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  numbers                                                               NEWS
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Version 0.9-2 (2025-11-19)

  o polygonal() generates sequences of polygonal numbers, including
    triangular, square, pentagonal and hexagonal numbers.
  o arithmetic_progression() generates arithmetic progressions.
  o unitary divisors are introduced on the help page of divisors().

Version 0.8-9 (2022-12-19)

  o modNthroot() finds n-th roots of integers modulo a prime number.

Version 0.8-7 (2022-12-16)

  o cf2num() improved, scaled version, replacing the alternating series.
  o num2cf() direct implementation that allows for 'mpfr' numbers.

Version 0.8-5 (2022-11-22)

  o periodicCF() determines the the full and exact period of the 
    periodic continued fraction of sqrt(d), d a non-square integer.
  o solvePellsEq() returns the fundamental solution of Pell's equation.

Version 0.8-4 (2022-11-17)

  o contFrac() renamed to contfrac().
  o contfrac() additionally returns the convergents 'p' and 'q'.
  o chinese() and isNatural(): Corrected "coerce to logical" bug.

Version 0.8-3 (2022-11-11)

  o Added isSquare() and isSquarefree() for convenience.
  o Changed the default tolerance of contFrac() to 1e-12.
  o Corrected some misuses of '&' resp '|'.

Version 0.8-2 (2021-05-13)

  o Removed example for farey_seq() from the 'ratFarey' help page
    because apparently 'gmp' causes problems for macOS on CRAN servers.

Version 0.8-1 (2021-04-11)

  o carmichael() determines Carmichael numbers.
  o Corrected all old and 'insecure' Internet links with 'https:'.

Version 0.7-9 (2021-04-10)

  o stern_brocot_seq() generates the Stern-Brocot sequence (fast).
  o farey_seq() generates the full n-th Farey series (slow).

Version 0.7-8 (2021-04-07)

  o bernoulli_numbers() the Bernoulli numbers w/ and w/o 'big rationals'.
  o pascal_triangle() generates Pascal numbers in a rectangle.
  o modq() extends the modulo operator to rational numbers.

Version 0.7-6 (2021-03-17)

  o Help clarified for omega() and Omega() functions.

Version 0.7-5 (2019-11-26)

  o collatz() calculates generalized Collatz sequences.

Version 0.7-4 (2019-08-03)

  o "length > 1 in coercion to logical" error corrected in mGCD() and mLCM().
  o Corrected hermiteNF(), suggested by Martin Hoffmann.

Version 0.7-3 (2018-12-02)

  o modsqrt() calculates the square root modulo primes.

Version 0.7-1 (2018-05-16)

  o Removed 'numbers-package.Rd' on request of K. Hornick, CRAN.

Version 0.6-8 (2017-03-26)

  o intnthroot() calculates the integer n-th root.

Version 0.6-7 (2017-01-15)

  o modlog() the modular (or: discrete) logarithm.
  o primroot() got a new keyword 'all=FALSE' to return all primitive
    roots if it is TRUE. Also, isPrimroot() with the obvious meaning.

Version 0.6-6 (2017-01-10)

  o Extended the description line considerably by request of CRAN.
  o Finally completed the "?`numbers-package`" entry of the help.

Version 0.6-5 (2017-01-10)

  o cf2num() converts (generalized) continued fractions to numbers,
    with special care for approximating infinite fractions.

Version 0.6-3 (2016-12-20)

  o divisors() lists all divisors of a number n from its prime factors.
  o necklace() and bracelet() compute the number of necklaces resp.
    bracelets in combinatorics, suggested by David Sterratt.
  o corrected a 'tiny' bug in modpower(), pointed out by Nathan Carter.

Version 0.6-1 (2015-07-13)

  o bell() generates Bell numbers.
  o Spelling changes in the documentation.

Version 0.5-9 (2015-07-09)

  o Changed package 'gmp' status from "Imports:" to "Suggests:";
    functions miller_rabin() and mersenne() require 'gmp' to be loaded.
  o sigma() renamed to Sigma() to avoid name clash.

Version 0.5-8 (2015-07-01)

  o atkin_sieve(): Atkin's prime number sieve.
  o Small bug corrected: eulerPhi(1) == 1 .

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.

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