# The GAP 4 Reference Manual - Index R

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r_N 18.4
RadicalGroup 37.12.9
RadicalOfAlgebra 60.8.16
Random 14.5.2
random element, of a list or collection 28.6
Random Elements 28.6
Random Isomorphism Testing 44.10
Random Matrices 24.5
random seed 28.6
Random Sources 14.5
Random, [coll] 28.6.1
Random, for integers 14.1.11
Random, for rationals 16.1.7
RandomBinaryRelationOnPoints 32.3.2
RandomInvertibleMat 24.5.2
RandomIsomorphismTest 44.10.1
Randomized Methods for Permutation Groups 41.6
RandomList 28.6.4
RandomMat 24.5.1
RandomPrimitivePolynomial 57.5.3
RandomSource 14.5.5
RandomTransformation 52.0
RandomUnimodularMat 24.5.3
Range 31.2.7
range 21.22
Ranges 21.22
RankAction 39.9.3
RankFilter 13.2.1
RankMat 24.6.1
RankOfTransformation 52.0
RankPGroup 37.15.17
Rat 16.1.6
Rat, for strings 26.7.1
Rational Function Families 64.18
Rational Numbers 16.0
RationalClass 37.10.6
RationalClasses 37.10.7
RationalFunctionByExtRep 64.21.1
RationalFunctionByExtRepNC 64.21.1
RationalFunctionByExtRepWithCancellation 64.23.1
RationalFunctionsFamily 64.18.1
RationalizedMat 18.5.6
Rationals 16.0
RClassOfHClass 49.5.5
Read 9.7.1
read eval print loop 6.1
Read, for streams 10.3.1
ReadAll 10.3.6
ReadAllLine 10.8.3
ReadAsFunction 9.7.2
ReadAsFunction, for streams 10.3.2
ReadByte 10.3.4
ReadLine 10.3.5
ReadPackage 74.3.1
ReadPkg 75.2
ReadTest 7.9.1
ReadTest, for streams 10.3.3
RealClasses 69.8.15
RealizableBrauerCharacters 70.15.4
RecNames 27.0
Recognizing Characters 26.3
Record Access Operations 27.6
Record Assignment 27.2
record assignment, operation 27.6.3
record boundness test, operation 27.6.3
record component, operation 27.6.3
record unbind, operation 27.6.3
record, component access 27.1.1
record, component assignment 27.2.1
record, component variable 27.1.2
record, component variable assignment 27.2.2
Records 27.0
Recovery from NoMethodFound-Errors 7.1
recursion 4.22
redisplay a help section 2.2.6
redisplay with next help viewer 2.2.6
ReduceCoeffs 23.6.3
ReduceCoeffsMod 23.6.4
ReducedAdditiveInverse 36.2.4
ReducedCharacters 70.10.2
ReducedClassFunctions 70.10.1
ReducedComm 36.2.5
ReducedConfluentRewritingSystem 51.5.1
ReducedConjugate 36.2.6
ReducedDifference 36.2.7
ReducedForm 36.1.4
ReducedGroebnerBasis 64.17.2
ReducedInverse 36.2.8
ReducedLeftQuotient 36.2.9
ReducedOne 36.2.3
ReducedPcElement 43.5.10
ReducedPower 36.2.10
ReducedProduct 36.2.1
ReducedQuotient 36.2.11
ReducedScalarProduct 36.2.12
ReducedSum 36.2.2
ReducedZero 36.2.13
ReduceRules 36.1.8
ReduceStabChain 41.10.5
Reducing Virtual Characters 70.10
Ree 48.1.11
ReeGroup 48.1.11
Rees Matrix Semigroups 49.6
ReesCongruenceOfSemigroupIdeal 49.2.2
ReesMatrixSemigroup 49.6.1
ReesMatrixSemigroupElement 49.6.5
ReesZeroMatrixSemigroup 49.6.2
ReesZeroMatrixSemigroupElement 49.6.5
ReesZeroMatrixSemigroupElementIsZero 49.6.9
RefinedPcGroup 44.4.9
ReflectionMat 24.4.9
reflexive relation 32.2
ReflexiveClosureBinaryRelation 32.4.1
regular 39.9
regular action 39.6
RegularActionHomomorphism 39.7.2
RegularModule 69.13.3
Relations 32.0
relations 31.0
Relations Between Domains 30.13
RelationsOfFpSemigroup 51.3.3
RelativeBasis 59.4.4
RelativeBasisNC 59.4.4
relatively prime 4.12
RelativeOrderOfPcElement 43.5.1
RelativeOrders, of a pcgs 43.4.1
Relators in a Presentation 46.4
RelatorsOfFpGroup 45.3.3
remainder of a quotient 14.2
remainder, operation 30.12.1
RemInt 14.2.3
Remove 21.4.5
remove, an element from a set 21.19
RemoveCharacters 26.5.10
RemoveFile 9.7.12
RemoveOuterCoeffs 23.4.4
RemoveRelator 46.6.4
RemoveSet 21.19.5
RemoveStabChain 41.10.6
Repeat 4.18
repeat loop 4.18.1
Replaced and Removed Command Names 75.0
ReplacedString 26.5.7
Representation 13.4
representation, as a sum of two squares 15.6
Representations for Associative Words 35.6
Representations for Group Homomorphisms 38.10
Representations given by modules 69.13
Representations of Algebras 60.10
RepresentationsOfObject 13.4.1
Representative 28.3.7
representative, of a list or collection 28.3
RepresentativeAction 39.5.1
RepresentativeLinearOperation 60.9.12
RepresentativeOperation 75.1
RepresentativesContainedRightCosets 37.9.2
RepresentativesFusions 71.2.8
RepresentativeSmallest 28.3.8
RepresentativesMinimalBlocks 39.10.3
RepresentativesPerfectSubgroups 37.20.5
RepresentativesPowerMaps 71.1.6
RepresentativesSimpleSubgroups 37.20.5
RepresentativeTom 68.11.4
RepresentativeTomByGenerators 68.11.4
RepresentativeTomByGeneratorsNC 68.11.4
RequirePackage 75.2
Reread 9.7.13
REREADING 9.7.13
RereadPackage 74.3.1
RereadPkg 75.2
Reset 14.5.3
ResetOptionsStack 8.0
Residue Class Rings 14.4
residue, quadratic 15.3
RespectsAddition 31.9.1
RespectsAdditiveInverses 31.9.2
RespectsInverses 31.8.3
RespectsMultiplication 31.8.1
RespectsOne 31.8.2
RespectsScalarMultiplication 31.10.1
RespectsZero 31.9.3
RestoreStateRandom 28.6.2
Restricted and Induced Class Functions 70.9
Restricted Lie algebras 61.8
RestrictedClassFunction 70.9.1
RestrictedClassFunctions 70.9.2
RestrictedMapping 31.1.12
RestrictedPartitions 17.2.21
RestrictedPerm 40.4.4
RestrictedPermNC 40.4.4
RestrictedTransformation 52.0
RestrictOutputsOfSLP 35.8.9
Resultant 64.6.7
ResultOfStraightLineProgram 35.8.5
Return 4.23
return 6.4
return from break loop 6.4.2
return, no value 4.23.1
return, with value 4.23.2
ReturnFail 5.3.3
ReturnFalse 5.3.2
ReturnTrue 5.3.1
Reversed 21.20.7
RewindStream 10.3.9
RewriteWord 45.8.4
Rewriting in Groups and Monoids 36.4
Rewriting Systems 36.0
Rewriting Systems and the Knuth-Bendix Procedure 51.5
right cosets 37.7
RightActingAlgebra 60.10.12
RightActingRingOfIdeal 54.2.10
RightAlgebraModule 60.10.5
RightAlgebraModuleByGenerators 60.10.2
RightCoset 37.7.1
RightCosets 37.7.2
RightCosetsNC 37.7.2
RightDerivations 61.2.5
RightIdeal 54.2.1
RightIdealByGenerators 54.2.6
RightIdealNC 54.2.2
RightModuleByHomomorphismToMatAlg 60.10.18
RightShiftRowVector 23.4.2
RightTransversal 37.8.1
Ring 54.1.2
Ring Homomorphisms 31.11
RingByGenerators 54.1.4
Rings 54.0
Rings With One 54.3
RingWithOne 54.3.2
RingWithOneByGenerators 54.3.3
RNamObj 27.6.2
root, of 1 modulo an integer 15.3
root, of an integer 14.1
root, of an integer modulo another 15.3
root, of an integer, smallest 14.1
RootInt 14.1.9
RootMod 15.3.3
RootOfDefiningPolynomial 56.2.8
Roots Modulo Integers 15.3
roots of unity 18.1
RootsMod 15.3.4
RootsOfUPol 64.5.4
RootsUnityMod 15.3.5
RootSystem 61.7.5
RoundCyc 18.1.7
Row and Matrix Spaces 59.8
row spaces 59.8
Row Vectors 23.0
Row Vectors over Finite Fields 23.2
RowIndexOfReesMatrixSemigroupElement 49.6.8
RowIndexOfReesZeroMatrixSemigroupElement 49.6.8
Rules 36.1.2
Running GAP 3.0
Running GAP under MacOS 3.3
Runtime 7.6.2
Runtimes 7.6.1

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GAP 4 manual
October 2007