NEWS

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numbers 0.8-5 (2022-11-23)

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

numbers 0.8-4

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

numbers 0.8-3

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

numbers 0.8-2 (2021-05-14)

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

numbers 0.8-1 (2021-04-11)

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

numbers 0.7-9

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

numbers 0.7-8

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

numbers 0.7-6

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

numbers 0.7-5 (2019-11-26)

• collatz() calculates generalized Collatz sequences.

numbers 0.7-4

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

numbers 0.7-3

• modsqrt() calculates the square root modulo primes.

numbers 0.7-1 (2018-05-17)

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

numbers 0.6-8

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

numbers 0.6-7

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

numbers 0.6-6 (2017-01-10)

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

numbers 0.6-5

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

numbers 0.6-3

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

numbers 0.6-1 (2015-07-14)

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

numbers 0.5-9 (2015-07-10)

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

numbers 0.5-8

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

numbers 0.5-6 (2015-03-14)

• 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().

numbers 0.5-3

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

numbers 0.5-2 (2015-01-28)

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

numbers 0.5-1

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

numbers 0.4-9

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

numbers 0.4-7

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

numbers 0.4-5 (2014-01-08)

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

numbers 0.4-3

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

numbers 0.4-1

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

numbers 0.3-5

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

numbers 0.3-3 (2012-11-21)

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

numbers 0.3-1 (2012-10-05)

• chinese() Chinese Remainder Theorem.
• egypt_methods(), egypt_complete() Egyptian fractions
• zeck() Zeckendorf representation.
• Improving modular arithmetics: mod(), rem(), div().

numbers 0.2-1

• agm() algebraic-geometric mean.
• fibonacci() Fibonacci sequence.
• droplet_e() for generating digits of e.
• Modular functions: - modinv(), modlin() modular inverses; - primroot() primitive roots.
• Greatest common divisor, least common multiple: - extGCD(), GCD(), mGCD(), LCM(), mLCM(), coprime().

numbers 0.1-1

• More Number-theoretic functions: - eulersPhi; moebius(), mertens(); - sigma(), tau(), omega(), Omega().
• Shifted number-theoretic functions from 'pracma' to 'numbers': - contFrac() continuous fractions; - ratFarey() rational approximation through Farey sequence.
• Prime number functions: - primeSieve(), Primes(), isPrime(), factorize(); - twinPrimes(), nextPrime(), previousPrime(); - isNatural(), isIntpower().
• New package 'numbers' on R-Forge.