| numbers-package {numbers} | R Documentation |
Number-Theoretic Functions
Description
Provides number-theoretic functions for factorization, prime numbers, twin primes, primitive roots, modular logarithm and inverses, extended GCD, Farey series and continued fractions. Includes Legendre and Jacobi symbols, some divisor functions, Euler's Phi function, etc.
Details
The DESCRIPTION file:
| Package: | numbers |
| Type: | Package |
| Title: | Number-Theoretic Functions |
| Version: | 0.8-5 |
| Date: | 2022-11-22 |
| Author: | Hans Werner Borchers |
| Maintainer: | Hans W. Borchers <hwborchers@googlemail.com> |
| Depends: | R (>= 4.1.0) |
| Suggests: | gmp (>= 0.5-1) |
| Description: | Provides number-theoretic functions for factorization, prime numbers, twin primes, primitive roots, modular logarithm and inverses, extended GCD, Farey series and continued fractions. Includes Legendre and Jacobi symbols, some divisor functions, Euler's Phi function, etc. |
| License: | GPL (>= 3) |
Index of help topics:
GCD GCD and LCM Integer Functions Primes Prime Numbers Sigma Divisor Functions agm Arithmetic-geometric Mean bell Bell Numbers bernoulli_numbers Bernoulli Numbers carmichael Carmichael Numbers catalan Catalan Numbers cf2num Generalized Continous Fractions chinese Chinese Remainder Theorem collatz Collatz Sequences contfrac Continued Fractions coprime Coprimality div Integer Division divisors List of Divisors dropletPi Droplet Algorithm for pi and e egyptian_complete Egyptian Fractions - Complete Search egyptian_methods Egyptian Fractions - Specialized Methods eulersPhi Eulers's Phi Function extGCD Extended Euclidean Algorithm fibonacci Fibonacci and Lucas Series hermiteNF Hermite Normal Form iNthroot Integer N-th Root isIntpower Powers of Integers isNatural Natural Number isPrime isPrime Property isPrimroot Primitive Root Test legendre_sym Legendre and Jacobi Symbol mersenne Mersenne Numbers miller_rabin Miller-Rabin Test mod Modulo Operator modinv Modular Inverse and Square Root modlin Modular Linear Equation Solver modlog Modular (or: Discrete) Logarithm modpower Power Function modulo m moebius Moebius Function necklace Necklace and Bracelet Functions nextPrime Next Prime numbers-package Number-Theoretic Functions omega Number of Prime Factors ordpn Order in Faculty pascal_triangle Pascal Triangle periodicCF Periodic continued fraction previousPrime Previous Prime primeFactors Prime Factors primroot Primitive Root pythagorean_triples Pythagorean Triples quadratic_residues Quadratic Residues ratFarey Farey Approximation and Series rem Integer Remainder solvePellsEq Solve Pell's Equation stern_brocot_seq Stern-Brocot Sequence twinPrimes Twin Primes zeck Zeckendorf Representation
Although R does not have a true integer data type, integers can be represented exactly up to 2^53-1 . The numbers package attempts to provided basic number-theoretic functions that will work correcty and relatively fast up to this level.
Author(s)
Hans Werner Borchers
Maintainer: Hans W. Borchers <hwborchers@googlemail.com>
References
Hardy, G. H., and E. M. Wright (1980). An Introduction to the Theory of Numbers. 5th Edition, Oxford University Press.
Riesel, H. (1994). Prime Numbers and Computer Methods for Factorization. Second Edition, Birkhaeuser Boston.
Crandall, R., and C. Pomerance (2005). Prime Numbers: A Computational Perspective. Springer Science+Business.
Shoup, V. (2009). A Computational Introduction to Number Theory and Algebra. Second Edition, Cambridge University Press.
Arndt, J. (2010). Matters Computational: Ideas, Algorithms, Source Code. 2011 Edition, Springer-Verlag, Berlin Heidelberg.
Forster, O. (2014). Algorithmische Zahlentheorie. 2. Auflage, Springer Spektrum Wiesbaden.