Subgroups (SOLUBLE GROUPS)

subgroup-classes

Conjugacy Classes of Subgroups (GROUPS)

subgroup-poset

The Poset of Subgroup Classes (GROUPS)

subgroup-presentation

Constructing a Presentation for a Subgroup (FINITELY PRESENTED GROUPS)

subgroup-quotient

Construction of Subgroups and Quotient Groups (ABELIAN GROUPS)

subgroup-quotient-extension

Subgroups, Quotient Groups and Extensions (SOLUBLE GROUPS)

subgroup-series

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 (PERMUTATION GROUPS)

Characteristic Subgroups and Subgroup Series (SOLUBLE GROUPS)

subgroup-structure

Subgroup Structure (ABELIAN GROUPS)

Subgroup Structure (SOLUBLE GROUPS)

The Subgroup Structure (ABELIAN GROUPS)

The Subgroup Structure (SOLUBLE GROUPS)

SubgroupClasses

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

SubgroupConstructions

GrpPerm_SubgroupConstructions (Example H20E16)

SubgroupLattice

SubgroupLattice(G) : GrpFin -> SubGrpLat

SubgroupOps

GrpFP_SubgroupOps (Example H16E19)

Subgroups

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

GrpMat_Subgroups (Example H21E7)

Grp_Subgroups (Example H15E14)

Subgroups1

GrpFP_Subgroups1 (Example H16E14)

Subgroups2

GrpFP_Subgroups2 (Example H16E15)

Submatrix

Submatrix(a, i, j, p, q) : AlgMatElt, RngIntElt, RngIntElt, RngIntElt, RngIntElt -> ModMatRngElt

Submatrix(a, i, j, p, q) : ModMatRngElt, RngIntElt, RngIntElt, RngIntElt, RngIntElt -> ModMatRngElt

submatrix

Extracting and Inserting Blocks (MATRIX ALGEBRAS)

Extracting and Inserting Blocks (THE MODULES Hom_(R)(M, N) AND End(M))

Submodule

RMod_Submodule (Example H41E16)

submodule

Construction of Submodules (GENERAL MODULES)

Minimal Submodules and Socle Series (GENERAL MODULES)

Operations on Submodules (GENERAL MODULES)

Submodule Lattices (GENERAL MODULES)

Submodules, Quotient Modules and Homomorphisms (GENERAL MODULES)

submodule-lattice

Submodule Lattices (GENERAL MODULES)

submodule-quotient-homomorphism

Submodules, Quotient Modules and Homomorphisms (GENERAL MODULES)

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

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

Subplanes (FINITE PLANES)

SubQuo

PMod_SubQuo (Example H43E3)

subring

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

subring-ideal-quotient

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

subroutine

Functions, Procedures, and Mappings (OVERVIEW)

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)

Subsequences

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

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

subset

x in R : AlgMatElt, AlgMat -> BoolElt

[Future release] x in I : AlgMatElt, AlgMatIdl -> BoolElt

e le f : SubGrpLatElt, SubGrpLatElt -> BoolElt

C subset D : Code, Code -> BoolElt

H subset G : GrpAb, GrpAb -> BoolElt

H subset G : GrpFin, GrpFin -> BoolElt

H subset K : GrpFP, GrpFP -> BoolElt

H subset G : GrpPC, GrpPC -> BoolElt

H subset G : GrpPerm, GrpPerm -> BoolElt

M subset N : ModMPol, ModMPol -> BoolElt

U subset V : ModTupFld, ModTupFld -> BoolElt

N subset M : ModTupRng, ModTupRng -> BoolElt

P subset Q : Plane, Plane -> BoolElt

I subset J : RngIdl, RngIdl -> BoolElt

I subset J : RngMPol, RngMPol -> BoolElt

I subset J : RngUPol, RngUPol -> BoolElt

R subset S : SetEnum, Set -> BoolElt

e subset f : SubModLatElt, SubModLatElt -> SubModLatElt

S subset G : { GrpAbElt } , GrpAb -> BoolElt

S subset G : { GrpBBElt } , GrpBB -> BoolElt

S subset G : { GrpFinElt }, GrpFin -> BoolElt

S subset G : { GrpMatElt }, GrpMat -> BoolElt

S subset G : { GrpPCElt } , GrpPC -> BoolElt

S subset G : { GrpPermElt }, GrpPerm -> BoolElt

S subset B : { IncPt }, IncBlk -> BoolElt

S subset l : { PlanePt }, PlaneLn -> BoolElt

Subsets

Subsets(S) : SetEnum -> SetEnum

Subsets(S) : SetEnum -> SetEnum

subsets

Subsets of a Finite Set (ENUMERATIVE COMBINATORICS)

subspace

Construction of Subspaces (VECTOR SPACES)

Operations on Subspaces (VECTOR SPACES)

Subspaces, Quotient Spaces and Homomorphisms (VECTOR SPACES)

subspace-quotient-homomorphism

Subspaces, Quotient Spaces and Homomorphisms (VECTOR SPACES)

Subspace1

KMod_Subspace1 (Example H40E7)

Subspace2

KMod_Subspace2 (Example H40E8)

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

subtraction

Operators (OVERVIEW)

Subword

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

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

Sum

Sum(Q) : [ Inc ] -> Inc

sum

Sum, Intersection and Dual (ERROR-CORRECTING CODES)

sum-intersection-dual

Sum, Intersection and Dual (ERROR-CORRECTING CODES)

summation

Summation of Infinite Series (REAL AND COMPLEX FIELDS)

SumNorm

SumNorm(f) : RngMPolElt -> RngIntElt

SumNorm(p) : RngUPolElt -> RngIntElt

SumOfDivisors

SumOfDivisors(n) : RngIntElt -> RngIntElt

supergraph

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

Support

Support(u) : AlgFPElt -> [ MonElt ]

[Future release] Support(V) : GrpFPCos -> { GSetElt }

Support(G) : Grph -> SetIndx

Support(g, Y) : GrpPermElt, GSet -> { Elt }

Support(D) : Inc -> { Elt }

Support(B) : IncBlk -> { Elt }

Support(u) : ModTupFldElt -> { RngElt }

Support(w) : ModTupFldElt -> { RngIntElt }

Support(u) : ModTupRngElt -> { RngElt }

Support(P) : Plane -> { Elt }

Support(l) : PlaneLn -> SetEnum

support

Operations on the Support (GRAPHS)

The Support (MATRIX GROUPS)

Suzuki

GrpMat_Suzuki (Example H21E10)

suzuki

Suzuki Groups (MATRIX GROUPS)

SuzukiGroup

SuzukiGroup(arguments)

SVPermutation

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

SVWord

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

SwapColumns

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

SwapColumns(~a, i, j) : ModMatElt, RngIntElt, RngIntElt ->

SwapColumns(~a, i, j) : ModMatRngElt, RngIntElt, RngIntElt ->

SwapRows

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

SwapRows(~a, i, j) : ModMatElt, RngIntElt, RngIntElt ->

SwapRows(~a, i, j) : ModMatRngElt, RngIntElt, RngIntElt ->

Switch

Switch(u) : GrphVert -> GrphUnd

switching

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

Sylow

Hall pi-Subgroups and Sylow Systems (SOLUBLE GROUPS)

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

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

Sym(GrpPerm, n) : Cat, RngIntElt -> GrpPerm

Sym(n) : RngIntElt -> GrpPerm

SymmetricGroup(C, n) : Cat, RngIntElt -> GrpFin

SymmetricGroup(GrpFP, n) : Cat, RngIntElt -> GrpFP

GrpPerm_Sym (Example H20E1)

Sym8

GrpFP_Sym8 (Example H16E10)

symmetric

Construction of Elements (GROUPS)

Creation of the Symmetric Group and Arithmetic with Permutations (PERMUTATION GROUPS)

Symmetric Polynomials (MULTIVARIATE POLYNOMIAL RINGS)

Symmetric1

GrpFP_Symmetric1 (Example H16E3)

Symmetric2

GrpFP_Symmetric2 (Example H16E4)

SymmetricComponents

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

SymmetricGroup

Sym(GrpPerm, n) : Cat, RngIntElt -> GrpPerm

Sym(n) : RngIntElt -> GrpPerm

SymmetricGroup(C, n) : Cat, RngIntElt -> GrpFin

SymmetricGroup(GrpFP, n) : Cat, RngIntElt -> GrpFP

SymmetricNormaliser

SymmetricNormalizer(G) : GrpPerm -> GrpPerm

SymmetricNormalizer

SymmetricNormalizer(G) : GrpPerm -> GrpPerm

SymmetricSquare

SymmetricSquare(a) : AlgMatElt -> AlgMatElt

SymmetricSquare(M) : ModTupRng -> ModTupRng

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)

Transitivity Properties (INCIDENCE STRUCTURES AND DESIGNS)

symmetry-regularity

Symmetry and Regularity Properties of Graphs (GRAPHS)

Transitivity Properties (FINITE PLANES)

Transitivity Properties (INCIDENCE STRUCTURES AND DESIGNS)

Symplectic

GrpMat_Symplectic (Example H21E9)

symplectic

Symplectic Groups (MATRIX GROUPS)

SymplecticComponent

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

SymplecticComponents

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

SymplecticGroup

SymplecticGroup(arguments)

SymTensorProdInfoTup

SymTensorProdInfoTup(MGT) : SetCartElt -> SetCartElt

SymTensorProdTup

SymTensorProdTup(MGT) : SetCartElt -> MonStgElt

Syndrome

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

SyndromeSpace

SyndromeSpace(C) : Code -> ModTupFld

System

system

System Calls (INPUT AND OUTPUT)

System Features (OVERVIEW)

system-calls

System Calls (INPUT AND OUTPUT)

SystemNormaliser

SystemNormalizer(G) : GrpPC -> GrpPC

SystemNormalizer

SystemNormalizer(G) : GrpPC -> GrpPC

syzygy

Syzygy Modules (MODULES OVER K[x_1, ..., x_n])

Syzygy Modules (MULTIVARIATE POLYNOMIAL RINGS)

syzygy-module

Syzygy Modules (MULTIVARIATE POLYNOMIAL RINGS)

SyzygyMatrix

SyzygyMatrix(Q) : [ RngMPolElt ] -> ModMatRngElt

SyzygyModule

SyzygyModule(M) : ModMPol -> [ ModMPolElt ]

SyzygyModule(Q) : [ RngMPolElt ] -> ModTupRng

RngMPol_SyzygyModule (Example H29E25)

Sz

SuzukiGroup(arguments)

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