mathslib

======== Overview

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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) | +----------------+------------------------------------------------------------+

.. _Project Euler: https://projecteuler.net .. _ivl-projecteuler.com: https://ivl-projecteuler.com .. _mathslib1: https://pypi.python.org/pypi/mathslib .. here: https://mathslib.readthedocs.io/en/latest/index.html __ mathslib1