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arithmoi v0.9.0.0 Release Notes

  • ➕ Added

    • Introduce Prime newtype. This newtype is now used extensively in public API:
      primes :: Integral a => [Prime a]
  primeList :: Integral a => PrimeSieve -> [Prime a]
  sieveFrom :: Integer -> [Prime Integer]
  nthPrime :: Integer -> Prime Integer
    • 🆕 New functions nextPrime and precPrime. Implement an instance of Enum for primes (#153):
      > [nextPrime 101 .. precPrime 130]
  [Prime 101,Prime 103,Prime 107,Prime 109,Prime 113,Prime 127]

    • ➕ Add the Hurwitz zeta function on non-negative integer arguments (#126).

    • 👀 Implement efficient tests of n-freeness: pointwise and in interval. See isNFree and nFreesBlock (#145).

    • Generate preimages of the totient and the sum-of-divisors functions (#142):

      > inverseTotient 120 :: [Integer]
  [155,310,183,366,225,450,175,350,231,462,143,286,244,372,396,308,248]
    • Generate coefficients of Faulhaber polynomials faulhaberPoly (#70).

    🔄 Changed

    • 👌 Support Gaussian and Eisenstein integers in smooth numbers (#138).

    • 🔄 Change types of primes, primeList, sieveFrom, nthPrime, etc., to use Prime newtype.

    • ✅ Math.NumberTheory.Primes.{Factorisation,Testing,Counting,Sieve} are no longer re-exported from Math.NumberTheory.Primes. Merge Math.NumberTheory.UniqueFactorisation into Math.NumberTheory.Primes (#135, #153).

    • From now on Math.NumberTheory.Primes.Factorisation.factorise and similar functions return [(Integer, Word)] instead of [(Integer, Int)].

    • sbcFunctionOnPrimePower now accepts Prime Word instead of Word.

    • 👍 Better precision for exact values of Riemann zeta and Dirichlet beta functions (#123).

    • Speed up certain cases of modular multiplication (#160).

    • Extend Chinese theorem to non-coprime moduli (#71).

    🗄 Deprecated

    • 🗄 Deprecate Math.NumberTheory.Recurrencies.*. Use Math.NumberTheory.Recurrences.* instead (#146).

    ✂ Removed

    • ✂ Remove Prime type family.

    • ✂ Remove deprecated Math.NumberTheory.GCD and Math.NumberTheory.GCD.LowLevel.