mathslib 3.3.0

Library of Mathematical functions and Algorithms

mathslib is a compilation of Mathematical Functions and Algorithms. Unless credit was given all of the functions were written by me. Relevant articles are also linked where the implementation is complex.

I have used most of these for Project Euler.

See my website ivl-projecteuler.com for their implementation

See the full documentation here

Breakdown

numtheory.py	phi(x) phi_sieve(x) phi_sum(x) mobius(x) mobius_k_sieve(limit, k) count_k_free(n, k) pythagorean_triples(limit, non_primitive) count_primitive_pythagorean_triples(n) k_smooth_numbers(max_prime, limit) k_powerful(k, limit, count) legendre_factorial(x) tonelli_shanks(a, p) chinese_remainder_theorem(a1, a2, n1, n2) generalised_CRT(a1, a2, n1, n2) frobenius_number(*integers) continued_fraction(x) overall_fraction(x) partition(x, L, show)
primes.py	prime_sieve(limit, block_size, segment, values) prime_sieve_in_range(low_limit, upp_limit, values) is_prime(x) prime_factors(x) spf_sieve(x) primepi(x) primepi_sieve(x) sum_of_primes(x) fermat_primality_test(x) miller_primality_test(n, millerrabin, numoftests)
divisors.py	divisors(x, proper) divisor(x, n) divisor_sieve(x, n)
linalg.py	gauss_jordan_elimination(matrix, augmentedpart) solve(M, b) inverse(matrix) determinant(matrix) matrix_addition(A, B, subtract) identity(l, val) concatenate(A, B) argmax(alist) fillmatrix(size, val) matrix_mul(A, B) matrix_pow(A, n)
fib.py	fibonacci(n, m) fib_till(limit) zeckendorf_representation(x)
algorithms.py	prims_algorithm(matrix) dijkstras_algorithm(graph, start_node, INFINITY) floyd_warshall_algorithm(graph, INFINITY) knap_sack(values, weights, n, W, no_values) knap_sack_values(values, weights, n, W, no_values) BFS(g, start_node, end_node) DFS(g, start_node, end_node) convex_hull_gift_wrapping(pts) convex_hull_DC(pts)
gaussianint.py	GI conj(self) norm_sq(self) prime_fac(self) rem(x, y) gcd(x, y)
simple.py	bin_exp(a, b, c, n, m) number_to_base(n, b) extended_euclidean_algorithm(n, b) lcm(a_list) mod_division(a, b, m) binom(n, k, p) bisect(alist, goal) is_clockwise(a, b, c)