arithmoi-0.12.1.0: Efficient basic number-theoretic functions.

Index

:+ |
1 (Data Constructor) | Math.NumberTheory.Quadratic.GaussianIntegers
2 (Data Constructor) | Math.NumberTheory.Quadratic.EisensteinIntegers
additive | Math.NumberTheory.ArithmeticFunctions
additiveSieveBlockConfig | Math.NumberTheory.ArithmeticFunctions.SieveBlock
allChars | Math.NumberTheory.DirichletCharacters
approxPrimeCount | Math.NumberTheory.Primes.Counting
approxPrimeCountOverestimateLimit | Math.NumberTheory.Primes.Counting
ArithmeticFunction |
1 (Type/Class) | Math.NumberTheory.ArithmeticFunctions
2 (Data Constructor) | Math.NumberTheory.ArithmeticFunctions
asSetOfPreimages | Math.NumberTheory.ArithmeticFunctions.Inverse
associates | Math.NumberTheory.Quadratic.EisensteinIntegers
bailliePSW | Math.NumberTheory.Primes.Testing
bernoulli | Math.NumberTheory.Recurrences.Bilinear, Math.NumberTheory.Recurrences
betas | Math.NumberTheory.Zeta
betasOdd | Math.NumberTheory.Zeta
bigOmega | Math.NumberTheory.ArithmeticFunctions
bigOmegaA | Math.NumberTheory.ArithmeticFunctions
binomial | Math.NumberTheory.Recurrences.Bilinear, Math.NumberTheory.Recurrences
binomialDiagonal | Math.NumberTheory.Recurrences.Bilinear, Math.NumberTheory.Recurrences
binomialFactors | Math.NumberTheory.Recurrences.Bilinear, Math.NumberTheory.Recurrences
binomialLine | Math.NumberTheory.Recurrences.Bilinear, Math.NumberTheory.Recurrences
binomialRotated | Math.NumberTheory.Recurrences.Bilinear, Math.NumberTheory.Recurrences
carmichael | Math.NumberTheory.ArithmeticFunctions
carmichaelA | Math.NumberTheory.ArithmeticFunctions
CG2 | Math.NumberTheory.Moduli.Singleton, Math.NumberTheory.Moduli
CG4 | Math.NumberTheory.Moduli.Singleton, Math.NumberTheory.Moduli
CGDoubleOddPrimePower | Math.NumberTheory.Moduli.Singleton, Math.NumberTheory.Moduli
CGOddPrimePower | Math.NumberTheory.Moduli.Singleton, Math.NumberTheory.Moduli
characterNumber | Math.NumberTheory.DirichletCharacters
chinese | Math.NumberTheory.Moduli.Chinese, Math.NumberTheory.Moduli
chineseSomeMod | Math.NumberTheory.Moduli.Chinese, Math.NumberTheory.Moduli
conjugate |
1 (Function) | Math.NumberTheory.Quadratic.GaussianIntegers
2 (Function) | Math.NumberTheory.Quadratic.EisensteinIntegers
Coprimes | Math.NumberTheory.Euclidean.Coprimes
cornacchia | Math.NumberTheory.Diophantine
cornacchiaPrimitive | Math.NumberTheory.Diophantine
CubicSymbol | Math.NumberTheory.Moduli.Cbrt
cubicSymbol | Math.NumberTheory.Moduli.Cbrt
CyclicGroup | Math.NumberTheory.Moduli.Singleton, Math.NumberTheory.Moduli
cyclicGroup | Math.NumberTheory.Moduli.Singleton, Math.NumberTheory.Moduli
cyclicGroupFromFactors | Math.NumberTheory.Moduli.Singleton, Math.NumberTheory.Moduli
cyclicGroupFromModulo | Math.NumberTheory.Moduli.Singleton, Math.NumberTheory.Moduli
cyclicGroupToSFactors | Math.NumberTheory.Moduli.Singleton, Math.NumberTheory.Moduli
delete | Math.NumberTheory.Primes.IntSet
deleteMax | Math.NumberTheory.Primes.IntSet
deleteMin | Math.NumberTheory.Primes.IntSet
difference | Math.NumberTheory.Primes.IntSet
DirichletCharacter | Math.NumberTheory.DirichletCharacters
discreteLogarithm | Math.NumberTheory.Moduli.Multiplicative, Math.NumberTheory.Moduli
disjoint | Math.NumberTheory.Primes.IntSet
divisorCount | Math.NumberTheory.ArithmeticFunctions
divisors | Math.NumberTheory.ArithmeticFunctions
divisorsA | Math.NumberTheory.ArithmeticFunctions
divisorsList | Math.NumberTheory.ArithmeticFunctions
divisorsListA | Math.NumberTheory.ArithmeticFunctions
divisorsSmall | Math.NumberTheory.ArithmeticFunctions
divisorsSmallA | Math.NumberTheory.ArithmeticFunctions
divisorsTo | Math.NumberTheory.ArithmeticFunctions
divisorsToA | Math.NumberTheory.ArithmeticFunctions
EisensteinInteger | Math.NumberTheory.Quadratic.EisensteinIntegers
euler | Math.NumberTheory.Recurrences.Bilinear, Math.NumberTheory.Recurrences
eulerian1 | Math.NumberTheory.Recurrences.Bilinear, Math.NumberTheory.Recurrences
eulerian2 | Math.NumberTheory.Recurrences.Bilinear, Math.NumberTheory.Recurrences
eulerPolyAt1 | Math.NumberTheory.Recurrences.Bilinear, Math.NumberTheory.Recurrences
eval | Math.NumberTheory.DirichletCharacters
evalAll | Math.NumberTheory.DirichletCharacters
evalGeneral | Math.NumberTheory.DirichletCharacters
expMangoldt | Math.NumberTheory.ArithmeticFunctions
expMangoldtA | Math.NumberTheory.ArithmeticFunctions
factorBack | Math.NumberTheory.Primes
factorial | Math.NumberTheory.Recurrences.Linear, Math.NumberTheory.Recurrences
factorialFactors | Math.NumberTheory.Recurrences.Linear, Math.NumberTheory.Recurrences
factorise | Math.NumberTheory.Primes
faulhaberPoly | Math.NumberTheory.Recurrences.Bilinear, Math.NumberTheory.Recurrences
fibonacci | Math.NumberTheory.Recurrences.Linear, Math.NumberTheory.Recurrences
fibonacciPair | Math.NumberTheory.Recurrences.Linear, Math.NumberTheory.Recurrences
filter | Math.NumberTheory.Primes.IntSet
findPrime |
1 (Function) | Math.NumberTheory.Quadratic.GaussianIntegers
2 (Function) | Math.NumberTheory.Quadratic.EisensteinIntegers
foldl | Math.NumberTheory.Primes.IntSet
foldl' | Math.NumberTheory.Primes.IntSet
foldr | Math.NumberTheory.Primes.IntSet
foldr' | Math.NumberTheory.Primes.IntSet
fromAscList | Math.NumberTheory.Primes.IntSet
fromDistinctAscList | Math.NumberTheory.Primes.IntSet
fromFactors | Math.NumberTheory.Prefactored
fromList |
1 (Function) | Math.NumberTheory.SmoothNumbers
2 (Function) | Math.NumberTheory.Primes.IntSet
fromRootOfUnity | Math.NumberTheory.DirichletCharacters
fromTable | Math.NumberTheory.DirichletCharacters
fromValue | Math.NumberTheory.Prefactored
GaussianInteger | Math.NumberTheory.Quadratic.GaussianIntegers
generalInversion | Math.NumberTheory.MoebiusInversion
generalLucas | Math.NumberTheory.Recurrences.Linear, Math.NumberTheory.Recurrences
getMod | Math.NumberTheory.Moduli.Class, Math.NumberTheory.Moduli
getNatMod | Math.NumberTheory.Moduli.Class, Math.NumberTheory.Moduli
getNatVal | Math.NumberTheory.Moduli.Class, Math.NumberTheory.Moduli
getPrimitiveChar | Math.NumberTheory.DirichletCharacters
getRealChar | Math.NumberTheory.DirichletCharacters
getVal | Math.NumberTheory.Moduli.Class, Math.NumberTheory.Moduli
ids | Math.NumberTheory.Quadratic.EisensteinIntegers
imag | Math.NumberTheory.Quadratic.GaussianIntegers
indexToChar | Math.NumberTheory.DirichletCharacters
indicesToChars | Math.NumberTheory.DirichletCharacters
induced | Math.NumberTheory.DirichletCharacters
Infinity | Math.NumberTheory.ArithmeticFunctions.Inverse
InfMod | Math.NumberTheory.Moduli.Class, Math.NumberTheory.Moduli
insert |
1 (Function) | Math.NumberTheory.Euclidean.Coprimes
2 (Function) | Math.NumberTheory.Primes.IntSet
intersection | Math.NumberTheory.Primes.IntSet
inverseJordan | Math.NumberTheory.ArithmeticFunctions.Inverse
inverseSigma | Math.NumberTheory.ArithmeticFunctions.Inverse
inverseSigmaK | Math.NumberTheory.ArithmeticFunctions.Inverse
inverseTotient | Math.NumberTheory.ArithmeticFunctions.Inverse
invertGroup | Math.NumberTheory.Moduli.Multiplicative, Math.NumberTheory.Moduli.Class, Math.NumberTheory.Moduli
invertMod | Math.NumberTheory.Moduli.Class, Math.NumberTheory.Moduli
invertSomeMod | Math.NumberTheory.Moduli.Class, Math.NumberTheory.Moduli
isCertifiedPrime | Math.NumberTheory.Primes.Testing
isFermatPP | Math.NumberTheory.Primes.Testing
isMultElement | Math.NumberTheory.Moduli.Multiplicative, Math.NumberTheory.Moduli.Class, Math.NumberTheory.Moduli
isNFree | Math.NumberTheory.ArithmeticFunctions
isNFreeA | Math.NumberTheory.ArithmeticFunctions
isPrime |
1 (Function) | Math.NumberTheory.Primes.Testing
2 (Function) | Math.NumberTheory.Primes
isPrimitive | Math.NumberTheory.DirichletCharacters
isPrimitiveRoot | Math.NumberTheory.Moduli.Multiplicative, Math.NumberTheory.Moduli
isPrincipal | Math.NumberTheory.DirichletCharacters
isProperSubsetOf | Math.NumberTheory.Primes.IntSet
isRealCharacter | Math.NumberTheory.DirichletCharacters
isSmooth | Math.NumberTheory.SmoothNumbers
isStrongFermatPP | Math.NumberTheory.Primes.Testing
isSubsetOf | Math.NumberTheory.Primes.IntSet
jacobi | Math.NumberTheory.Moduli.Sqrt, Math.NumberTheory.Moduli
jacobiCharacter | Math.NumberTheory.DirichletCharacters
JacobiSymbol | Math.NumberTheory.Moduli.Sqrt, Math.NumberTheory.Moduli
jordan | Math.NumberTheory.ArithmeticFunctions
jordanA | Math.NumberTheory.ArithmeticFunctions
KnownNat | Math.NumberTheory.Moduli.Class, Math.NumberTheory.Moduli
lah | Math.NumberTheory.Recurrences.Bilinear, Math.NumberTheory.Recurrences
liouville | Math.NumberTheory.ArithmeticFunctions
liouvilleA | Math.NumberTheory.ArithmeticFunctions
lookupEQ | Math.NumberTheory.Primes.IntSet
lookupGE | Math.NumberTheory.Primes.IntSet
lookupGT | Math.NumberTheory.Primes.IntSet
lookupLE | Math.NumberTheory.Primes.IntSet
lookupLT | Math.NumberTheory.Primes.IntSet
lucas | Math.NumberTheory.Recurrences.Linear, Math.NumberTheory.Recurrences
lucasPair | Math.NumberTheory.Recurrences.Linear, Math.NumberTheory.Recurrences
makePrimitive | Math.NumberTheory.DirichletCharacters
MaxNatural |
1 (Type/Class) | Math.NumberTheory.ArithmeticFunctions.Inverse
2 (Data Constructor) | Math.NumberTheory.ArithmeticFunctions.Inverse
maxView | Math.NumberTheory.Primes.IntSet
MaxWord |
1 (Type/Class) | Math.NumberTheory.ArithmeticFunctions.Inverse
2 (Data Constructor) | Math.NumberTheory.ArithmeticFunctions.Inverse
member | Math.NumberTheory.Primes.IntSet
mertens | Math.NumberTheory.ArithmeticFunctions.Mertens
millerRabinV | Math.NumberTheory.Primes.Testing
MinNatural |
1 (Type/Class) | Math.NumberTheory.ArithmeticFunctions.Inverse
2 (Data Constructor) | Math.NumberTheory.ArithmeticFunctions.Inverse
MinusOne | Math.NumberTheory.Moduli.Sqrt, Math.NumberTheory.Moduli
minView | Math.NumberTheory.Primes.IntSet
MinWord |
1 (Type/Class) | Math.NumberTheory.ArithmeticFunctions.Inverse
2 (Data Constructor) | Math.NumberTheory.ArithmeticFunctions.Inverse
Mod | Math.NumberTheory.Moduli.Class, Math.NumberTheory.Moduli
modulo | Math.NumberTheory.Moduli.Class, Math.NumberTheory.Moduli
Moebius | Math.NumberTheory.ArithmeticFunctions.Moebius, Math.NumberTheory.ArithmeticFunctions
moebius | Math.NumberTheory.ArithmeticFunctions
moebiusA | Math.NumberTheory.ArithmeticFunctions
MoebiusN | Math.NumberTheory.ArithmeticFunctions.Moebius, Math.NumberTheory.ArithmeticFunctions
MoebiusP | Math.NumberTheory.ArithmeticFunctions.Moebius, Math.NumberTheory.ArithmeticFunctions
MoebiusZ | Math.NumberTheory.ArithmeticFunctions.Moebius, Math.NumberTheory.ArithmeticFunctions
multElement | Math.NumberTheory.Moduli.Multiplicative, Math.NumberTheory.Moduli.Class, Math.NumberTheory.Moduli
multiplicative | Math.NumberTheory.ArithmeticFunctions
multiplicativeSieveBlockConfig | Math.NumberTheory.ArithmeticFunctions.SieveBlock
MultMod | Math.NumberTheory.Moduli.Multiplicative, Math.NumberTheory.Moduli.Class, Math.NumberTheory.Moduli
nextPrime | Math.NumberTheory.Primes
nFrees | Math.NumberTheory.ArithmeticFunctions.NFreedom, Math.NumberTheory.ArithmeticFunctions
nFreesBlock | Math.NumberTheory.ArithmeticFunctions.NFreedom, Math.NumberTheory.ArithmeticFunctions
NonZero | Math.NumberTheory.DirichletCharacters
norm |
1 (Function) | Math.NumberTheory.Quadratic.GaussianIntegers
2 (Function) | Math.NumberTheory.Quadratic.EisensteinIntegers
notMember | Math.NumberTheory.Primes.IntSet
nthPrime | Math.NumberTheory.Primes.Counting
nthPrimeApprox | Math.NumberTheory.Primes.Counting
nthPrimeApproxUnderestimateLimit | Math.NumberTheory.Primes.Counting
null | Math.NumberTheory.Primes.IntSet
Omega | Math.NumberTheory.Moduli.Cbrt
OmegaSquare | Math.NumberTheory.Moduli.Cbrt
One |
1 (Data Constructor) | Math.NumberTheory.Moduli.Sqrt, Math.NumberTheory.Moduli
2 (Data Constructor) | Math.NumberTheory.Moduli.Cbrt
orderChar | Math.NumberTheory.DirichletCharacters
OrZero | Math.NumberTheory.DirichletCharacters
orZeroToNum | Math.NumberTheory.DirichletCharacters
partition |
1 (Function) | Math.NumberTheory.Recurrences
2 (Function) | Math.NumberTheory.Primes.IntSet
powMod |
1 (Function) | Math.NumberTheory.Powers.Modular
2 (Function) | Math.NumberTheory.Moduli.Class, Math.NumberTheory.Moduli
powModInt | Math.NumberTheory.Powers.Modular
powModWord | Math.NumberTheory.Powers.Modular
powSomeMod | Math.NumberTheory.Moduli.Class, Math.NumberTheory.Moduli
precPrime | Math.NumberTheory.Primes
Prefactored | Math.NumberTheory.Prefactored
prefFactors | Math.NumberTheory.Prefactored
prefValue | Math.NumberTheory.Prefactored
Prime | Math.NumberTheory.Primes
primeCount | Math.NumberTheory.Primes.Counting
primeCountMaxArg | Math.NumberTheory.Primes.Counting
PrimeIntSet | Math.NumberTheory.Primes.IntSet
primes |
1 (Function) | Math.NumberTheory.Primes
2 (Function) | Math.NumberTheory.Quadratic.GaussianIntegers
3 (Function) | Math.NumberTheory.Quadratic.EisensteinIntegers
PrimitiveCharacter | Math.NumberTheory.DirichletCharacters
PrimitiveRoot | Math.NumberTheory.Moduli.Multiplicative, Math.NumberTheory.Moduli
principalChar | Math.NumberTheory.DirichletCharacters
proofFromCyclicGroup | Math.NumberTheory.Moduli.Singleton, Math.NumberTheory.Moduli
proofFromSFactors | Math.NumberTheory.Moduli.Singleton, Math.NumberTheory.Moduli
ramanujan | Math.NumberTheory.ArithmeticFunctions
ramanujanA | Math.NumberTheory.ArithmeticFunctions
real | Math.NumberTheory.Quadratic.GaussianIntegers
RealCharacter | Math.NumberTheory.DirichletCharacters
RootOfUnity |
1 (Type/Class) | Math.NumberTheory.DirichletCharacters
2 (Data Constructor) | Math.NumberTheory.DirichletCharacters
runFunction | Math.NumberTheory.ArithmeticFunctions
runFunctionOnFactors | Math.NumberTheory.ArithmeticFunctions
runFunctionOverBlock | Math.NumberTheory.ArithmeticFunctions.SieveBlock
runMoebius | Math.NumberTheory.ArithmeticFunctions.Moebius, Math.NumberTheory.ArithmeticFunctions
sbcAppend | Math.NumberTheory.ArithmeticFunctions.SieveBlock
sbcEmpty | Math.NumberTheory.ArithmeticFunctions.SieveBlock
sbcFunctionOnPrimePower | Math.NumberTheory.ArithmeticFunctions.SieveBlock
SFactors | Math.NumberTheory.Moduli.Singleton, Math.NumberTheory.Moduli
sfactors | Math.NumberTheory.Moduli.Singleton, Math.NumberTheory.Moduli
sfactorsToCyclicGroup | Math.NumberTheory.Moduli.Singleton, Math.NumberTheory.Moduli
sieveBlock | Math.NumberTheory.ArithmeticFunctions.SieveBlock
SieveBlockConfig |
1 (Type/Class) | Math.NumberTheory.ArithmeticFunctions.SieveBlock
2 (Data Constructor) | Math.NumberTheory.ArithmeticFunctions.SieveBlock
sieveBlockMoebius | Math.NumberTheory.ArithmeticFunctions.Moebius, Math.NumberTheory.ArithmeticFunctions.SieveBlock
sieveBlockNFree | Math.NumberTheory.ArithmeticFunctions.NFreedom
sieveBlockUnboxed | Math.NumberTheory.ArithmeticFunctions.SieveBlock
sigma | Math.NumberTheory.ArithmeticFunctions
sigmaA | Math.NumberTheory.ArithmeticFunctions
singleton |
1 (Function) | Math.NumberTheory.Euclidean.Coprimes
2 (Function) | Math.NumberTheory.Primes.IntSet
size | Math.NumberTheory.Primes.IntSet
smallOmega | Math.NumberTheory.ArithmeticFunctions
smallOmegaA | Math.NumberTheory.ArithmeticFunctions
SmoothBasis | Math.NumberTheory.SmoothNumbers
smoothOver | Math.NumberTheory.SmoothNumbers
smoothOver' | Math.NumberTheory.SmoothNumbers
solveLinear | Math.NumberTheory.Moduli.Equations
solveQuadratic | Math.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
someSFactors | Math.NumberTheory.Moduli.Singleton, Math.NumberTheory.Moduli
split | Math.NumberTheory.Primes.IntSet
splitIntoCoprimes | Math.NumberTheory.Euclidean.Coprimes
splitLookupEQ | Math.NumberTheory.Primes.IntSet
splitMember | Math.NumberTheory.Primes.IntSet
splitRoot | Math.NumberTheory.Primes.IntSet
sqrtsMod | Math.NumberTheory.Moduli.Sqrt, Math.NumberTheory.Moduli
sqrtsModFactorisation | Math.NumberTheory.Moduli.Sqrt, Math.NumberTheory.Moduli
sqrtsModPrime | Math.NumberTheory.Moduli.Sqrt, Math.NumberTheory.Moduli
sqrtsModPrimePower | Math.NumberTheory.Moduli.Sqrt, Math.NumberTheory.Moduli
stirling1 | Math.NumberTheory.Recurrences.Bilinear, Math.NumberTheory.Recurrences
stirling2 | Math.NumberTheory.Recurrences.Bilinear, Math.NumberTheory.Recurrences
symbolToNum |
1 (Function) | Math.NumberTheory.Moduli.Sqrt, Math.NumberTheory.Moduli
2 (Function) | Math.NumberTheory.Moduli.Cbrt
symmetricDifference | Math.NumberTheory.Primes.IntSet
tau | Math.NumberTheory.ArithmeticFunctions
tauA | Math.NumberTheory.ArithmeticFunctions
toAscList | Math.NumberTheory.Primes.IntSet
toComplex | Math.NumberTheory.DirichletCharacters
toDescList | Math.NumberTheory.Primes.IntSet
toPrimeIntegral | Math.NumberTheory.Primes
toRealFunction | Math.NumberTheory.DirichletCharacters
toRootOfUnity | Math.NumberTheory.DirichletCharacters
totient | Math.NumberTheory.ArithmeticFunctions
totientA | Math.NumberTheory.ArithmeticFunctions
totientSum | Math.NumberTheory.MoebiusInversion
trialDivisionPrimeTo | Math.NumberTheory.Primes.Testing
unCoprimes | Math.NumberTheory.Euclidean.Coprimes
UniqueFactorisation | Math.NumberTheory.Primes
unMaxNatural | Math.NumberTheory.ArithmeticFunctions.Inverse
unMaxWord | Math.NumberTheory.ArithmeticFunctions.Inverse
unMinNatural | Math.NumberTheory.ArithmeticFunctions.Inverse
unMinWord | Math.NumberTheory.ArithmeticFunctions.Inverse
unPrime | Math.NumberTheory.Primes
unPrimeIntSet | Math.NumberTheory.Primes.IntSet
unPrimitiveRoot | Math.NumberTheory.Moduli.Multiplicative, Math.NumberTheory.Moduli
unSFactors | Math.NumberTheory.Moduli.Singleton, Math.NumberTheory.Moduli
unSmoothBasis | Math.NumberTheory.SmoothNumbers
validChar | Math.NumberTheory.DirichletCharacters
WithNat |
1 (Type/Class) | Math.NumberTheory.DirichletCharacters
2 (Data Constructor) | Math.NumberTheory.DirichletCharacters
Zero |
1 (Data Constructor) | Math.NumberTheory.Moduli.Sqrt, Math.NumberTheory.Moduli
2 (Data Constructor) | Math.NumberTheory.Moduli.Cbrt
3 (Data Constructor) | Math.NumberTheory.DirichletCharacters
zetaHurwitz | Math.NumberTheory.Zeta
zetas | Math.NumberTheory.Zeta
zetasEven | Math.NumberTheory.Zeta
\\ | Math.NumberTheory.Primes.IntSet
^% | Math.NumberTheory.Moduli.Class, Math.NumberTheory.Moduli
ι | Math.NumberTheory.Quadratic.GaussianIntegers
ω | Math.NumberTheory.Quadratic.EisensteinIntegers