------------------------------------------------------------------------------
  numbers                                                               NEWS
------------------------------------------------------------------------------


Version 0.5-6 (2015-03-14)

   o Pi-day 3.14.15 9:26:53.58 contribution:
     dropletPi() realizes the droplet/spigot algorithm for pi;
     droplet_e() has been renamed to dropletE().

Version 0.5-3 (2015-02-12)

   o radical() computes the radical of n, i.e the product of
     unique prime factors of n.

Version 0.5-2 (2015-01-28)

  o miller_rabin() executes the probabilistic Miller-Rabin primality
    test, faster than isPrime(), but still slower than gmp::isprime().

Version 0.5-1 (2015-01-27)

  o egyptian_complete() returns the number of solutions found.
  o legendre_sym() returned Boolean nonsense, has been corrected. 

Version 0.4-9 (2014-12-30)

  o ordpn() order of a prime number in n!, i.e. n faculty.
  o fibonacci() and lucas() corrected; the recursive computation
    has been replaced by an iterative approach.

Version 0.4-7 (2014-08-03)

  o agm() exact to machine accuracy; returns only the AGM value. 

Version 0.4-5 (2014-01-03)

  o Imports 'gmp'.
  o Primes() avoids creating additional memory, doubled its speed.

Version 0.4-3 (2013-11-16)

  o legendre_sym() Legendre and Jacobi symbol.
  o quadratic_residues() lists all quadratic residues.

Version 0.4-1 (2013-03-30)

  o mersenne() computes Mersenne prime numbers.
  o Renamed factorize() to primeFactors() (avoid masking ...)

Version 0.3-5 (2013-01-12)

  o catalan() Catalan numbers.
  o pythagorean_triple() generating Pythagorean triples.

Version 0.3-3 (2012-11-20)

  o hermiteNF() Hermite normal form.
  o lucas() Lucas numbers as sequence.
  o Added corrections to mGCD() and mLCM().

Version 0.3-1 (2012-10-04)

  o chinese() Chinese Remainder Theorem.
  o egypt_methods(), egypt_complete() Egyptian fractions
  o zeck() Zeckendorf representation

  o Improving modular arithmetics:
      - mod(), rem(), div().

Version 0.2-1 (2012-09-25)

  o agm() algebraic-geometric mean.
  o fibonacci() Fibonacci sequence.
  o droplet_e() for generating digits of e.

  o Modular functions:
      - modinv(), modlin() modular inverses;
      - primroot() primitive roots.

  o Greatest common divisor, least common multiple:
      - extGCD(), GCD(), mGCD(), LCM(), mLCM(), coprime().

Version 0.1-1 (2012-09-24)

  o More Number-theoretic functions:
      - eulersPhi; moebius(), mertens();
      - sigma(), tau(), omega(), Omega().

  o Shifted number-theoretic functions from 'pracma' to 'numbers':
      - contFrac() continuous fractions;
      - ratFarey() rational approximation through Farey sequence.

  o Prime number functions:
      - primeSieve(), Primes(), isPrime(), factorize();
      - twinPrimes(), nextPrime(), previousPrime();
      - isNatural(), isIntpower().

  o New package 'numbers' on R-Forge.

------------------------------------------------------------------------------
