arithmoi-0.11.0.1: Efficient basic number-theoretic functions.

Index

:+ 
1 (Data Constructor)Math.NumberTheory.Quadratic.GaussianIntegers
2 (Data Constructor)Math.NumberTheory.Quadratic.EisensteinIntegers
additiveMath.NumberTheory.ArithmeticFunctions
additiveSieveBlockConfigMath.NumberTheory.ArithmeticFunctions.SieveBlock
allCharsMath.NumberTheory.DirichletCharacters
approxPrimeCountMath.NumberTheory.Primes.Counting
approxPrimeCountOverestimateLimitMath.NumberTheory.Primes.Counting
ArithmeticFunction 
1 (Type/Class)Math.NumberTheory.ArithmeticFunctions
2 (Data Constructor)Math.NumberTheory.ArithmeticFunctions
asSetOfPreimagesMath.NumberTheory.ArithmeticFunctions.Inverse
associatesMath.NumberTheory.Quadratic.EisensteinIntegers
bailliePSWMath.NumberTheory.Primes.Testing
bernoulliMath.NumberTheory.Recurrences.Bilinear, Math.NumberTheory.Recurrences
betasMath.NumberTheory.Zeta
betasOddMath.NumberTheory.Zeta
bigOmegaMath.NumberTheory.ArithmeticFunctions
bigOmegaAMath.NumberTheory.ArithmeticFunctions
binomialMath.NumberTheory.Recurrences.Bilinear, Math.NumberTheory.Recurrences
binomialDiagonalMath.NumberTheory.Recurrences.Bilinear, Math.NumberTheory.Recurrences
binomialFactorsMath.NumberTheory.Recurrences.Bilinear, Math.NumberTheory.Recurrences
binomialLineMath.NumberTheory.Recurrences.Bilinear, Math.NumberTheory.Recurrences
binomialRotatedMath.NumberTheory.Recurrences.Bilinear, Math.NumberTheory.Recurrences
carmichaelMath.NumberTheory.ArithmeticFunctions
carmichaelAMath.NumberTheory.ArithmeticFunctions
CG2Math.NumberTheory.Moduli.Singleton, Math.NumberTheory.Moduli
CG4Math.NumberTheory.Moduli.Singleton, Math.NumberTheory.Moduli
CGDoubleOddPrimePowerMath.NumberTheory.Moduli.Singleton, Math.NumberTheory.Moduli
CGOddPrimePowerMath.NumberTheory.Moduli.Singleton, Math.NumberTheory.Moduli
characterNumberMath.NumberTheory.DirichletCharacters
chineseMath.NumberTheory.Moduli.Chinese, Math.NumberTheory.Moduli
chineseCoprimeMath.NumberTheory.Moduli.Chinese, Math.NumberTheory.Moduli
chineseCoprimeSomeModMath.NumberTheory.Moduli.Chinese, Math.NumberTheory.Moduli
chineseRemainderMath.NumberTheory.Moduli.Chinese, Math.NumberTheory.Moduli
chineseRemainder2Math.NumberTheory.Moduli.Chinese, Math.NumberTheory.Moduli
chineseSomeModMath.NumberTheory.Moduli.Chinese, Math.NumberTheory.Moduli
conjugate 
1 (Function)Math.NumberTheory.Quadratic.GaussianIntegers
2 (Function)Math.NumberTheory.Quadratic.EisensteinIntegers
coprimeMath.NumberTheory.Euclidean
CoprimesMath.NumberTheory.Euclidean.Coprimes
CyclicGroupMath.NumberTheory.Moduli.Singleton, Math.NumberTheory.Moduli
cyclicGroupMath.NumberTheory.Moduli.Singleton, Math.NumberTheory.Moduli
cyclicGroupFromFactorsMath.NumberTheory.Moduli.Singleton, Math.NumberTheory.Moduli
cyclicGroupFromModuloMath.NumberTheory.Moduli.Singleton, Math.NumberTheory.Moduli
cyclicGroupToSFactorsMath.NumberTheory.Moduli.Singleton, Math.NumberTheory.Moduli
degreeMath.NumberTheory.Euclidean
DirichletCharacterMath.NumberTheory.DirichletCharacters
discreteLogarithmMath.NumberTheory.Moduli.Multiplicative, Math.NumberTheory.Moduli.DiscreteLogarithm, Math.NumberTheory.Moduli
divideMath.NumberTheory.Euclidean
divisorCountMath.NumberTheory.ArithmeticFunctions
divisorsMath.NumberTheory.ArithmeticFunctions
divisorsAMath.NumberTheory.ArithmeticFunctions
divisorsListMath.NumberTheory.ArithmeticFunctions
divisorsListAMath.NumberTheory.ArithmeticFunctions
divisorsSmallMath.NumberTheory.ArithmeticFunctions
divisorsSmallAMath.NumberTheory.ArithmeticFunctions
divisorsToMath.NumberTheory.ArithmeticFunctions
divisorsToAMath.NumberTheory.ArithmeticFunctions
EisensteinIntegerMath.NumberTheory.Quadratic.EisensteinIntegers
EuclideanMath.NumberTheory.Euclidean
eulerMath.NumberTheory.Recurrences.Bilinear, Math.NumberTheory.Recurrences
eulerian1Math.NumberTheory.Recurrences.Bilinear, Math.NumberTheory.Recurrences
eulerian2Math.NumberTheory.Recurrences.Bilinear, Math.NumberTheory.Recurrences
eulerPolyAt1Math.NumberTheory.Recurrences.Bilinear, Math.NumberTheory.Recurrences
evalMath.NumberTheory.DirichletCharacters
evalAllMath.NumberTheory.DirichletCharacters
evalGeneralMath.NumberTheory.DirichletCharacters
exactCubeRootMath.NumberTheory.Powers.Cubes, Math.NumberTheory.Powers
exactFourthRootMath.NumberTheory.Powers.Fourth, Math.NumberTheory.Powers
exactRootMath.NumberTheory.Powers.General, Math.NumberTheory.Powers
exactSquareRootMath.NumberTheory.Powers.Squares, Math.NumberTheory.Powers
expMangoldtMath.NumberTheory.ArithmeticFunctions
expMangoldtAMath.NumberTheory.ArithmeticFunctions
extendedGCDMath.NumberTheory.Euclidean
factorBackMath.NumberTheory.Primes
factorialMath.NumberTheory.Recurrences.Linear, Math.NumberTheory.Recurrences
factorialFactorsMath.NumberTheory.Recurrences.Linear, Math.NumberTheory.Recurrences
factoriseMath.NumberTheory.Primes
faulhaberPolyMath.NumberTheory.Recurrences.Bilinear, Math.NumberTheory.Recurrences
fibonacciMath.NumberTheory.Recurrences.Linear, Math.NumberTheory.Recurrences
fibonacciPairMath.NumberTheory.Recurrences.Linear, Math.NumberTheory.Recurrences
findPrime 
1 (Function)Math.NumberTheory.Quadratic.GaussianIntegers
2 (Function)Math.NumberTheory.Quadratic.EisensteinIntegers
fromFactorsMath.NumberTheory.Prefactored
fromListMath.NumberTheory.SmoothNumbers
fromRootOfUnityMath.NumberTheory.DirichletCharacters
fromTableMath.NumberTheory.DirichletCharacters
fromValueMath.NumberTheory.Prefactored
GaussianIntegerMath.NumberTheory.Quadratic.GaussianIntegers
gcdMath.NumberTheory.Euclidean
GcdDomainMath.NumberTheory.Euclidean
generalInversionMath.NumberTheory.MoebiusInversion
generalLucasMath.NumberTheory.Recurrences.Linear, Math.NumberTheory.Recurrences
getModMath.NumberTheory.Moduli.Class, Math.NumberTheory.Moduli
getNatModMath.NumberTheory.Moduli.Class, Math.NumberTheory.Moduli
getNatValMath.NumberTheory.Moduli.Class, Math.NumberTheory.Moduli
getPrimitiveCharMath.NumberTheory.DirichletCharacters
getRealCharMath.NumberTheory.DirichletCharacters
getValMath.NumberTheory.Moduli.Class, Math.NumberTheory.Moduli
highestPowerMath.NumberTheory.Powers.General, Math.NumberTheory.Powers
idsMath.NumberTheory.Quadratic.EisensteinIntegers
imag 
1 (Function)Math.NumberTheory.Quadratic.GaussianIntegers
2 (Function)Math.NumberTheory.Quadratic.EisensteinIntegers
indexToCharMath.NumberTheory.DirichletCharacters
indicesToCharsMath.NumberTheory.DirichletCharacters
inducedMath.NumberTheory.DirichletCharacters
InfinityMath.NumberTheory.ArithmeticFunctions.Inverse
InfModMath.NumberTheory.Moduli.Class, Math.NumberTheory.Moduli
insertMath.NumberTheory.Euclidean.Coprimes
integerCubeRootMath.NumberTheory.Powers.Cubes, Math.NumberTheory.Powers
integerCubeRoot'Math.NumberTheory.Powers.Cubes
integerFourthRootMath.NumberTheory.Powers.Fourth, Math.NumberTheory.Powers
integerFourthRoot'Math.NumberTheory.Powers.Fourth
integerRootMath.NumberTheory.Powers.General, Math.NumberTheory.Powers
integerSquareRootMath.NumberTheory.Powers.Squares, Math.NumberTheory.Powers
integerSquareRoot'Math.NumberTheory.Powers.Squares
integerSquareRootRemMath.NumberTheory.Powers.Squares
integerSquareRootRem'Math.NumberTheory.Powers.Squares
inverseJordanMath.NumberTheory.ArithmeticFunctions.Inverse
inverseSigmaMath.NumberTheory.ArithmeticFunctions.Inverse
inverseSigmaKMath.NumberTheory.ArithmeticFunctions.Inverse
inverseTotientMath.NumberTheory.ArithmeticFunctions.Inverse
invertGroupMath.NumberTheory.Moduli.Multiplicative, Math.NumberTheory.Moduli.Class, Math.NumberTheory.Moduli
invertModMath.NumberTheory.Moduli.Class, Math.NumberTheory.Moduli
invertSomeModMath.NumberTheory.Moduli.Class, Math.NumberTheory.Moduli
isCertifiedPrimeMath.NumberTheory.Primes.Testing
isCubeMath.NumberTheory.Powers.Cubes, Math.NumberTheory.Powers
isCube'Math.NumberTheory.Powers.Cubes
isFermatPPMath.NumberTheory.Primes.Testing
isFourthPowerMath.NumberTheory.Powers.Fourth, Math.NumberTheory.Powers
isFourthPower'Math.NumberTheory.Powers.Fourth
isKthPowerMath.NumberTheory.Powers.General, Math.NumberTheory.Powers
isMultElementMath.NumberTheory.Moduli.Multiplicative, Math.NumberTheory.Moduli.Class, Math.NumberTheory.Moduli
isNFreeMath.NumberTheory.ArithmeticFunctions
isNFreeAMath.NumberTheory.ArithmeticFunctions
isPerfectPowerMath.NumberTheory.Powers.General, Math.NumberTheory.Powers
isPossibleCubeMath.NumberTheory.Powers.Cubes
isPossibleFourthPowerMath.NumberTheory.Powers.Fourth
isPossibleSquareMath.NumberTheory.Powers.Squares
isPossibleSquare2Math.NumberTheory.Powers.Squares
isPrime 
1 (Function)Math.NumberTheory.Primes.Testing
2 (Function)Math.NumberTheory.Primes
isPrimitiveMath.NumberTheory.DirichletCharacters
isPrimitiveRootMath.NumberTheory.Moduli.Multiplicative, Math.NumberTheory.Moduli.PrimitiveRoot, Math.NumberTheory.Moduli
isPrincipalMath.NumberTheory.DirichletCharacters
isRealCharacterMath.NumberTheory.DirichletCharacters
isSmoothMath.NumberTheory.SmoothNumbers
isSquareMath.NumberTheory.Powers.Squares, Math.NumberTheory.Powers
isSquare'Math.NumberTheory.Powers.Squares
isStrongFermatPPMath.NumberTheory.Primes.Testing
isUnitMath.NumberTheory.Euclidean
jacobiMath.NumberTheory.Moduli.Jacobi, Math.NumberTheory.Moduli.Sqrt, Math.NumberTheory.Moduli
jacobiCharacterMath.NumberTheory.DirichletCharacters
JacobiSymbolMath.NumberTheory.Moduli.Jacobi, Math.NumberTheory.Moduli.Sqrt, Math.NumberTheory.Moduli
jordanMath.NumberTheory.ArithmeticFunctions
jordanAMath.NumberTheory.ArithmeticFunctions
KnownNatMath.NumberTheory.Moduli.Class, Math.NumberTheory.Moduli
lahMath.NumberTheory.Recurrences.Bilinear, Math.NumberTheory.Recurrences
largePFPowerMath.NumberTheory.Powers.General
lcmMath.NumberTheory.Euclidean
liouvilleMath.NumberTheory.ArithmeticFunctions
liouvilleAMath.NumberTheory.ArithmeticFunctions
lucasMath.NumberTheory.Recurrences.Linear, Math.NumberTheory.Recurrences
lucasPairMath.NumberTheory.Recurrences.Linear, Math.NumberTheory.Recurrences
makePrimitiveMath.NumberTheory.DirichletCharacters
MaxNatural 
1 (Type/Class)Math.NumberTheory.ArithmeticFunctions.Inverse
2 (Data Constructor)Math.NumberTheory.ArithmeticFunctions.Inverse
MaxWord 
1 (Type/Class)Math.NumberTheory.ArithmeticFunctions.Inverse
2 (Data Constructor)Math.NumberTheory.ArithmeticFunctions.Inverse
mertensMath.NumberTheory.ArithmeticFunctions.Mertens
millerRabinVMath.NumberTheory.Primes.Testing
MinNatural 
1 (Type/Class)Math.NumberTheory.ArithmeticFunctions.Inverse
2 (Data Constructor)Math.NumberTheory.ArithmeticFunctions.Inverse
MinusOneMath.NumberTheory.Moduli.Jacobi, Math.NumberTheory.Moduli.Sqrt, Math.NumberTheory.Moduli
MinWord 
1 (Type/Class)Math.NumberTheory.ArithmeticFunctions.Inverse
2 (Data Constructor)Math.NumberTheory.ArithmeticFunctions.Inverse
ModMath.NumberTheory.Moduli.Class, Math.NumberTheory.Moduli
moduloMath.NumberTheory.Moduli.Class, Math.NumberTheory.Moduli
MoebiusMath.NumberTheory.ArithmeticFunctions.Moebius, Math.NumberTheory.ArithmeticFunctions
moebiusMath.NumberTheory.ArithmeticFunctions
moebiusAMath.NumberTheory.ArithmeticFunctions
MoebiusNMath.NumberTheory.ArithmeticFunctions.Moebius, Math.NumberTheory.ArithmeticFunctions
MoebiusPMath.NumberTheory.ArithmeticFunctions.Moebius, Math.NumberTheory.ArithmeticFunctions
MoebiusZMath.NumberTheory.ArithmeticFunctions.Moebius, Math.NumberTheory.ArithmeticFunctions
multElementMath.NumberTheory.Moduli.Multiplicative, Math.NumberTheory.Moduli.Class, Math.NumberTheory.Moduli
multiplicativeMath.NumberTheory.ArithmeticFunctions
multiplicativeSieveBlockConfigMath.NumberTheory.ArithmeticFunctions.SieveBlock
MultModMath.NumberTheory.Moduli.Multiplicative, Math.NumberTheory.Moduli.Class, Math.NumberTheory.Moduli
nextPrimeMath.NumberTheory.Primes
nFreesMath.NumberTheory.ArithmeticFunctions.NFreedom, Math.NumberTheory.ArithmeticFunctions
nFreesBlockMath.NumberTheory.ArithmeticFunctions.NFreedom, Math.NumberTheory.ArithmeticFunctions
NonZeroMath.NumberTheory.DirichletCharacters
norm 
1 (Function)Math.NumberTheory.Quadratic.GaussianIntegers
2 (Function)Math.NumberTheory.Quadratic.EisensteinIntegers
nthPrimeMath.NumberTheory.Primes.Counting
nthPrimeApproxMath.NumberTheory.Primes.Counting
nthPrimeApproxUnderestimateLimitMath.NumberTheory.Primes.Counting
OneMath.NumberTheory.Moduli.Jacobi, Math.NumberTheory.Moduli.Sqrt, Math.NumberTheory.Moduli
orderCharMath.NumberTheory.DirichletCharacters
OrZeroMath.NumberTheory.DirichletCharacters
orZeroToNumMath.NumberTheory.DirichletCharacters
partitionMath.NumberTheory.Recurrences
powMod 
1 (Function)Math.NumberTheory.Powers.Modular, Math.NumberTheory.Powers
2 (Function)Math.NumberTheory.Moduli.Class, Math.NumberTheory.Moduli
powModIntMath.NumberTheory.Powers.Modular
powModWordMath.NumberTheory.Powers.Modular
powSomeModMath.NumberTheory.Moduli.Class, Math.NumberTheory.Moduli
precPrimeMath.NumberTheory.Primes
PrefactoredMath.NumberTheory.Prefactored
prefFactorsMath.NumberTheory.Prefactored
prefValueMath.NumberTheory.Prefactored
PrimeMath.NumberTheory.Primes
primeCountMath.NumberTheory.Primes.Counting
primeCountMaxArgMath.NumberTheory.Primes.Counting
primes 
1 (Function)Math.NumberTheory.Primes
2 (Function)Math.NumberTheory.Quadratic.GaussianIntegers
3 (Function)Math.NumberTheory.Quadratic.EisensteinIntegers
PrimitiveCharacterMath.NumberTheory.DirichletCharacters
PrimitiveRootMath.NumberTheory.Moduli.Multiplicative, Math.NumberTheory.Moduli.PrimitiveRoot, Math.NumberTheory.Moduli
principalCharMath.NumberTheory.DirichletCharacters
proofFromCyclicGroupMath.NumberTheory.Moduli.Singleton, Math.NumberTheory.Moduli
proofFromSFactorsMath.NumberTheory.Moduli.Singleton, Math.NumberTheory.Moduli
quotMath.NumberTheory.Euclidean
quotRemMath.NumberTheory.Euclidean
ramanujanMath.NumberTheory.ArithmeticFunctions
ramanujanAMath.NumberTheory.ArithmeticFunctions
real 
1 (Function)Math.NumberTheory.Quadratic.GaussianIntegers
2 (Function)Math.NumberTheory.Quadratic.EisensteinIntegers
RealCharacterMath.NumberTheory.DirichletCharacters
remMath.NumberTheory.Euclidean
RootOfUnity 
1 (Type/Class)Math.NumberTheory.DirichletCharacters
2 (Data Constructor)Math.NumberTheory.DirichletCharacters
runFunctionMath.NumberTheory.ArithmeticFunctions
runFunctionOnFactorsMath.NumberTheory.ArithmeticFunctions
runFunctionOverBlockMath.NumberTheory.ArithmeticFunctions.SieveBlock
runMoebiusMath.NumberTheory.ArithmeticFunctions.Moebius, Math.NumberTheory.ArithmeticFunctions
sbcAppendMath.NumberTheory.ArithmeticFunctions.SieveBlock
sbcEmptyMath.NumberTheory.ArithmeticFunctions.SieveBlock
sbcFunctionOnPrimePowerMath.NumberTheory.ArithmeticFunctions.SieveBlock
SFactorsMath.NumberTheory.Moduli.Singleton, Math.NumberTheory.Moduli
sfactorsMath.NumberTheory.Moduli.Singleton, Math.NumberTheory.Moduli
sfactorsToCyclicGroupMath.NumberTheory.Moduli.Singleton, Math.NumberTheory.Moduli
sieveBlockMath.NumberTheory.ArithmeticFunctions.SieveBlock
SieveBlockConfig 
1 (Type/Class)Math.NumberTheory.ArithmeticFunctions.SieveBlock
2 (Data Constructor)Math.NumberTheory.ArithmeticFunctions.SieveBlock
sieveBlockMoebiusMath.NumberTheory.ArithmeticFunctions.Moebius, Math.NumberTheory.ArithmeticFunctions.SieveBlock
sieveBlockNFreeMath.NumberTheory.ArithmeticFunctions.NFreedom
sieveBlockUnboxedMath.NumberTheory.ArithmeticFunctions.SieveBlock
sigmaMath.NumberTheory.ArithmeticFunctions
sigmaAMath.NumberTheory.ArithmeticFunctions
singletonMath.NumberTheory.Euclidean.Coprimes
smallOmegaMath.NumberTheory.ArithmeticFunctions
smallOmegaAMath.NumberTheory.ArithmeticFunctions
SmoothBasisMath.NumberTheory.SmoothNumbers
smoothOverMath.NumberTheory.SmoothNumbers
smoothOver'Math.NumberTheory.SmoothNumbers
solveLinearMath.NumberTheory.Moduli.Equations
solveQuadraticMath.NumberTheory.Moduli.Equations
Some 
1 (Type/Class)Math.NumberTheory.Moduli.Singleton, Math.NumberTheory.Moduli
2 (Data Constructor)Math.NumberTheory.Moduli.Singleton, Math.NumberTheory.Moduli
SomeMod 
1 (Type/Class)Math.NumberTheory.Moduli.Class, Math.NumberTheory.Moduli
2 (Data Constructor)Math.NumberTheory.Moduli.Class, Math.NumberTheory.Moduli
someSFactorsMath.NumberTheory.Moduli.Singleton, Math.NumberTheory.Moduli
splitIntoCoprimesMath.NumberTheory.Euclidean.Coprimes
sqrtsModMath.NumberTheory.Moduli.Sqrt, Math.NumberTheory.Moduli
sqrtsModFactorisationMath.NumberTheory.Moduli.Sqrt, Math.NumberTheory.Moduli
sqrtsModPrimeMath.NumberTheory.Moduli.Sqrt, Math.NumberTheory.Moduli
sqrtsModPrimePowerMath.NumberTheory.Moduli.Sqrt, Math.NumberTheory.Moduli
stirling1Math.NumberTheory.Recurrences.Bilinear, Math.NumberTheory.Recurrences
stirling2Math.NumberTheory.Recurrences.Bilinear, Math.NumberTheory.Recurrences
symbolToNumMath.NumberTheory.Moduli.Jacobi, Math.NumberTheory.Moduli.Sqrt, Math.NumberTheory.Moduli
tauMath.NumberTheory.ArithmeticFunctions
tauAMath.NumberTheory.ArithmeticFunctions
toComplexMath.NumberTheory.DirichletCharacters
toRealFunctionMath.NumberTheory.DirichletCharacters
toRootOfUnityMath.NumberTheory.DirichletCharacters
totientMath.NumberTheory.ArithmeticFunctions
totientAMath.NumberTheory.ArithmeticFunctions
totientSumMath.NumberTheory.MoebiusInversion
trialDivisionPrimeToMath.NumberTheory.Primes.Testing
unCoprimesMath.NumberTheory.Euclidean.Coprimes
UniqueFactorisationMath.NumberTheory.Primes
unMaxNaturalMath.NumberTheory.ArithmeticFunctions.Inverse
unMaxWordMath.NumberTheory.ArithmeticFunctions.Inverse
unMinNaturalMath.NumberTheory.ArithmeticFunctions.Inverse
unMinWordMath.NumberTheory.ArithmeticFunctions.Inverse
unPrimeMath.NumberTheory.Primes
unPrimitiveRootMath.NumberTheory.Moduli.Multiplicative, Math.NumberTheory.Moduli.PrimitiveRoot, Math.NumberTheory.Moduli
unSFactorsMath.NumberTheory.Moduli.Singleton, Math.NumberTheory.Moduli
unSmoothBasisMath.NumberTheory.SmoothNumbers
unwrapIntegralMath.NumberTheory.Euclidean
validCharMath.NumberTheory.DirichletCharacters
WithNat 
1 (Type/Class)Math.NumberTheory.DirichletCharacters
2 (Data Constructor)Math.NumberTheory.DirichletCharacters
WrapIntegralMath.NumberTheory.Euclidean
WrappedIntegralMath.NumberTheory.Euclidean
Zero 
1 (Data Constructor)Math.NumberTheory.Moduli.Jacobi, Math.NumberTheory.Moduli.Sqrt, Math.NumberTheory.Moduli
2 (Data Constructor)Math.NumberTheory.DirichletCharacters
zetaHurwitzMath.NumberTheory.Zeta
zetasMath.NumberTheory.Zeta
zetasEvenMath.NumberTheory.Zeta
^%Math.NumberTheory.Moduli.Class, Math.NumberTheory.Moduli
ιMath.NumberTheory.Quadratic.GaussianIntegers
ωMath.NumberTheory.Quadratic.EisensteinIntegers