[____] [____] [_____] [____] [__] [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) ->
SearchForDecomposition
SearchForDecomposition (G, S) : GrpMat, [GrpMatElt] -> BoolElt
Sec
Sec(c) : FldComElt -> FldComElt
Sech
Sech(s) : FldPrElt -> FldPrElt
secondary
Secondary Invariants (INVARIANT RINGS OF FINITE GROUPS)
SecondaryInvariants
R`SecondaryInvariants
SecondaryInvariants(R) : RngInvar -> [ RngMPolElt ]
RngInvar_SecondaryInvariants (Example H30E7)
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)
SemiLinearGroup
SemiLinearGroup(G, S) : GrpMat, FldFin -> GrpMat
Semilinearity
GrpMat_Semilinearity (Example H21E19)
semilinearity
Semilinearity (MATRIX GROUPS)
semisimple
The Type of a Semisimple Lie Algebra (LIE ALGEBRAS)
semisimple-type
The Type of a Semisimple Lie Algebra (LIE ALGEBRAS)
SemiSimpleType
SemiSimpleType(L) : AlgLie -> AlgLie
AlgLie_SemiSimpleType (Example H49E8)
SeparableDegree
SeparableDegree(I) : Map -> RngIntElt
Seqelt
SequenceToElement(s, F) : [ FldFinElt ] -> FldFinElt
SequenceToElement(s, R) : [ RngIntElt ] -> FldLocElt
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
SequenceToElement(s, R) : [ RngIntElt ] -> FldLocElt
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
AlgLie_Series (Example H49E5)
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 (LIE ALGEBRAS)
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)
SetAllInvariantsOfDegree
SetAllInvariantsOfDegree(R, d, Q) : RngInvar, RngIntElt, [ RngMPolElt ] ->
SetAssertions
SetAssertions(b) : BoolElt ->
SetAutoColumns
SetAutoColumns(b) : BoolElt ->
SetAutoCompact
SetAutoCompact(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 ->
SetIgnoreSpaces
SetIgnoreSpaces(b) : BoolElt ->
SetIndent
SetIndent(n) : RngIntElt ->
SetIndx
Sets (OVERVIEW)
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("Cunningham", b) : MonStgElt, Boolean ->
SetVerbose("Decomposition", v) : MonStgElt, RngIntElt ->
SetVerbose("Factorization", v) : MonStgElt, RngIntElt ->
SetVerbose("Groebner", v) : MonStgElt, RngIntElt ->
SetVerbose("HilbertGroebner", v) : MonStgElt, RngIntElt ->
SetVerbose("Invariants", v) : MonStgElt, RngIntElt ->
SetVerbose("LLL", v) : MonStgElt, RngIntElt ->
SetVerbose("SubgroupLattice", i) : MonStgElt, RngIntElt ->
SetVerbose("SubmoduleLattice", i) : MonStgElt, RngIntElt ->
SetVerbose(s, i) : MonStgElt, RngIntElt ->
SetViMode
SetViMode(b) : BoolElt ->
Seysen
Seysen(L) : Lat -> Lat, AlgMatElt
Seysen(X) : ModMatRngElt -> ModMatRngElt, AlgMatElt
Lat_Seysen (Example H45E14)
seysen
Seysen Reduction (LATTICES)
SeysenGram
SeysenGram(F) : ModMatRngElt -> ModMatRngElt, AlgMatElt, RngIntElt
SgpFP
Semigroups (OVERVIEW)
shell
Performing shell commands from Magma (OVERVIEW)
shell-escape
Performing shell commands from Magma (OVERVIEW)
short
Short and Close Vectors (LATTICES)
short-close
Short and Close Vectors (LATTICES)
ShortenCode
ShortenCode(C, i) : Code, RngIntElt -> Code
shortest
Shortest and Closest Vectors (LATTICES)
shortest-closest
Shortest and Closest Vectors (LATTICES)
ShortestVectors
ShortestVectors(L) : Lat -> [ LatElt ], RngElt
ShortestVectorsMatrix
ShortestVectorsMatrix(L) : Lat -> ModMatRngElt
ShortPrimitiveElement
[Future release] ShortPrimitiveElement(O) : RngOrd -> RngOrdElt
ShortVectors
ShortVectors(L, u) : Lat, RngElt -> [ <LatElt, RngElt> ]
ShortVectorsMatrix
ShortVectorsMatrix(L, u) : Lat, RngElt -> ModMatRngElt
ShortVectorsProcess
ShortVectorsProcess(L, u) : Lat, RngElt -> LatEnumProc
ShowIdentifiers
ShowIdentifiers() : ->
ShowPrevious
ShowPrevious() : ->
ShowValues
ShowValues() : ->
Sign
Sign(s) : FldPrElt -> RngIntElt
Sign(q) : FldRatElt -> RngIntElt
Sign(x) : Infty -> 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) : FldFun -> [ <RngIntElt, RngIntElt> ]
Signature(K) : FldQuad -> RngIntElt
Signature(O) : RngOrd -> RngIntElt, RngIntElt
signature
Signature (OVERVIEW)
SilvermanBound
SilvermanBound(E) : CurveEll -> FldPrElt
simgps
Database of Simple Groups: Permutations, Presentations, Conjugacy Classes, Maximal Subgroups and Sylow Subgroups (OVERVIEW)
simple
Construction of Simple Lie Algebras (LIE ALGEBRAS)
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)
SimpleLieAlgebra
SimpleLieAlgebra(X, n, F) : MonStgElt, RngIntElt, Fld -> AlgLie
AlgLie_SimpleLieAlgebra (Example H49E1)
SimpleSubgroups
SimpleSubgroups(G: parameters) : GrpFin -> [ rec< Grp, RngIntElt, RngIntElt, GrpFP> ]
SimplexCode
SimplexCode(r) : RngIntElt -> Code
simplification
Simplification (FINITELY PRESENTED GROUPS)
SimplifiedModel
SimplifiedModel(E): CurveEll -> CurveEll, Map, Map
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
SingularElements
Lat_SingularElements (Example H45E10)
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)
SmallGroup
SmallGroup(o, n) : RngIntElt, RngIntElt -> Grp
SmallGroupProcess
SmallGroupProcess(o: parameters) : RngIntElt -> Process
SmallGroups
SmallGroups(o: parameters) : RngIntElt -> [* Grp *]
SmithForm
SmithForm(a) : AlgMatElt -> AlgMatElt, AlgMatElt, AlgMatElt
SmithForm(X) : 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 GROUPS
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
ChineseRemainderTheorem(a, b, m) : RngIntElt, RngIntElt, RngIntElt -> RngIntElt
Solution(a, v) : ModMatFldElt, ModTupFld -> ModTupFldElt, ModTupFld
Solution(A, w) : ModMatRngElt, ModTupRng -> ModTupRngElt, ModTupRng
Solution(A, w) : ModMatRngElt, ModTupRng -> ModTupRngElt, ModTupRng
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
SolvableRadical(L) : AlgLie -> AlgLie
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)
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, PROCEDURES AND PACKAGES)
User Startup Specification Files (FUNCTIONS, PROCEDURES AND PACKAGES)
Func_spec (Example H2E8)
special
Other Element Functions (RESIDUE CLASS RINGS)
Other Special Functions (REAL AND COMPLEX FIELDS)
Special Lattices (LATTICES)
Special Options (REAL AND COMPLEX FIELDS)
special-lattices
Special Lattices (LATTICES)
SpecialLinearGroup
SpecialLinearGroup(arguments)
SpecialOrthogonalGroup
SpecialOrthogonalGroup(arguments)
SpecialOrthogonalGroupMinus
SpecialOrthogonalGroupMinus(arguments)
SpecialOrthogonalGroupPlus
SpecialOrthogonalGroupPlus(arguments)
SpecialUnitaryGroup
SpecialUnitaryGroup(arguments)
specific
Specific Factorization Algorithms (RING OF INTEGERS)
Spectrum
Spectrum(G) : GrphUnd -> SetEnum
Sphere
Sphere(u, n) : GrphVert, RngIntElt -> { GrphVert }
Split
Split(K) : FldFun -> SeqEnum
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
sprint
Printing to a String (INPUT AND OUTPUT)
Sprintf
Sprintf(F, ...) : MonStElt, ... -> MonStgElt
IO_Sprintf (Example H3E8)
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
SquareFreeFactorization(n) : RngIntElt -> RngIntElt, RngIntElt
SquareFreeFactorization
SquareFreeFactorization(n) : RngIntElt -> RngIntElt, RngIntElt
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
SQUOFOF
SQUOFOF(n) : RngIntElt -> RngIntEltFact, [ RngIntElt ]
SrivastavaCode
SrivastavaCode(A, W, mu, S) : [ FldFinElt ], [ FldFinElt ], RngIntElt, FldFin -> Code
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 H58E14)
StandardGraph
StandardGraph(G) : Grph -> Grph
StandardGroup
StandardGroup(G) : GrpPerm -> GrpPerm, Map
StandardGroups
GrpPerm_StandardGroups (Example H20E7)
Grp_StandardGroups (Example H15E6)
StandardLattice
StandardLattice(n) : RngIntElt -> Lat
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, 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 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)
steenrod
Steenrod Operations (INVARIANT RINGS OF FINITE GROUPS)
SteenrodOperation
SteenrodOperation(f, i) : RngMPolElt, RngIntElt -> RngMPolElt
RngInvar_SteenrodOperation (Example H30E12)
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 AFFINE ALGEBRAS)
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<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<L | S> : Lat, List -> Lat
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 | a_1, ..., a_r > : RngOrd, RngOrdElt, ..., RngOrdElt -> RngOrd
sub< O | f > : RngQuad, RngIntElt ->
sub<S | L_1, ..., L_r> : SgpFP, SgpFPElt, ..., SgpFPElt -> SgpFP
Plane_sub (Example H57E4)
Plane_sub (Example H57E5)
sub-quo
Creation of Submodules and Quotient Modules (MODULES OVER AFFINE ALGEBRAS)
sub-super-quo
Sublattices, Superlattices and Quotients (LATTICES)
SubAlgebra
AlgMat_SubAlgebra (Example H51E4)
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
Construction of Subcodes of Linear Codes (ERROR-CORRECTING CODES)
SubfieldLattice
SubfieldLattice(K) : FldNum -> SubFldLat
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(E, r) : CurveEll, RngUPolElt -> CurveEll
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)
subgroup_ops
Subgroups of Elliptic Curves (ELLIPTIC CURVES)
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)
subgroups
Creation of Subgroups of Elliptic Curves (ELLIPTIC CURVES)
Subgroups1
GrpFP_Subgroups1 (Example H16E14)
Subgroups2
GrpFP_Subgroups2 (Example H16E15)
sublattice
G-invariant Sublattices (LATTICES)
Sublattices
Sublattices(G, p) : GrpMat, RngIntElt -> [ AlgMatElt ]
Lat_Sublattices (Example H45E22)
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))
Joining Matrices (MATRIX ALGEBRAS)
Joining Matrices (THE MODULES Hom_(R)(M, N) AND End(M))
Submodule
RMod_Submodule (Example H42E16)
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 H44E3)
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
Subscheme(E, I) : CurveEll, RngMPol -> CurveEll
subscheme_ops
Subschemes of Elliptic Curves (ELLIPTIC CURVES)
subschemes
Creation of Subschemes of Elliptic Curves (ELLIPTIC CURVES)
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
e le f : SubGrpLatElt, SubGrpLatElt -> BoolElt
A subset B : AlgGen, AlgGen -> 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 : RngMPolRes, RngMPolRes -> 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 H41E7)
Subspace2
KMod_Subspace2 (Example H41E8)
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 H45E5)
subtraction
Operators (OVERVIEW)
Subword
Subword(u, f, n) : GrpFPElt, RngIntElt, RngIntElt -> GrpFPElt
Subword(u, f, n) : SgpFPElt, RngIntElt, RngIntElt -> SgpFPElt
SuccessiveMinima
SuccessiveMinima(L) : Lat, RngIntElt -> [ RngIntElt ], [ LatElt ]
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
SUnitGroup
SUnitGroup(I) : RngOrdIdl -> GrpAb, map
super
Sublattices, Superlattices and Quotients (LATTICES)
supergraph
Subgraphs, Quotient Graphs, and Super-graphs (GRAPHS)
supp
Plane_supp (Example H57E3)
Support
Support(u) : AlgFPElt -> [ MonElt ]
Support(a) : AlgGenElt -> SetEnum
Support(a) : AlgGrpElt -> SeqEnum
[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
Operations on the Support (GRAPHS)
The Defining Points of a Plane (FINITE PLANES)
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(~X, i, j) : ModMatRngElt, RngIntElt, RngIntElt ->
SwapRows
SwapRows(~a, i, j) : AlgMatElt, RngIntElt, RngIntElt ->
SwapRows(~a, i, j) : ModMatElt, RngIntElt, RngIntElt ->
SwapRows(~X, 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
SymmetricForms
SymmetricForms(G) : GrpMat -> [ AlgMatElt ]
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(L) : Lat -> Lat
SymmetricSquare(M) : ModTupRng -> ModTupRng
SymmetricTensor
GrpMat_SymmetricTensor (Example H21E23)
SymmetricTensorBasis
SymmetricTensorBasis(G) : GrpMat -> AlgMatGrp
SymmetricTensorFactors
SymmetricTensorFactors(G) : GrpMat -> SeqEnum
SymmetricTensorPermutations
SymmetricTensorPermutations(G) : GrpMat -> SeqEnum
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)
Syndrome
Syndrome(w, C) : ModTupFldElt, Code -> ModTupFldElt
SyndromeSpace
SyndromeSpace(C) : Code -> ModTupFld
System
System(c)
system
Predefined System Attributes (FUNCTIONS, PROCEDURES AND PACKAGES)
Root Systems (LIE ALGEBRAS)
System Calls (INPUT AND OUTPUT)
System Features (OVERVIEW)
system-calls
System Calls (INPUT AND OUTPUT)
SystemAttributes
Func_SystemAttributes (Example H2E10)
SystemNormaliser
SystemNormalizer(G) : GrpPC -> GrpPC
SystemNormalizer
SystemNormalizer(G) : GrpPC -> GrpPC
syzygy
Syzygy Modules (MODULES OVER AFFINE ALGEBRAS)
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 H29E27)
Sz
SuzukiGroup(arguments)
[____] [____] [_____] [____] [__] [Index] [Root]