Python Number theory library
Algorithms:
-
Greatest common divisor:
gdc(a, b)- complexity:
O(log(min(a,b))) - memory:
O(log(min(a,b))) - description: computes the greatest common divisor between a and b
- complexity:
-
Modular Exponentiation:
modexp(base, power, mod)- complexity:
O(log(power)) - memory:
O(log(power)) - description: computes (base^power) % mod
- complexity:
-
Pell's Equation:
pell_solutions(n, k)- complexity:
O(n^(1/2) log n) - memory:
O(k) - desciption: computes a list with the first k solutions of the Pell equation: x^2 - n(y^2) = 1
- complexity:
-
Eratosthenes' Sieve:
sieve(n)- complexity:
O(n (log log n)) - memory:
O(n) - description: sieve of eratosthenes to find primes less than n
- complexity:
-
Miller Rabin Primality Test:
miller_rabin(n, k=10)- complexity:
O(k*(log n)^3) - memory:
- description: find primes less than n with 4^(-k) probability
- complexity: