# The GAP 4 Reference Manual - Index S

_ A B C D E F G H I J K L M N O P Q R S T U V W X Y Z

s_N 18.4
SameBlock 69.9.2
SandwichMatrixOfReesMatrixSemigroup 49.6.7
SandwichMatrixOfReesZeroMatrixSemigroup 49.6.7
save 3.11
SaveOnExitFile 6.7.3
SaveWorkspace 3.11.1
Saving a Pc Group 44.6
Saving and Loading a Workspace 3.11
saving on exit 6.7
ScalarProduct, for characters 70.8.5
Schreier 46.3
Schreier-Sims, random 41.6
Schur Covers and Multipliers 37.24
Schur multiplier 37.24
SchurCover 37.24.2
scope 4.8
ScriptFromString 68.10.2
Searching for Homomorphisms 38.9
SecHMSM 26.8.8
secondary subgroup generators 46.11
SecondsDMYhms 26.8.10
SeekPositionStream 10.3.10
Selecting a Different MeatAxe 67.3
Selection Functions 48.5
Semidirect Products 47.2
SemidirectProduct 47.2.1
SemiEchelonBasis 59.8.8
SemiEchelonBasisNC 59.8.8
SemiEchelonMat 24.9.1
SemiEchelonMatDestructive 24.9.2
SemiEchelonMats 24.9.4
SemiEchelonMatsDestructive 24.9.5
SemiEchelonMatTransformation 24.9.3
Semigroup 49.0 49.0
semigroup 49.0
SemigroupByGenerators 49.0
SemigroupByMultiplicationTable 49.0
SemigroupIdealByGenerators 49.2.1
SemigroupOfRewritingSystem 51.5.4
Semigroups 49.0
semiregular 39.9
Semisimple Lie Algebras and Root Systems 61.7
SemiSimpleType 61.7.1
sequence, Bernoulli 17.1
sequence, Fibonacci 17.3
sequence, Lucas 17.3
Series of Ideals 61.4
Set 28.2.6
set difference, of collections 28.4
Set Operations via Boolean Lists 22.2
set stabilizer 39.4
SetAssertionLevel 7.5.1
SetCommutator 44.4.4
SetConjugate 44.4.3
SetCrystGroupDefaultAction 42.6.2
SetEntrySCTable 60.3.2
SetGasmanMessageStatus 7.11.2
SetHelpViewer 2.3.1
SetIndeterminateName 64.1.4
SetInfoLevel 7.4.3
SetName 12.8.1
SetParent 30.7.1
SetPower 44.4.5
SetPrintFormattingStatus 10.4.8
SetRecursionTrapInterval 7.10.1
SetReducedMultiplication 45.2.4
Sets 12.3
sets 21.19
Sets of Subgroups 37.19
Setter 13.6.2
setter 13.6
Setter and Tester for Attributes 13.6
SetX 21.21.2
ShallowCopy 12.7.1
ShallowCopy, for lists 21.7
ShiftedCoeffs 23.6.6
ShiftedPadicNumber 66.1.4
Shifting and Trimming Coefficient Lists 23.4
short vectors spanning a lattice 25.5 70.10
ShortestVectors 25.6.2
ShortLexOrdering 29.3.6
ShowArgument 7.1.2
ShowArguments 7.1.1
ShowDetails 7.1.3
ShowImpliedFilters 13.2.3
ShowMethods 7.1.4
ShowOtherMethods 7.1.5
ShrinkCoeffs 23.6.7
ShrinkRowVector 23.4.3
SiftedPcElement 43.5.8
SiftedPermutation 41.9.11
SiftedVector 59.8.12
Sigma 15.4.1
Sign and Cycle Structure 40.3
sign, of an integer 14.1
SignInt 14.1.7
SignPartition 17.2.23
SignPerm 40.3.1
SimpleLieAlgebra 61.2.6
SimpleSystem 61.7.11
SimplifiedFpGroup 46.2 46.2.1
SimplifyPresentation 46.7.2
SimsNo 48.10.2
SimultaneousEigenvalues 24.13.4
SingleCollector 44.4.2
singlequote character 26.1
singlequotes 26.0
SINT_CHAR 26.6.3
Size 28.3.6
Size, for character tables 69.8
Size, for groups with pcgs 43.16
size, of a list or collection 28.3
SizeBlist 22.1.3
SizeConsiderFunction 37.21.4
SizeNumbersPerfectGroups 48.8.6
SizeOfFieldOfDefinition 70.15.3
SizesCentralizers 69.8.6
SizesConjugacyClasses 69.8.7
SizeScreen 6.11 6.11.1
SizesPerfectGroups 48.8.1
SizeStabChain 41.9.3
SL 48.2.2
Small Groups 48.7
smaller or equal 4.11.2
smaller test 4.11.2
smaller, associative words 35.3.2
smaller, elements of finitely presented groups 45.2.2
smaller, nonassociative words 34.2.2
smaller, pcwords 44.2.1
smaller, rational functions 64.3.2
SmallerDegreePermutationRepresentation 41.2.2
SmallestGeneratorPerm 40.1.2
SmallestMovedPoint 40.2.1
SmallestRootInt 14.1.10
SmallGeneratingSet 37.22.4
SmallGroup 48.7.1
SmallGroupsInformation 48.7.8
Smash MeatAxe Flags 67.11
Smith normal form 75.3
SmithNormalFormIntegerMat 25.2.6
SmithNormalFormIntegerMatTransforms 25.2.7
SMTX.AbsoluteIrreducibilityTest 67.10.8
SMTX.AlgEl 67.11.2
SMTX.AlgElCharPol 67.11.4
SMTX.AlgElCharPolFac 67.11.5
SMTX.AlgElMat 67.11.3
SMTX.AlgElNullspaceDimension 67.11.7
SMTX.AlgElNullspaceVec 67.11.6
SMTX.CentMat 67.11.8
SMTX.CentMatMinPoly 67.11.9
SMTX.CompleteBasis 67.10.11
SMTX.Getter 67.10.6
SMTX.GoodElementGModule 67.10.2
SMTX.IrreducibilityTest 67.10.7
SMTX.MatrixSum 67.10.10
SMTX.MinimalSubGModule 67.10.9
SMTX.MinimalSubGModules 67.10.4
SMTX.RandomIrreducibleSubGModule 67.10.1
SMTX.Setter 67.10.5
SMTX.SortHomGModule 67.10.3
SMTX.Subbasis 67.11.1
SO 48.2.7
Socle 37.12.10
SocleTypePrimitiveGroup 41.4.2
SolutionIntMat 25.1.2
SolutionMat 24.6.5
SolutionMatDestructive 24.6.6
SolutionNullspaceIntMat 25.1.3
Some Remarks about Character Theory in GAP 69.1
Some Special Algebras 60.4
Sort 21.18.1
Sorted Character Tables 69.19
sorted list 21.17
Sorted Lists and Sets 21.19
Sorted Lists as Collections 28.2
SortedCharacters 69.19.2
SortedCharacterTable 69.19.4
SortedList 28.2.5
SortedSparseActionHomomorphism 39.6.3
SortedTom 68.5.1
Sortex 21.18.3
Sorting Lists 21.18
Sorting Tables of Marks 68.5
SortingPerm 21.18.4
SortParallel 21.18.2
Source 31.2.8
SourceOfIsoclinicTable 69.18.5
SP 48.2.5
Sp 48.2.5
space 4.4
SparseActionHomomorphism 39.6.3
SparseCartanMatrix 61.7.16
special character sequences 26.1
Special Characters 26.1
Special Filenames 9.5
Special Generating Sets 37.22
Special Multiplication Algorithms for Matrices over GF(2) 24.14
Special Pcgs 43.13
SpecialLinearGroup 48.2.2
SpecialOrthogonalGroup 48.2.7
SpecialPcgs, attribute 43.13.2
SpecialUnitaryGroup 48.2.4
Specific and Parametrized Subgroups 37.12
Specific Methods for Subgroup Lattice Computations 37.21
SplitCharacters 69.15.7
SplitExtension 44.8.6
SplitExtensions 44.8.10
SplitString 26.5.6
SplittingField 64.4.13
Sqrt 30.12.5
square root, of an integer 14.1
SquareRoots 33.4.13
SSortedList 28.2.6
StabChain 41.7.1
StabChainBaseStrongGenerators 41.7.4
StabChainImmutable 41.7.1
StabChainMutable 41.7.1
StabChainOp 41.7.1
StabChainOptions 41.7.2
Stabilizer 39.4.2
Stabilizer Chain Records 41.8
Stabilizer Chains 41.5
StabilizerOfExternalSet 39.11.10
StabilizerPcgs 43.15.1
Stabilizers 39.4
Standard Generators of Groups 68.10
StandardAssociate 54.5.5
StandardGeneratorsFunctions 68.10.3
StandardGeneratorsInfo, for groups 68.10.1
StandardGeneratorsInfo, for tables of marks 68.11.5
StandardGeneratorsOfGroup 68.10.5
Standardization of coset tables 45.6
StandardizeTable 45.6.2
StarCyc 18.5.3
Statements 4.13
StateRandom 28.6.2
Stirling number of the first kind 17.1
Stirling number of the second kind 17.1
Stirling1 17.1.5
Stirling2 17.1.6
StoredGroebnerBasis 64.17.3
StoreFusion 71.2.4
Storing Normal Subgroup Information 69.21
Straight Line Program Elements 35.9
Straight Line Programs 35.8
StraightLineProgElm 35.9.2
StraightLineProgGens 35.9.3
StraightLineProgram 35.8.2
StraightLineProgramNC 35.8.2
StraightLineProgramsTom 68.11.2
Streams 10.0
StreamsFamily 10.1.9
StretchImportantSLPElement 35.9.5
strictly sorted list 21.17
String 26.5.1
String Streams 10.7
String, for cyclotomics 18.1
StringDate 26.8.6
StringOfResultOfStraightLineProgram 35.8.6
StringPP 26.5.3
Strings and Characters 26.0
strings, equality of 26.4.1
strings, inequality of 26.4.1
strings, lexicographic ordering of 26.4.2
StringTime 26.8.9
StrongGeneratorsStabChain 41.9.4
StronglyConnectedComponents 32.4.5
Struct 30.3.1
StructByGenerators 30.3.4
StructuralCopy 12.7.2
StructuralCopy, for lists 21.7
structure constant 69.10
Structure Descriptions 37.6
StructureConstantsTable 59.6.4
StructureDescription 37.6.1
StructWithGenerators 30.3.5
SU 48.2.4
Subalgebra 60.5.1
SubAlgebraModule 60.10.16
SubalgebraNC 60.5.2
Subalgebras 60.5
SubalgebraWithOne 60.5.3
SubalgebraWithOneNC 60.5.4
Subdirect Products 47.3
SubdirectProduct 47.3.1
SubdirectProducts 47.3.2
Subdomains 30.8
Subfield 56.2.1
SubfieldNC 56.2.1
Subfields 56.2.10
Subfields of Fields 56.2
Subgroup 37.3.1
subgroup fusions 71.2
subgroup generators tree 46.11
Subgroup Lattice 37.20
Subgroup Presentations 46.3
Subgroup Series 37.17
SubgroupByPcgs 43.7.9
SubgroupByProperty 37.3.11
SubgroupNC 37.3.1
SubgroupOfWholeGroupByCosetTable 45.7.2
SubgroupOfWholeGroupByQuotientSubgroup 45.12.1
SubgroupProperty 41.11.1
Subgroups 37.3
Subgroups characterized by prime powers 37.14
Subgroups of Polycyclic Groups - Canonical Pcgs 43.8
Subgroups of Polycyclic Groups - Induced Pcgs 43.7
subgroups, polyhedral 69.10
SubgroupShell 37.3.12
SubgroupsSolvableGroup 37.21.3
sublist 21.3
sublist assignment, operation 21.4.3
sublist, access 21.3.2
sublist, assignment 21.4.2
sublist, operation 21.3.3
Submagma 33.2.7
SubmagmaNC 33.2.7
SubmagmaWithInverses 33.2.9
SubmagmaWithInversesNC 33.2.9
SubmagmaWithOne 33.2.8
SubmagmaWithOneNC 33.2.8
Submodule 55.2.1
SubmoduleNC 55.2.2
Submodules 55.2
Submonoid 50.0
SubmonoidNC 50.0
SubnearAdditiveGroup 53.2.9
SubnearAdditiveGroupNC 53.2.9
SubnearAdditiveMagma 53.2.7
SubnearAdditiveMagmaNC 53.2.7
SubnearAdditiveMagmaWithZero 53.2.8
SubnearAdditiveMagmaWithZeroNC 53.2.8
SubnormalSeries 37.17.4
Subring 54.1.8
SubringNC 54.1.8
SubringWithOne 54.3.5
SubringWithOneNC 54.3.5
Subroutines for the Construction of Class Fusions 71.5
Subroutines for the Construction of Power Maps 71.4
Subsemigroup 49.0
SubsemigroupNC 49.0
subset test, for collections 28.4
subsets 17.2
Subspace 59.1.2
SubspaceNC 59.1.2
Subspaces 59.3.1
SubstitutedWord 35.4.5
SubsTom 68.7.1
Substruct 30.8.1
SubstructNC 30.8.2
SubSyllables 35.5.4
subtract, a set from another 21.19
SubtractBlist 22.3.4
subtraction 4.12.1
subtraction, matrices 24.2.3
subtraction, matrix and scalar 24.2.3
subtraction, rational functions 64.2.1
subtraction, scalar and matrix 24.2.3
subtraction, scalar and matrix list 24.2.12
subtraction, scalar and vector 23.1.3
subtraction, vector and scalar 23.1.3
subtraction, vectors 23.1.3
SubtractSet 21.19.8
Subword 35.4.3
Successors 32.2.9
Suitability for Compilation 3.8
Sum 21.20.24
Sum and Intersection of Pcgs 43.12
SumFactorizationFunctionPcgs 43.12.1
SumIntersectionMat 24.10.4
SumX 21.21.3
SupersolvableResiduum 37.12.11
support, email address 73.9
SupportedCharacterTableInfo 69.3.3
SurjectiveActionHomomorphismAttr 39.11.17
SuzukiGroup 48.1.10
Sylow Subgroups and Hall Subgroups 37.13
SylowComplement 37.13.2
SylowSubgroup 37.13.1
SylowSystem 37.13.4
Symbols 4.3
Symmetric and Alternating Groups 41.3
symmetric group, powermap 17.2
symmetric relation 32.2
SymmetricClosureBinaryRelation 32.4.2
SymmetricGroup 48.1.8
SymmetricParentGroup 41.3.5
SymmetricParts 70.11.2
SymmetricPowerOfAlgebraModule 61.14.3
Symmetrizations 70.11.1
Symmetrizations of Class Functions 70.11
symmetrizations, orthogonal 70.11
symmetrizations, symplectic 70.11
SymplecticComponents 70.11.5
SymplecticGroup 48.2.5
syntax errors 6.1
Sz 48.1.10

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GAP 4 manual
August 2005