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numbers NEWS
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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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