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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 links

Key dates

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Credits

Author: Igor van Loo

Requires

Python <4, >=3.7

Tags

numbertheory maths algorithms

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