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‎Converters/any2mp3.sf

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# Daniel "Trizen" Șuteu
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# Date: 17 June 2014
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# Edit: 21 March 2020
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# Website: http://github.com/trizen
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# Website: https://github.com/trizen
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# Convert any media file to MP3, using `n` parallel processes of ffmpeg.
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‎Digest/md5.sf

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#!/usr/bin/ruby
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#
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## http://rosettacode.org/wiki/MD5/Implementation
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## https://rosettacode.org/wiki/MD5/Implementation
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#
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class MD5(String msg) {

‎Games/bulls_and_cows.sf

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#!/usr/bin/ruby
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#
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## http://rosettacode.org/wiki/Bulls_and_cows#Sidef
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## https://rosettacode.org/wiki/Bulls_and_cows#Sidef
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#
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var size = 4;

‎Games/bulls_and_cows_player.sf

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#!/usr/bin/ruby
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#
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## http://rosettacode.org/wiki/Bulls_and_cows/Player#Sidef
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## https://rosettacode.org/wiki/Bulls_and_cows/Player#Sidef
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#
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# Build a list of all possible solutions. The regular expression weeds

‎Games/maze_generation.sf

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#!/usr/bin/ruby
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#
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## http://rosettacode.org/wiki/Maze_generation#Sidef
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## https://rosettacode.org/wiki/Maze_generation#Sidef
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#
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var(w, h) = (5, 5);

‎Games/rock-paper-scissors.sf

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#!/usr/bin/ruby
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#
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## http://rosettacode.org/wiki/Rock-paper-scissors
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## https://rosettacode.org/wiki/Rock-paper-scissors
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#
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const rps = %w(r p s)

‎Games/snake_game_oo.sf

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#!/usr/bin/ruby
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#
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## http://rosettacode.org/wiki/Snake
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## https://rosettacode.org/wiki/Snake
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#
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class SnakeGame(w, h) {

‎Graph/dijkstra_s_algorithm.sf

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#!/usr/bin/ruby
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#
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## http://rosettacode.org/wiki/Dijkstra%27s_algorithm
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## https://rosettacode.org/wiki/Dijkstra%27s_algorithm
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#
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class Graph(*args) {

‎Image/color_wheel.sf

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#!/usr/bin/ruby
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#
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## http://rosettacode.org/wiki/Color_wheel
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## https://rosettacode.org/wiki/Color_wheel
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#
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require('Imager')

‎Image/curlicue_fractal.sf

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# Generates a Curlicue Fractal
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# See also:
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# http://mathworld.wolfram.com/CurlicueFractal.html
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# https://mathworld.wolfram.com/CurlicueFractal.html
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require('GD::Simple')
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‎Image/plasma_effect.sf

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#!/usr/bin/ruby
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#
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## http://rosettacode.org/wiki/Plasma_effect
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## https://rosettacode.org/wiki/Plasma_effect
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#
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require('Imager')

‎Image/pythagoras_tree.sf

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#!/usr/bin/ruby
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#
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## http://rosettacode.org/wiki/Pythagoras_tree
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## https://rosettacode.org/wiki/Pythagoras_tree
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#
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require('Imager')

‎LICENSE

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GNU GENERAL PUBLIC LICENSE
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Version 3, 29 June 2007
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Copyright (C) 2007 Free Software Foundation, Inc. <http://fsf.org/>
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Copyright (C) 2007 Free Software Foundation, Inc. <https://fsf.org/>
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Everyone is permitted to copy and distribute verbatim copies
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of this license document, but changing it is not allowed.
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@@ -645,7 +645,7 @@ the "copyright" line and a pointer to where the full notice is found.
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GNU General Public License for more details.
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You should have received a copy of the GNU General Public License
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along with this program. If not, see <http://www.gnu.org/licenses/>.
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along with this program. If not, see <https://www.gnu.org/licenses/>.
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Also add information on how to contact you by electronic and paper mail.
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You should also get your employer (if you work as a programmer) or school,
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if any, to sign a "copyright disclaimer" for the program, if necessary.
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For more information on this, and how to apply and follow the GNU GPL, see
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<http://www.gnu.org/licenses/>.
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<https://www.gnu.org/licenses/>.
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The GNU General Public License does not permit incorporating your program
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into proprietary programs. If your program is a subroutine library, you
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may consider it more useful to permit linking proprietary applications with
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the library. If this is what you want to do, use the GNU Lesser General
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Public License instead of this License. But first, please read
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<http://www.gnu.org/philosophy/why-not-lgpl.html>.
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<https://www.gnu.org/philosophy/why-not-lgpl.html>.

‎Math/AGM_calculate_pi.sf

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# The AGM method for efficiently computing an arbitrary number of digits of PI.
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# See also:
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# http://rosettacode.org/wiki/Arithmetic-geometric_mean/Calculate_Pi
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# https://rosettacode.org/wiki/Arithmetic-geometric_mean/Calculate_Pi
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# https://en.wikipedia.org/wiki/Arithmetic%E2%80%93geometric_mean#The_number_%CF%80
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func AGM_PI(digits=100) {

‎Math/bernoulli_numbers_seidel.sf

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# Seidel's algorithm for computing Bernoulli numbers.
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# Algorithm from:
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# http://oeis.org/wiki/User:Peter_Luschny/ComputationAndAsymptoticsOfBernoulliNumbers#Seidel
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# https://oeis.org/wiki/User:Peter_Luschny/ComputationAndAsymptoticsOfBernoulliNumbers#Seidel
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func bernoulli_seidel(n) {
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‎Math/cauchy_numbers_of_first_type_recurrence.sf

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# C_n = a(n) * n!
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# See also:
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# http://oeis.org/A006232 (numerators)
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# http://oeis.org/A006233 (denominators)
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# https://oeis.org/A006232 (numerators)
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# https://oeis.org/A006233 (denominators)
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func a((0)) { 1 }
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‎Math/central_trinomial_triangle.sf

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# See also:
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# https://oeis.org/A097893
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# http://mathworld.wolfram.com/CentralTrinomialCoefficient.html
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# https://mathworld.wolfram.com/CentralTrinomialCoefficient.html
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func central_trinomial_triangle(num, callback) {
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var row = [1]

‎Math/confluent_hypergeometric_function_of_the_first_kind.sf

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# See also:
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# https://en.wikipedia.org/wiki/Confluent_hypergeometric_function
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# http://mathworld.wolfram.com/ConfluentHypergeometricFunctionoftheFirstKind.html
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# https://mathworld.wolfram.com/ConfluentHypergeometricFunctionoftheFirstKind.html
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func F1(a, b, z, limit=1000) {
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sum(0..limit, {|k|

‎Math/elementary_cellular_automaton_generalized.sf

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# See also:
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# https://en.wikipedia.org/wiki/Cellular_automaton
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# https://en.wikipedia.org/wiki/Elementary_cellular_automaton
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# http://rosettacode.org/wiki/Elementary_cellular_automaton
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# https://rosettacode.org/wiki/Elementary_cellular_automaton
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# YouTube lectures:
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# https://www.youtube.com/watch?v=S3tYzCPuVsA

‎Math/faulhaber_double_series.sf

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# where p is a positive integer.
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# See also:
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# http://mathworld.wolfram.com/PowerSum.html
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# https://mathworld.wolfram.com/PowerSum.html
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# https://en.wikipedia.org/wiki/Faulhaber's_formula
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func faulhaber_double_series(n, p) {

‎Math/fubini_numbers.sf

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# A new algorithm for computing the first n Fubini numbers.
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# See also:
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# http://oeis.org/A000670
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# https://oeis.org/A000670
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func fubini_numbers(n) {
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‎Math/gamma_function.sf

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#!/usr/bin/ruby
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#
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## http://rosettacode.org/wiki/Gamma_function
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## https://rosettacode.org/wiki/Gamma_function
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#
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define ℯ = Num.e

‎Math/harmonic_numbers_of_k-th_order.sf

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# Formula in terms of the Harmonic numbers, due to Conway and Guy (1996), for computing the Harmonic numbers of the k-th order.
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# See also:
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# http://mathworld.wolfram.com/HarmonicNumber.html
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# https://mathworld.wolfram.com/HarmonicNumber.html
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func harmonic_kth_order(n, k) {
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binomial(n + k - 1, k - 1) * (harmonic(n + k - 1) - harmonic(k - 1))

‎Math/haversine_formula.sf

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#!/usr/bin/ruby
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#
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## http://rosettacode.org/wiki/Haversine_formula
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## https://rosettacode.org/wiki/Haversine_formula
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#
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class EarthPoint(lat, lon) {

‎Math/holf_factorization.sf

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# Hart’s One-Line Factoring Algorithm.
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# See also:
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# http://wrap.warwick.ac.uk/54707/1/WRAP_Hart_S1446788712000146a.pdf
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# https://wrap.warwick.ac.uk/54707/1/WRAP_Hart_S1446788712000146a.pdf
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# https://programmingpraxis.com/2014/01/28/harts-one-line-factoring-algorithm/
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func HOLF_factor(n, iter=100000) {

‎Math/is_carmichael_number.sf

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# https://en.wikipedia.org/wiki/Von_Staudt%E2%80%93Clausen_theorem
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# C. Pomerance, J. L. Selfridge, and S. S. Wagstaff, Jr., The pseudoprimes to 25*10^9, Math. Comp., 35 (1980), 1003-1026.
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# http://www.ams.org/journals/mcom/1980-35-151/S0025-5718-1980-0572872-7/home.html
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# https://www.ams.org/journals/mcom/1980-35-151/S0025-5718-1980-0572872-7/home.html
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func bernoulli_denominator (n) {
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‎Math/julia_set.sf

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#!/usr/bin/ruby
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#
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## http://rosettacode.org/wiki/Julia_set
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## https://rosettacode.org/wiki/Julia_set
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#
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var (w, h) = (80, 30)

‎Math/knapsack_problem_0_1.sf

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#!/usr/bin/ruby
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#
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## http://rosettacode.org/wiki/Knapsack_problem/0-1
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## https://rosettacode.org/wiki/Knapsack_problem/0-1
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#
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var raw = <<'TABLE'

‎Math/knapsack_problem_bounded.sf

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#!/usr/bin/ruby
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#
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## http://rosettacode.org/wiki/Knapsack_problem/Bounded
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## https://rosettacode.org/wiki/Knapsack_problem/Bounded
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#
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var raw = <<'TABLE'

‎Math/knapsack_problem_unbounded.sf

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#!/usr/bin/ruby
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#
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## http://rosettacode.org/wiki/Knapsack_problem/Unbounded
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## https://rosettacode.org/wiki/Knapsack_problem/Unbounded
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#
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struct KnapsackItem {

‎Math/laguerre_polynomials.sf

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# See also:
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# https://en.wikipedia.org/wiki/Laguerre_polynomials
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# http://mathworld.wolfram.com/LaguerrePolynomial.html
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# https://mathworld.wolfram.com/LaguerrePolynomial.html
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func laguerre_polynomial(n, x) {
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sum(0..n, {|k|

‎Math/levenshtein_distance_iter.sf

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#!/usr/bin/ruby
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#
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## http://rosettacode.org/wiki/Levenshtein_distance
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## https://rosettacode.org/wiki/Levenshtein_distance
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#
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func lev(s, t) {

‎Math/levenshtein_distance_rec.sf

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#!/usr/bin/ruby
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#
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## http://rosettacode.org/wiki/Levenshtein_distance
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## https://rosettacode.org/wiki/Levenshtein_distance
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#
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func lev(s, t) is cached {

‎Math/linear_diophantine_equation.sf

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# See also:
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# https://en.wikipedia.org/wiki/Diophantine_equation
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# http://mathworld.wolfram.com/DiophantineEquation.html
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# https://mathworld.wolfram.com/DiophantineEquation.html
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func solve(a, b, c) {
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‎Math/linear_diophantine_equation_invmod_search.sf

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# See also:
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# https://en.wikipedia.org/wiki/Diophantine_equation
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# http://mathworld.wolfram.com/DiophantineEquation.html
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# https://mathworld.wolfram.com/DiophantineEquation.html
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func modular_inverse_search (a, n, z) {
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‎Math/log10_digit_by_digit.sf

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# https://github.com/trizen/sidef/issues/37
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# Computing Logarithms Digit-by-Digit:
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# http://brics.dk/RS/04/17/BRICS-RS-04-17.pdf
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# https://brics.dk/RS/04/17/BRICS-RS-04-17.pdf
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func Log10 (x, prec=48) {
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var k = x.float

‎Math/lucas-pocklington_primality_proving.sf

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# See also:
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# https://en.wikipedia.org/wiki/Pocklington_primality_test
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# https://en.wikipedia.org/wiki/Primality_certificate
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# http://mathworld.wolfram.com/PrattCertificate.html
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# https://mathworld.wolfram.com/PrattCertificate.html
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# https://math.stackexchange.com/questions/663341/n1-primality-proving-is-slow
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func lucas_pocklington_primality_proving(n, lim=2**64) is cached {

‎Math/modular_bell_numbers_recurrence.sf

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# See also:
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# https://oeis.org/A166226 -- Bell number n modulo n.
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# https://oeis.org/A325630 -- Numbers k such that Bell(k) is divisible by k.
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# http://mathworld.wolfram.com/BellNumber.html
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# https://mathworld.wolfram.com/BellNumber.html
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func modular_binomial(n, k, m) is cached {
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‎Math/modular_exponentiation.sf

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#!/usr/bin/ruby
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#
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## http://rosettacode.org/wiki/Modular_exponentiation
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## https://rosettacode.org/wiki/Modular_exponentiation
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#
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func expmod(a, b, n) {

‎Math/number_of_representations_as_sum_of_3_triangles.sf

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# Compute the number of ordered ways of writing `n` as the sum of 3 triangular numbers.
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# See also:
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# http://oeis.org/A008443
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# https://oeis.org/A008443
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# https://projecteuler.net/problem=621
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func count_sums_of_two_squares (n) {

‎Math/pell-holf_factorization.sf

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# See also:
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# https://en.wikipedia.org/wiki/Pell%27s_equation
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# http://wrap.warwick.ac.uk/54707/1/WRAP_Hart_S1446788712000146a.pdf
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# https://wrap.warwick.ac.uk/54707/1/WRAP_Hart_S1446788712000146a.pdf
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func pell_holf_factorization(n) {
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