------------------------------------------------------------------------------ numbers NEWS ------------------------------------------------------------------------------ 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. ------------------------------------------------------------------------------