[____] [____] [_____] [____] [__] [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 }
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: parameters) : Process(Tietze) ->
Sec
Sec(c) : FldComElt -> FldComElt
Sech
Sech(s) : FldPrElt -> FldPrElt
select
Expression (OVERVIEW)
The select expression (OVERVIEW)
Self
Self(n) : RngIntElt -> Elt
Seq_Self (Example H5E5)
semantics
MAGMA SEMANTICS
Semantics (MAGMA LANGUAGE)
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 H17E17)
GrpPerm_Series (Example H16E17)
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 (SYSTEM FEATURES)
Set(F) : FldFin -> SetEnum
Set(B) : IncBlk -> { IncPt }
Set(l) : PlaneLn -> { PlanePt }
Set(R) : RngIntRes -> SetEnum
Set(M) : Struct -> SetEnum
GrpPC_Set (Example H15E3)
set
Automorphism Group of a Design or Set System (GRAPHS)
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 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 (SYSTEM FEATURES)
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 ->
SetMemoryExtensionSize
SetMemoryExtensionSize(n) : RngIntElt ->
SetMemoryLimit
SetMemoryLimit(n) : RngIntElt ->
SetOperations
GrpPerm_SetOperations (Example H16E11)
Grp_SetOperations (Example H11E12)
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 ->
SetRows
SetRows(n) : RngIntElt ->
sets
Creating Point-Sets and Block-Sets (INCIDENCE STRUCTURES AND DESIGNS)
Creating Point-Sets and Line-Sets (FINITE PLANES)
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, BoolElt ->
SetVerbose("Groebner", v) : MonStgElt, BoolElt ->
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() : -> Ids
ShowPrevious
ShowPrevious() : ->
ShowValues
ShowValues() : -> Vals
Sign
Sign(s) : FldPrElt -> RngIntElt
Sign(q) : FldRatElt -> RngIntElt
Sign(n) : RngIntElt -> RngIntElt
Sign(p) : RngMPolElt -> RngIntElt
Sign(p) : RngUPolElt -> RngIntElt
sign
Absolute Value and Sign (RATIONAL FIELD)
Signature
Signature(K) : FldQuad -> RngIntElt
Signature(O) : RngOrd -> RngIntElt, RngIntElt
signature
Signature (OVERVIEW)
simgps
Database of Simple Groups: Permutations, Presentations, Conjugacy Classes, Maximal Subgroups and Sylow Subgroups (OVERVIEW)
simple
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 Element Functions (REAL AND COMPLEX FIELDS)
SimpleSubgroups
SimpleSubgroups(G: parameters) : GrpFin -> [ rec< Grp, RngIntElt, RngIntElt, GrpFP> ]
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)
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(n, q) : RngIntElt, RngIntElt -> GrpMat
Slope
Slope(l) : PlaneLn -> FldFinElt
smaller
Comparison (OVERVIEW)
Smash
Smash(~MGT, ~S, mode) : SetCartElt, [GrpMatElt], MonStgElt ->
Smash1
GrpMat_Smash1 (Example H17E18)
Smash2
GrpMat_Smash2 (Example H17E19)
SmithForm
SmithForm(a) : AlgMatElt -> AlgMatElt, AlgMatElt, AlgMatElt
SmithForm(a) : ModMatRngElt -> ModMatRngElt, ModMatRngElt, ModMatRngElt
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)
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)
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))
SolvableResidual
SolubleResidual(G) : GrpFin -> GrpFin
SolubleResidual(G) : GrpMat -> GrpMat
SolubleResidual(G) : GrpPerm -> GrpPerm
SolvableSubgroups
SolubleSubgroups(G: parameters) : GrpFin -> [ rec< Grp, RngIntElt, RngIntElt, GrpFP> ]
Sort
Sort(~S) : SeqEnum ->
Sp
SymplecticGroup(n, q) : RngIntElt, RngIntElt -> GrpMat
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)
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
Spec files (MAGMA LANGUAGE)
User startup spec file list (MAGMA LANGUAGE)
Lang_spec (Example H1E24)
special
Other Element Functions (RESIDUE CLASS RINGS)
Other Special Functions (REAL AND COMPLEX FIELDS)
Special Options (REAL AND COMPLEX FIELDS)
SpecialLinearGroup
SpecialLinearGroup(n, q) : RngIntElt, RngIntElt -> GrpMat
SpecialUnitaryGroup
SpecialUnitaryGroup(n, q) : RngIntElt, RngIntElt -> GrpMat
Spectrum
Spectrum(G) : GrphUnd -> SetEnum
Sphere
Sphere(u, n) : Vert, RngIntElt -> { Vert }
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) : RngMPolElt, RngMPolElt -> RngMPolElt
Sqrt
Sqrt(a) : FldLocElt -> FldLocElt
Sqrt(a) : RngIntResElt -> RngIntResElt
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(p) : RngMPolElt -> [ <RngMPolElt, RngIntElt> ]
SquareFreeFactorization(p) : RngUPolElt -> [ <RngUPolElt, RngIntElt> ]
SquareRoot
Sqrt(a) : RngIntResElt -> RngIntResElt
SquareRoot(c) : FldComElt -> FldComElt
SquareRoot(a) : FldFinElt -> FldFinElt
SquareRoot(f) : RngPowElt -> RngPowElt
Stab
Plane_Stab (Example H43E6)
Stabiliser
Stabilizer(G, Y, y) : GrpPerm, GSet, Elt -> GrpPerm
Stabilizer
Stabilizer(G, y) : GrpMat, Elt -> GrpMat
Stabilizer(G, Y, y) : GrpPerm, GSet, Elt -> GrpPerm
Stabilizer(A, u) : GrpPerm, IncPt -> GrpPerm
Stabilizer(A, u) : GrpPerm, PlanePt -> GrpPerm
Stabilizer(A, u) : GrpPerm, Vert -> GrpPerm
stabilizer
Images, Orbits and Stabilizers (MATRIX GROUPS)
Images, Orbits and Stabilizers (PERMUTATION GROUPS)
Stabilizers of Points and Blocks (INCIDENCE STRUCTURES AND DESIGNS)
Stabilizers of Points and Lines (FINITE PLANES)
Stabilizers of Vertices and Edges (GRAPHS)
Stabilizers
GrpPerm_Stabilizers (Example H16E12)
Standard
GrpPC_Standard (Example H15E2)
standard
Construction of a Classical Matrix Group (MATRIX GROUPS)
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)
Standard Constructions (ABELIAN GROUPS)
Standard Groups and Extensions (FINITELY PRESENTED GROUPS)
Standard Groups and Extensions (GROUPS)
Standard Groups and Extensions (MATRIX GROUPS)
Standard Groups and Extensions (PERMUTATION GROUPS)
Standard Presentation Algorithm (SOLUBLE GROUPS)
The Standard Form (ERROR-CORRECTING CODES)
standard-construction
Standard Constructions (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 H44E14)
StandardGroup
StandardGroup(G) : GrpPerm -> GrpPerm, Map
StandardGroups
GrpPerm_StandardGroups (Example H16E7)
Grp_StandardGroups (Example H11E6)
StandardPresentation
StandardPresentation(F, p, c: parameters): GrpFP, RngIntElt, RngIntElt -> GrpPC, Map, [Map]
GrpPC_StandardPresentation (Example H15E6)
StandardPresentationProcess
StandardPresentationProcess(F, p, k : parameters): GrpFP, RngIntElt, RngIntElt -> StdPresP
start
Loading files (OVERVIEW)
Overview (OVERVIEW)
start-up
Loading files (OVERVIEW)
starting
Starting and Terminating (MAGMA LANGUAGE)
starting-quitting
Starting and Terminating (MAGMA LANGUAGE)
startup
Loading files (OVERVIEW)
User startup spec file list (MAGMA LANGUAGE)
startup-spec
User startup spec file list (MAGMA LANGUAGE)
Lang_startup-spec (Example H1E25)
statement
Statements (OVERVIEW)
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
StirlingSecond
StirlingSecond(m, n) : RngIntElt, RngIntElt -> RngIntElt
stop
Control-C key (OVERVIEW)
Quitting (OVERVIEW)
storage
Identifiers and variables (OVERVIEW)
store
Identifiers and variables (OVERVIEW)
string
Strings (MAGMA LANGUAGE)
Strings (OVERVIEW)
Strings
Lang_Strings (Example H1E29)
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)
structs
The Structures Associated with a Plane (FINITE PLANES)
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)
Construction of an Incidence Structure (INCIDENCE STRUCTURES AND DESIGNS)
Construction of Incidence Structures and Designs (INCIDENCE STRUCTURES AND DESIGNS)
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)
Magmas (or Structures) (OVERVIEW)
Normal Structure and Characteristic Subgroups (ABELIAN GROUPS)
Normal Structure and Characteristic Subgroups (SOLUBLE GROUPS)
Structure of a Module (GENERAL MODULES)
Structure Operations (CYCLOTOMIC FIELDS)
Structure Operations (ELLIPTIC CURVES)
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 Normal Structure of a Primitive Group (PERMUTATION GROUPS)
The Subgroup Structure (ABELIAN GROUPS)
The Subgroup Structure (SOLUBLE GROUPS)
StructureConstant
StructureConstant(G, i, j, k) : Grp, RngIntElt, RngIntElt, RngIntElt -> RngIntElt
structures
Incidence Structures, Graphs and Codes (FINITE PLANES)
Incidence Structures, Graphs and Codes (INCIDENCE STRUCTURES AND DESIGNS)
SU
SpecialUnitaryGroup(n, q) : RngIntElt, RngIntElt -> GrpMat
sub
Constructor (OVERVIEW)
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, VertSet, EdgeSet
sub<G | L> : GrpMat, List -> GrpMat
sub<G | L> : GrpPC, List -> GrpPC, Map
sub<G | L> : GrpPerm, List -> GrpPerm
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 H43E3)
SubAlgebra
AlgMat_SubAlgebra (Example H38E4)
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 H11E4)
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 H16E16)
SubgroupLattice
SubgroupLattice(G) : GrpFin -> SubGrpLat
SubgroupOps
GrpFP_SubgroupOps (Example H14E19)
Subgroups
SubgroupClasses(G: parameters) : GrpFin -> [ rec< Grp, RngIntElt, RngIntElt, GrpFP> ]
GrpMat_Subgroups (Example H17E7)
Grp_Subgroups (Example H11E14)
Subgroups1
GrpFP_Subgroups1 (Example H14E14)
Subgroups2
GrpFP_Subgroups2 (Example H14E15)
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 H36E16)
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)
SubmoduleLattice
SubmoduleLattice(M) : ModRng -> ModLat, BoolElt
SubmoduleLatticeAbort
SubmoduleLatticeAbort(M, N) : ModRng, RngIntElt -> BoolElt, ModLat
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 ]
subplane
Subplanes (FINITE PLANES)
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)
subset
x in R : AlgMatElt, AlgMat -> BoolElt
[Future release] x in I : AlgMatElt, AlgMatIdl -> 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
e subset f : ModLatElt, ModLatElt -> ModLatElt
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 : SubGrpLatElt, SubGrpLatElt -> SubGrpLatElt
S subset T : VertSet, VertSet -> BoolElt
S subset G : { GrpAbElt } , GrpAb -> 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 l : { PlanePt }, PlaneLn -> BoolElt
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 H35E7)
Subspace2
KMod_Subspace2 (Example H35E8)
Substitute
Substitute(u, f, n, v) : GrpFPElt, RngIntElt, RngIntElt, GrpFPElt -> GrpFPElt
Substitute(u, f, n, v) : SgpFPElt, RngIntElt, SgpFPElt, RngIntElt -> SgpFPElt
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(p) : RngMPolElt -> RngIntElt
SumNorm(p) : RngUPolElt -> RngIntElt
supergraph
Subgraphs, Quotient Graphs, and Super-graphs (GRAPHS)
Support
Support(u) : AlgFPElt -> [ MonElt ]
[Future release] Support(V) : GrpFPCos -> { GSetElt }
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
The Support (MATRIX GROUPS)
Suzuki
GrpMat_Suzuki (Example H17E10)
SuzukiGroup
SuzukiGroup(q) : RngIntElt -> GrpMat
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) : Vert -> Grph
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 H16E1)
Sym8
GrpFP_Sym8 (Example H14E10)
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 H14E3)
Symmetric2
GrpFP_Symmetric2 (Example H14E4)
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 H17E9)
SymplecticGroup
SymplecticGroup(n, q) : RngIntElt, RngIntElt -> GrpMat
SymTensorProdInfoTup
SymTensorProdInfoTup(MGT) : SetCartElt -> SetCartElt
SymTensorProdTup
SymTensorProdTup(MGT) : SetCartElt -> MonStgElt
Syndrome
Syndrome(w, C) : ModTupFldElt, Code -> ModTupFldElt
SyndromeSpace
SyndromeSpace(C) : Code -> ModTupFld
System
System(c)
system
Automorphism Group of a Design or Set System (GRAPHS)
System Calls (SYSTEM FEATURES)
System Features (OVERVIEW)
SystemNormaliser
SystemNormalizer(G) : GrpPC -> GrpPC
SystemNormalizer
SystemNormalizer(G) : GrpPC -> GrpPC
syzygy
Syzygy Modules (MULTIVARIATE POLYNOMIAL RINGS)
syzygy-module
Syzygy Modules (MULTIVARIATE POLYNOMIAL RINGS)
SyzygyModule
SyzygyModule(Q) : [ RngMPolElt ] -> ModTupRng
RngMPol_SyzygyModule (Example H25E22)
Sz
SuzukiGroup(q) : RngIntElt -> GrpMat
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