README.md

In tiberius7777/R-numtheory: Number Theory

R-numtheory

R package that provides number theory functions, optimized for performance on large numbers.

Current status

At the moment this is still in experimental stage. I am using this as a replacement for Maple which I find difficult to use, therefore the plan is to re-engineer standard Maple functions and more exotic ones in standard R syntax, without linking any further code. Focus will be on factorization of large numbers and integer divisors. Use at your own risk, this is a work in progress.

Feel free to contribute, though.

Functions implemented so far:

• is.int(n): Check if numer is a whole number, as a workaround given that base::is.integer does not do this
• is.posint(n): Check for positive whole number
• is.prime(n): Check for prime number, working well for numbers up to 10¹¹.
• is.even(n): Check if number is even
• sieve(n): Sieve of Eratosthenes, optimized for large numbers up to 10⁸
• gcd(a,b): Greatest common divisor
• lcm(a,b): Least common multiple
• pollard_rho(n): Pollard's rho algorithm for prime factorization of large numbers
• divisors(n): List of all integer divisors of integer n. Works well up to around 10⁹.
• tau(n): number of divisors of n. Works well up to around 10⁹.
• sigma(n): sum of all divisors of n. Works well up to around 10⁹.
• primorial(n): factorial of all prime numbers < n. Works well up to n=700.
• phi(n): Euler's Phi function (also known as Euler's "totient" function). Works well up to 10¹¹
• legendre(a,p): Legendre symbol for quadratic residues
• igcdex(a,b): Extended Euclidean Algorithm to find s and t such that gcd(a,b) = sa + tb

To do:

• Within the is.prime function, should 'sieve(n)' be used rather than 'primes.below'? Should improve performance
• Check for prime numbers > 10¹¹
• AKS Primality Test
• Rabin-Miller Primality Test
• Modular Square Root
• Jacobi symbol

tiberius7777/R-numtheory documentation built on May 31, 2019, 11:20 a.m.