a-conjecture-of-mine

An exercise on polyglossy: the same problem solved on multiple languages

commit ea51224d227b1056ee562dba10f035f2a2729fa4
parent 20e70ab22a0de1ec9713cc6aeb61235ac9c64d16
Author: Gark Garcia <37553739+GarkGarcia@users.noreply.github.com>
Date:   Wed,  6 Mar 2019 18:18:12 -0300

Restructured the repository to include other language implementations.

Diffstat:
M.gitignore | 2--
DCargo.lock | 275-------------------------------------------------------------------------------
DCargo.toml | 10----------
AHaskell/.gitignore | 2++
AHaskell/LICENSE | 30++++++++++++++++++++++++++++++
AHaskell/app/Main.hs | 56++++++++++++++++++++++++++++++++++++++++++++++++++++++++
AHaskell/conjecture.cabal | 56++++++++++++++++++++++++++++++++++++++++++++++++++++++++
AHaskell/package.yaml | 47+++++++++++++++++++++++++++++++++++++++++++++++
AHaskell/src/Lib.hs | 2++
AHaskell/stack.yaml | 68++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
AHaskell/test/Spec.hs | 2++
ALatex/digital_sum.aux | 1+
ALatex/digital_sum.log | 384+++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
ALatex/digital_sum.pdf | 0
ALatex/digital_sum.synctex.gz | 0
ALatex/digital_sum.tex | 43+++++++++++++++++++++++++++++++++++++++++++
AREADME.md | 19+++++++++++++++++++
C.gitignore -> Rust/.gitignore | 0
ARust/Cargo.lock | 275+++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
ARust/Cargo.toml | 10++++++++++
Rsrc/main.rs -> Rust/src/main.rs | 0
ATypeScript/script.js | 109+++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
ATypeScript/script.min.js | 2++
ATypeScript/script.ts | 141+++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
Ascript.js | 97+++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
Ascript.min.js | 2++
Ascript.py | 84+++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
Ascript.rb | 99+++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
Ascript.ts | 141+++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
Ascript.ts.js | 2++
30 files changed, 1672 insertions(+), 287 deletions(-)
diff --git a/.gitignore b/.gitignore
@@ -1,2 +0,0 @@
-/target
-**/*.rs.bk
diff --git a/Cargo.lock b/Cargo.lock
@@ -1,275 +0,0 @@
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diff --git a/Cargo.toml b/Cargo.toml
@@ -1,9 +0,0 @@
-[package]
-name = "conjecture_tester"
-version = "0.1.0"
-authors = ["Gark Garcia <37553739+GarkGarcia@users.noreply.github.com>"]
-
-[dependencies]
-crossterm = "0.6"
-num_cpus = "1.0"
-rand = "0.6.1"-
\ No newline at end of file
diff --git a/Haskell/.gitignore b/Haskell/.gitignore
@@ -0,0 +1 @@
+.stack-work+
\ No newline at end of file
diff --git a/Haskell/LICENSE b/Haskell/LICENSE
@@ -0,0 +1,30 @@
+Copyright Author name here (c) 2019
+
+All rights reserved.
+
+Redistribution and use in source and binary forms, with or without
+modification, are permitted provided that the following conditions are met:
+
+    * Redistributions of source code must retain the above copyright
+      notice, this list of conditions and the following disclaimer.
+
+    * Redistributions in binary form must reproduce the above
+      copyright notice, this list of conditions and the following
+      disclaimer in the documentation and/or other materials provided
+      with the distribution.
+
+    * Neither the name of Author name here nor the names of other
+      contributors may be used to endorse or promote products derived
+      from this software without specific prior written permission.
+
+THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
+"AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT
+LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR
+A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT
+OWNER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL,
+SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT
+LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE,
+DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY
+THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT
+(INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE
+OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
diff --git a/Haskell/app/Main.hs b/Haskell/app/Main.hs
@@ -0,0 +1,55 @@
+module Main where
+
+import Numeric
+import Numeric.Natural
+import System.Clock
+
+main :: IO ()
+main = do
+    putStrLn "\nThis program is a simple test for the following conjecture:\n"
+    putStrLn "Let S: N -> N be the sum of the digits of a positive integer."
+    putStrLn "For all A and B in N, S(A + B) = S(A) + S(B) - 9k, where k is an interger.\n"
+    putStrLn "What value would you like to test the conjecture for?"
+
+    maxStr <- getLine
+    let max = readDec maxStr
+
+    if (not $ null max) && ((snd $ head max ) == "")
+        then let counter = exceptions' 0 (fst $ head max) in do
+            start <- getTime Monotonic
+            putStrLn "\nLOADING. . ."
+
+            if null counter
+                then do 
+                    end <- getTime Monotonic
+                    putStrLn $ "LOADED in " ++ formatTime (end - start) ++ "s [1 Thread]"
+                    putStrLn $ "\nThe conjecture is proved for all natural numbers smaller or equals to " ++ show (fst $ head max) ++ "!"
+                    exit
+                else do
+                    putStrLn $ "\nThe conjecture is disproved! Here are the counter examples:\n" ++ (init $ tail $ show counter)
+                    exit
+        else do
+            putStrLn $ "\n'" ++ maxStr ++ "' is not a natural number!"
+            exit
+
+exit :: IO ()
+exit = do
+    putStrLn "Press any key to continue. . ."
+    getChar
+    return ()
+
+digs :: Natural -> [Natural]
+digs 0 = [0]
+digs x = digs (x `div` 10) ++ [x `mod` 10]
+
+sum' :: Natural -> Natural
+sum' x = sum $ digs x
+
+test' :: Natural -> Natural -> Bool
+test' a b = ((fromEnum $ sum' (a + b)) - (fromEnum $ sum' a) - (fromEnum $ sum' b)) `mod` 9 == 0
+
+exceptions' :: Natural -> Natural -> [(Natural, Natural)]
+exceptions' min max = [(a, b) | a <- [min..max], b <- [a..max], not $ test' a b]
+
+formatTime :: TimeSpec -> [Char]
+formatTime t = show (sec t) ++ "." ++ show (nsec t `div` 10^8)+
\ No newline at end of file
diff --git a/Haskell/conjecture.cabal b/Haskell/conjecture.cabal
@@ -0,0 +1,56 @@
+cabal-version: 1.12
+
+-- This file has been generated from package.yaml by hpack version 0.31.1.
+--
+-- see: https://github.com/sol/hpack
+--
+-- hash: 3cf9a6d881ec7aedbc39501d43197ec9a1e4562b5d73a7f1f14420405cc67697
+
+name:           conjecture
+version:        1.0.0.0
+description:    This program is a simple test for a little conjecture of mine.
+author:         GarkGarcia
+maintainer:     thiago.brevidelli.garcia@gmail.com
+copyright:      2019 GarkGarcia
+license:        BSD3
+license-file:   LICENSE
+build-type:     Simple
+
+library
+  exposed-modules:
+      Lib
+  other-modules:
+      Paths_conjecture
+  hs-source-dirs:
+      src
+  build-depends:
+      base >=4.7 && <5
+    , clock ==0.7.2
+  default-language: Haskell2010
+
+executable conjecture-exe
+  main-is: Main.hs
+  other-modules:
+      Paths_conjecture
+  hs-source-dirs:
+      app
+  ghc-options: -threaded -rtsopts -with-rtsopts=-N
+  build-depends:
+      base >=4.7 && <5
+    , clock ==0.7.2
+    , conjecture
+  default-language: Haskell2010
+
+test-suite conjecture-test
+  type: exitcode-stdio-1.0
+  main-is: Spec.hs
+  other-modules:
+      Paths_conjecture
+  hs-source-dirs:
+      test
+  ghc-options: -threaded -rtsopts -with-rtsopts=-N
+  build-depends:
+      base >=4.7 && <5
+    , clock ==0.7.2
+    , conjecture
+  default-language: Haskell2010
diff --git a/Haskell/package.yaml b/Haskell/package.yaml
@@ -0,0 +1,47 @@
+name:                conjecture
+version:             1.0.0.0
+license:             BSD3
+author:              "GarkGarcia"
+maintainer:          "thiago.brevidelli.garcia@gmail.com"
+copyright:           "2019 GarkGarcia"
+
+extra-source-files: []
+
+# Metadata used when publishing your package
+# synopsis:            Short description of your package
+# category:            Web
+
+# To avoid duplicated efforts in documentation and dealing with the
+# complications of embedding Haddock markup inside cabal files, it is
+# common to point users to the README.md file.
+description: This program is a simple test for a little conjecture of mine.
+
+dependencies:
+  - base >= 4.7 && < 5
+  - clock == 0.7.2
+
+library:
+  source-dirs: src
+
+executables:
+  conjecture-exe:
+    main: Main.hs
+    source-dirs: app
+    ghc-options:
+      - -threaded
+      - -rtsopts
+      - -with-rtsopts=-N
+    dependencies:
+      - conjecture
+      - clock == 0.7.2
+
+tests:
+  conjecture-test:
+    main: Spec.hs
+    source-dirs: test
+    ghc-options:
+      - -threaded
+      - -rtsopts
+      - -with-rtsopts=-N
+    dependencies:
+      - conjecture
diff --git a/Haskell/src/Lib.hs b/Haskell/src/Lib.hs
@@ -0,0 +1 @@
+module Lib where+
\ No newline at end of file
diff --git a/Haskell/stack.yaml b/Haskell/stack.yaml
@@ -0,0 +1,68 @@
+# This file was automatically generated by 'stack init'
+#
+# Some commonly used options have been documented as comments in this file.
+# For advanced use and comprehensive documentation of the format, please see:
+# https://docs.haskellstack.org/en/stable/yaml_configuration/
+
+# Resolver to choose a 'specific' stackage snapshot or a compiler version.
+# A snapshot resolver dictates the compiler version and the set of packages
+# to be used for project dependencies. For example:
+#
+# resolver: lts-3.5
+# resolver: nightly-2015-09-21
+# resolver: ghc-7.10.2
+#
+# The location of a snapshot can be provided as a file or url. Stack assumes
+# a snapshot provided as a file might change, whereas a url resource does not.
+#
+# resolver: ./custom-snapshot.yaml
+# resolver: https://example.com/snapshots/2018-01-01.yaml
+resolver: lts-13.10
+
+# User packages to be built.
+# Various formats can be used as shown in the example below.
+#
+# packages:
+# - some-directory
+# - https://example.com/foo/bar/baz-0.0.2.tar.gz
+# - location:
+#    git: https://github.com/commercialhaskell/stack.git
+#    commit: e7b331f14bcffb8367cd58fbfc8b40ec7642100a
+# - location: https://github.com/commercialhaskell/stack/commit/e7b331f14bcffb8367cd58fbfc8b40ec7642100a
+#  subdirs:
+#  - auto-update
+#  - wai
+packages:
+  - .
+# Dependency packages to be pulled from upstream that are not in the resolver
+# using the same syntax as the packages field.
+# (e.g., acme-missiles-0.3)
+extra-deps:
+  - conduit-1.2.13.1@sha256:afd4db7fe66ae7af3d418e1a932384a8dee08df2f6299cca80e53ba964ce1228
+  - conduit-extra-1.1.17@sha256:a4e6f476ba86db2c7cb76993b43b2a156b010de2917d239af66f9d7e7599e269
+  - resourcet-1.1.11@sha256:096a3db6774a728bbe264e3e25c4e40d60e527ebd4b90c0b311deaa8d4cf4f27
+  - streaming-commons-0.1.19@sha256:3a02f84578f75eac1425dca877f8d697b68d379a21970c1dad96196620404803
+
+# Override default flag values for local packages and extra-deps
+# flags: {}
+
+# Extra package databases containing global packages
+# extra-package-dbs: []
+
+# Control whether we use the GHC we find on the path
+# system-ghc: true
+#
+# Require a specific version of stack, using version ranges
+# require-stack-version: -any # Default
+# require-stack-version: ">=1.9"
+#
+# Override the architecture used by stack, especially useful on Windows
+# arch: i386
+# arch: x86_64
+#
+# Extra directories used by stack for building
+# extra-include-dirs: [/path/to/dir]
+# extra-lib-dirs: [/path/to/dir]
+#
+# Allow a newer minor version of GHC than the snapshot specifies
+# compiler-check: newer-minor
diff --git a/Haskell/test/Spec.hs b/Haskell/test/Spec.hs
@@ -0,0 +1,2 @@
+main :: IO ()
+main = putStrLn "Test suite not yet implemented"
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diff --git a/Latex/digital_sum.pdf b/Latex/digital_sum.pdf
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diff --git a/Latex/digital_sum.synctex.gz b/Latex/digital_sum.synctex.gz
Binary files differ.
diff --git a/Latex/digital_sum.tex b/Latex/digital_sum.tex
@@ -0,0 +1,42 @@
+\documentclass{article}
+\usepackage{blindtext}
+\usepackage{amsfonts}
+\usepackage{mathtools}
+\pagenumbering{gobble}
+\usepackage[a4paper, total={6in, 9in}]{geometry}
+\usepackage[utf8]{inputenc}
+\title{Conjectura Mia}
+\author{Eli \& Thiago}
+\date{29 de dezembro de 2018}
+\begin{document}
+	\maketitle
+	\section*{\textit{Conjecture:}}
+		Let $S:\mathbb{N} \rightarrow \mathbb{N}$ be the sum of digits of a number $n \in \mathbb{N}$ --- represented in a \textit{base $\delta$ posicional system} --- and let $\nu \coloneqq \delta - 1$. We have:
+		
+		$$
+		\forall a, b \in \mathbb{N} : S_{a+b}=S_a + S_b + \nu k, k \in \mathbb{Z}
+		$$
+
+	\section*{\textit{Proof:}}
+		For all $a \in \mathbb{N}$:
+		$$
+		a = a_0 \cdot 10_\delta^0 + a_1 \cdot 10_\delta^1 + \dots + a_n \cdot 10_\delta^n \Rightarrow S_a = a_0 + a_1 + \dots + a_n
+		$$
+		\noindent Therefore:
+		$$
+		\begin{matrix}
+		a = a_0 \cdot (1 + \nu)^0 + \dots + a_n (1 + \nu)^n = a_0 \cdot (1 + \nu k_0) + \dots + a_n \cdot (1 + \nu k_n) \\ = a_0 + \dots + a_n + \nu k = S_a + \nu k, k \in \mathbb{Z}
+		\end{matrix}
+		$$
+		
+		\noindent Thus, for $c \coloneqq a + b$:
+		$$
+		\begin{cases}
+		& c = S_c + \nu k, k \in \mathbb{Z} \\
+		& a + b = (S_a + \nu k) + (S_b + \nu k') = S_a + S_b + \nu k''\;|\; k, k', k''\in \mathbb{Z}
+		\end{cases}
+		$$
+		
+		Therefore $c = a + b \Rightarrow S_c + \nu k = S_a + S_b + \nu k'\;|\; k, k'\in \mathbb{Z} \Rightarrow S_c = S_{a + b} = S_a + S_b + \nu k, k \in \mathbb{Z}$
+		\noindent \textbf{Q.E.D}
+\end{document}+
\ No newline at end of file
diff --git a/README.md b/README.md
@@ -0,0 +1,18 @@
+# Conjecture Testing
+An exercise on _polyglossy_. The same problem solved on multiple languages.
+
+## Problem
+Let  <img src="https://latex.codecogs.com/gif.latex?S:\mathbb{N}&space;\mapsto&space;\mathbb{N}" title="S:\mathbb{N} \mapsto \mathbb{N}" /> be the sum of the digits of a positive integer.
+
+Prove that <img src="https://latex.codecogs.com/gif.latex?\forall&space;a,&space;b&space;\in\mathbb{N}&space;:&space;S_{a&space;&plus;&space;b}&space;=&space;S_a&space;&plus;&space;S_b&space;&plus;&space;9&space;k,&space;k&space;\in&space;\mathbb{Z}" title="\forall a, b \in\mathbb{N} : S_{a + b} = S_a + S_b + \nu \cdot k, k \in \mathbb{Z}" />.
+
+## Performance
+The conjecture was [proved by exhaustion](https://en.wikipedia.org/wiki/Proof_by_exhaustion) for the interval <img src="https://latex.codecogs.com/gif.latex?[0;10^3]" title="[0;10^3]" /> in multiple language implementations. The performance of each language was then avaliated as the following:
+|Language      |Time   |Number of Threads Used|
+|--------------|-------|----------------------|
+|**Rust**      |22 _s_ |2                     |
+|**Haskell**   |60 _s_ |1                     |
+|**TypeScript**|198 _s_|1                     |
+|**JavaScript**|202 _s_|1                     |
+|**Ruby**      |273 _s_|1                     |
+|**Python**    |400 _s_|1                     |+
\ No newline at end of file
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diff --git a/src/main.rs b/Rust/src/main.rs
diff --git a/TypeScript/script.js b/TypeScript/script.js
@@ -0,0 +1,109 @@
+// The following script is a simple test for the following conjecture:
+// Let S: N -> N be the sum of the digits of a positive integer.
+// For all A and B in N, S(A + B) = S(A) + S(B) - 9k, where k is an interger.
+const readline = require('readline');
+class Int {
+    constructor(n) {
+        this.val = n;
+    }
+    add(n) {
+        return new Int(this.val + n.val);
+    }
+    subtrack(n) {
+        return new Int(this.val - n.val);
+    }
+    multiply(n) {
+        return new Int(this.val * n.val);
+    }
+    divide(n) {
+        return new Int(Math.floor(this.val / n.val));
+    }
+    incrementBy(n) {
+        this.val += n.val;
+    }
+    divides(n) {
+        return (n.val / this.val) % 1 == 0;
+    }
+    getDigits() {
+        return Array.from(this.val.toString()).map(char => Int.from(char));
+    }
+    sumDigits() {
+        let sum = Int.zero();
+        const digits = this.getDigits();
+        for (const n of digits)
+            sum.incrementBy(n);
+        return sum;
+    }
+    toString() {
+        return `${this.val}`;
+    }
+    static from(a) {
+        return new Int(Math.round(Number(a)));
+    }
+    static getRange(a, b) {
+        const start = a.val, end = b.val, range = [];
+        for (let i = start; i < end; i++) {
+            range.push(Int.from(i));
+        }
+        return range;
+    }
+    static zero() {
+        return new Int(0);
+    }
+    static one() {
+        return new Int(1);
+    }
+}
+function askQuestion(query) {
+    const rl = readline.createInterface({
+        input: process.stdin,
+        output: process.stdout,
+    });
+    return new Promise((resolve) => rl.question(query, (ans) => {
+        rl.close();
+        resolve(ans);
+    }));
+}
+function getCounterExp(max) {
+    const starTime = new Date(), counterexmpls = [], nine = Int.from(9);
+    let loadBar = Int.zero();
+    for (const a of Int.getRange(Int.one(), max)) {
+        const newLoadBar = a.multiply(Int.from(100)).divide(max);
+        if (loadBar != newLoadBar) {
+            console.clear();
+            loadBar = newLoadBar;
+            console.log(`LOADING. . . ${loadBar}%`);
+        }
+        for (const b of Int.getRange(a, max)) {
+            // Check if the difference between S(a + b) and (S(a) + S(b)) is a multiple of 9
+            const conjectureHolds = nine.divides(a.add(b).sumDigits().subtrack(a.sumDigits().add(b.sumDigits())));
+            if (!conjectureHolds)
+                counterexmpls.push([a, b]);
+        }
+    }
+    const elepsedTime = (new Date().getTime() - starTime.getTime()) / 1000;
+    console.clear();
+    console.log(`LOADED. . . ${loadBar}% in ${elepsedTime}s\n`);
+    return counterexmpls;
+}
+console.log(`This script is a simple test for the following conjecture:
+    
+Let S: N -> N be the sum of the digits of a positive integer.
+For all A and B in N, S(A + B) = S(A) + S(B) - 9k, where k is an interger.
+`);
+askQuestion("What value would you like to test the conjecture for? ").then(ans => {
+    if (!isNaN(Number(ans))) {
+        const max = Int.from(ans), counterexmpls = getCounterExp(max);
+        if (counterexmpls.length == 0)
+            console.log(`The conjecture is proved for all natural numbers smaller or equals to ${max}!`);
+        else {
+            console.log("The conjecture is disproved! Here are the counter examples:");
+            let counterexmplsStr = "";
+            for (const pair of counterexmpls)
+                counterexmplsStr = `${counterexmplsStr}, (${pair[0]}, ${pair[1]})`;
+            console.log(counterexmplsStr);
+        }
+    }
+    else
+        console.log(`'${ans}' is not an interger!`);
+}).catch(console.error);
diff --git a/TypeScript/script.min.js b/TypeScript/script.min.js
@@ -0,0 +1 @@
+const e=require("readline");class t{constructor(e){this.val=e}add(e){return new t(this.val+e.val)}subtrack(e){return new t(this.val-e.val)}multiply(e){return new t(this.val*e.val)}divide(e){return new t(Math.floor(this.val/e.val))}incrementBy(e){this.val+=e.val}divides(e){return e.val/this.val%1==0}getDigits(){return Array.from(this.val.toString()).map(e=>t.from(e))}sumDigits(){let e=t.zero();const o=this.getDigits();for(const t of o)e.incrementBy(t);return e}toString(){return`${this.val}`}static from(e){return new t(Math.round(Number(e)))}static getRange(e,o){const r=e.val,n=o.val,s=[];for(let e=r;e<n;e++)s.push(t.from(e));return s}static zero(){return new t(0)}static one(){return new t(1)}}console.log("This script is a simple test for the following conjecture:\n    \nLet S: N -> N be the sum of the digits of a positive integer.\nFor all A and B in N, S(A + B) = S(A) + S(B) - 9k, where k is an interger.\n"),function(t){const o=e.createInterface({input:process.stdin,output:process.stdout});return new Promise(e=>o.question(t,t=>{o.close(),e(t)}))}("What value would you like to test the conjecture for? ").then(e=>{if(isNaN(Number(e)))console.log(`'${e}' is not an interger!`);else{const o=t.from(e),r=function(e){const o=new Date,r=[],n=t.from(9);let s=t.zero();for(const o of t.getRange(t.one(),e)){const i=o.multiply(t.from(100)).divide(e);s!=i&&(console.clear(),s=i,console.log(`LOADING. . . ${s}%`));for(const s of t.getRange(o,e))n.divides(o.add(s).sumDigits().subtrack(o.sumDigits().add(s.sumDigits())))||r.push([o,s])}const i=((new Date).getTime()-o.getTime())/1e3;return console.clear(),console.log(`LOADED. . . ${s}% in ${i}s\n`),r}(o);if(0==r.length)console.log(`The conjecture is proved for all natural numbers smaller or equals to ${o}!`);else{console.log("The conjecture is disproved! Here are the counter examples:");let e="";for(const t of r)e=`${e}, (${t[0]}, ${t[1]})`;console.log(e)}}}).catch(console.error);+
\ No newline at end of file
diff --git a/TypeScript/script.ts b/TypeScript/script.ts
@@ -0,0 +1,140 @@
+// The following script is a simple test for the following conjecture:
+
+// Let S: N -> N be the sum of the digits of a positive integer.
+// For all A and B in N, S(A + B) = S(A) + S(B) - 9k, where k is an interger.
+
+const readline = require('readline');
+
+class Int {
+    private val: number;
+
+    private constructor(n: number) {
+        this.val = n;
+    }
+
+    public add(n: Int): Int {
+        return new Int(this.val + n.val);
+    }
+
+    public subtrack(n: Int): Int {
+        return new Int(this.val - n.val);
+    }
+
+    public multiply(n: Int): Int {
+        return new Int(this.val * n.val);
+    }
+
+    public divide(n: Int): Int {
+        return new Int(Math.floor(this.val / n.val));
+    }
+
+    public incrementBy(n: Int) {
+        this.val += n.val;
+    }
+
+    public divides(n: Int): boolean {
+        return (n.val / this.val) % 1 == 0;
+    }
+
+    public getDigits(): Int[] {
+        return Array.from(this.val.toString()).map(char => Int.from(char));
+    }
+
+    public sumDigits(): Int {
+        let sum = Int.zero();
+        const digits = this.getDigits();
+
+        for (const n of digits)
+            sum.incrementBy(n);
+
+        return sum;
+    }
+
+    public toString(): string {
+        return `${this.val}`;
+    }
+
+    static from(a: number | string): Int {
+        return new Int(Math.round(Number(a)));
+    }
+
+    static getRange(a: Int, b: Int): Int[] {
+        const start = a.val, end = b.val, range: Int[] = [];
+
+        for (let i = start; i < end; i++) {
+            range.push(Int.from(i));
+        }
+
+        return range;
+    }
+
+    static zero(): Int {
+        return new Int(0);
+    }
+
+    static one(): Int {
+        return new Int(1);
+    }
+}
+
+function askQuestion(query: string): Promise<string> {
+    const rl = readline.createInterface({
+        input: process.stdin,
+        output: process.stdout,
+    });
+
+    return new Promise(resolve => rl.question(query, (ans: string) => {
+        rl.close();
+        resolve(ans);
+    }));
+}
+
+function getCounterExp(max: Int) {
+    const starTime = new Date(), counterexmpls: [Int, Int][] = [], nine = Int.from(9);
+    let loadBar = Int.zero();
+
+    for (const a of Int.getRange(Int.one(), max)) {
+
+        const newLoadBar = a.multiply(Int.from(100)).divide(max);
+        if (loadBar != newLoadBar) {
+            console.clear();
+            loadBar = newLoadBar;
+            console.log(`LOADING. . . ${loadBar}%`);
+        }
+
+        for (const b of Int.getRange(a, max)) {
+            // Check if the difference between S(a + b) and (S(a) + S(b)) is a multiple of 9
+            const conjectureHolds = nine.divides(a.add(b).sumDigits().subtrack(a.sumDigits().add(b.sumDigits())));
+            if (!conjectureHolds) counterexmpls.push([a, b]);
+        }
+    }
+
+    const elepsedTime = (new Date().getTime() - starTime.getTime()) / 1000;
+    console.clear();
+    console.log(`LOADED. . . ${loadBar}% in ${elepsedTime}s\n`);
+    return counterexmpls;
+}
+
+console.log(`This script is a simple test for the following conjecture:
+    
+Let S: N -> N be the sum of the digits of a positive integer.
+For all A and B in N, S(A + B) = S(A) + S(B) - 9k, where k is an interger.
+`);
+
+askQuestion("What value would you like to test the conjecture for? ").then(ans => {
+    if (!isNaN(Number(ans))) {
+        const max = Int.from(ans), counterexmpls = getCounterExp(max);
+
+        if (counterexmpls.length == 0)
+            console.log(`The conjecture is proved for all natural numbers smaller or equals to ${max}!`);
+        else {
+            console.log("The conjecture is disproved! Here are the counter examples:");
+
+            let counterexmplsStr = "";
+            for (const pair of counterexmpls)
+                counterexmplsStr = `${counterexmplsStr}, (${pair[0]}, ${pair[1]})`;
+            
+            console.log(counterexmplsStr);
+        }
+    } else console.log(`'${ans}' is not an interger!`);
+}).catch(console.error);+
\ No newline at end of file
diff --git a/script.js b/script.js
@@ -0,0 +1,96 @@
+// The following script is a simple test for the following conjecture:
+
+// Let S: N -> N be the sum of the digits of a positive integer.
+// For all A and B in N, S(A + B) = S(A) + S(B) - 9k, where k is an interger.
+
+const readline = require('readline');
+
+Array.prototype.none = function() {
+    return this.length == 0;
+}
+
+Number.prototype.getDigits = function() {
+    return Array.from(String(this)).map(char => Number(char));
+}
+
+Number.prototype.divides = function(n) {
+    return (n / this) % 1 == 0;
+}
+
+Number.prototype.sumDigits = function() {
+    let sum = 0;
+    const digits = this.getDigits();
+
+    for (n of digits)
+        sum += n;
+
+    return sum;
+}
+
+function askQuestion(query) {
+    const rl = readline.createInterface({
+        input: process.stdin,
+        output: process.stdout,
+    });
+
+    return new Promise(resolve => rl.question(query, ans => {
+        rl.close();
+        resolve(ans);
+    }))
+}
+
+function getCounterExp(max) {
+    const starTime = new Date();
+
+    const counterexmpls = [];
+    let loadBar = 0;
+
+    for (let a = 1; a <= max; a++) {
+        
+        // Print the progress on the screen
+        const newLoadBar = Math.round(a * 100 / max);
+        if (loadBar != newLoadBar) {
+            console.clear();
+            loadBar = newLoadBar;
+            console.log(`LOADING. . . ${loadBar}%`);
+        }
+
+        for (b = a; b <= max; b++) {
+
+            // Check if the difference between S(a + b) and (S(a) + S(b)) is a multiple of 9
+            const conjectureHolds = (9).divides(
+                (a + b).sumDigits() - (a.sumDigits() + b.sumDigits())
+            );
+            if (!conjectureHolds) counterexmpls.push([a, b]);
+        }
+    }
+
+    const elepsedTime = (new Date() - starTime) / 1000;
+    console.clear();
+    console.log(`LOADED. . . ${loadBar}% in ${elepsedTime}s\n`);
+    return counterexmpls;
+}
+
+console.log(`This script is a simple test for the following conjecture:
+    
+Let S: N -> N be the sum of the digits of a positive integer.
+For all A and B in N, S(A + B) = S(A) + S(B) - 9k, where k is an interger.
+`);
+
+askQuestion("What value would you like to test the conjecture for? ").then(ans => {
+    if (!isNaN(Number(ans))) {
+        const max = Math.round(Number(ans)), counterexmpls = getCounterExp(max);
+
+        if (counterexmpls.none())
+            console.log(`The conjecture is proved for all natural numbers smaller or equals to ${max}!`);
+        else {
+            console.log("The conjecture is disproved! Here are the counter examples:");
+
+            let counterexmplsStr = "";
+            for (pair in counterexmpls)
+                counterexmpls = `${counterexmplsStr}, (${pair[0]}, ${pair[1]})`;
+            
+            console.log(counterexmplsStr);
+        }
+    } else console.log(`'${ans}' is not an interger!`);
+});+
\ No newline at end of file
diff --git a/script.min.js b/script.min.js
@@ -0,0 +1 @@
+const e=require("readline");Array.prototype.t=function(){return 0==this.length},Number.prototype.o=function(){return Array.from(String(this)).map(e=>Number(e))},Number.prototype.s=function(e){return e/this%1==0},Number.prototype.i=function(){let e=0;const t=this.o();for(n of t)e+=n;return e},console.log("This script is a simple test for the following conjecture:\n    \nLet S: N -> N be the sum of the digits of a positive integer.\nFor all A and B in N, S(A + B) = S(A) + S(B) - 9k, where k is an interger.\n"),function(n){const t=e.createInterface({input:process.stdin,output:process.stdout});return new Promise(e=>t.question(n,n=>{t.close(),e(n)}))}("What value would you like to test the conjecture for? ").then(e=>{if(isNaN(Number(e)))console.log(`'${e}' is not an interger!`);else{const n=Math.round(Number(e)),t=function(e){const n=new Date,t=[];let r=0;for(let n=1;n<=e;n++){const o=Math.round(100*n/e);for(r!=o&&(console.clear(),r=o,console.log(`LOADING. . . ${r}%`)),b=n;b<=e;b++)9..s((n+b).i()-(n.i()+b.i()))||t.push([n,b])}const o=(new Date-n)/1e3;return console.clear(),console.log(`LOADED. . . ${r}% in ${o}s\n`),t}(n);if(t.t())console.log(`The conjecture is proved for all natural numbers smaller or equals to ${n}!`);else{console.log("The conjecture is disproved! Here are the counter examples:");let e="";for(pair in t)t=`${e}, (${pair[0]}, ${pair[1]})`;console.log(e)}}});+
\ No newline at end of file
diff --git a/script.py b/script.py
@@ -0,0 +1,84 @@
+# The following script is a simple test for the following conjecture:
+
+# Let S: N -> N be the sum of the digits of a positive integer.
+# For all A and B in N, S(A + B) = S(A) + S(B) - 9k, where k is an interger.
+
+import sys
+import os
+import time
+
+# A function for clearing the prompt
+clear = (lambda : os.system("cls")) if sys.platform.startswith("win") else (lambda : os.system("clear"))
+
+def is_multiple_of_nine(n):
+    return (n / 9) % 1 == 0
+
+def get_digits(n):
+    output = []
+
+    for ch in str(n):
+        output.append(int(ch))
+    
+    return output
+
+def sum_digits(n):
+    digits = get_digits(n)
+    output = 0
+
+    for d in digits:
+        output += d 
+    
+    return output
+
+def get_counterexmpls(n):
+    start_time = time.time()
+
+    load_bar = 0
+    counterexmpls = []
+
+    for a in range(n + 1):
+        
+        # Print the progress on the screen
+        if not round(a * 100 / n) == load_bar:
+            load_bar = round(a * 100 / n)
+            clear()
+            print("LOADING. . . %s%%" % load_bar)
+
+        for b in range(a, n + 1):
+            difference = sum_digits(a + b) - (sum_digits(a) + sum_digits(b))
+
+            if not is_multiple_of_nine(difference):
+                counterexmpls.append([a, b])
+
+    # Mesure the elepsed time
+    elepsed_time = time.time() - start_time
+    clear()
+    print("LOADED. . . %s%% in %ds\n" % (load_bar, elepsed_time))
+    
+    return counterexmpls    
+
+
+print("""The following script is a simple test for the following conjecture:
+
+Let S: N -> N be the sum of the digits of a positive integer.
+For all A and B in N, S(A + B) = S(A) + S(B) - 9k, where k is an interger.
+""")
+user_input = input("What value would you like to test the conjecture for? ")
+
+try:
+    maximum = abs(int(user_input))
+    clear()
+    counterexmpls = get_counterexmpls(maximum)
+
+    if len(counterexmpls) == 0:
+        print("The conjecture is proved for all natural numbers smaller or equals to %s!" % maximum)
+    else:
+        print("The conjecture is disproved! Here are the counter examples:")
+
+        counterexmpls_str = ""
+        for pair in counterexmpls:
+            counterexmpls_str = "%s, (%d, %f)" % (counterexmpls_str, pair[0], pair[1])
+        
+        print(counterexmpls_str)
+except:
+    print("'%s' isn't a valid number!" % user_input)
diff --git a/script.rb b/script.rb
@@ -0,0 +1,98 @@
+class Integer
+    def divides n
+        return (n / self) * self == n
+    end
+
+    def digits base: 10
+        quotient, remainder = divmod(base)
+        return quotient == 0 ? [remainder] : [*quotient.digits(base: base), remainder]
+    end
+
+    def sum_digits
+        sum = 0
+
+        for n in self.digits
+            sum += n
+        end
+
+        return sum
+    end
+end
+
+def get_counterexpls max
+    start_time = Time.now
+
+    counterexpls = []
+    progress_percent = 0
+
+    for a in (0..max)
+        new_progress = a * 100 / max
+
+        if progress_percent != new_progress
+            progress_percent = new_progress
+            clear()
+            puts "LOADING. . . #{new_progress}%"
+        end
+
+        for b in (a..max)
+            difference = (a + b).sum_digits() - a.sum_digits() - b.sum_digits()
+
+            if !9.divides(difference)
+                counterexpls.push([a, b])
+            end
+        end
+    end
+
+    elepsed_time = Time.now - start_time
+    clear()
+    puts "LOADED. . . #{progress_percent}% in #{elepsed_time}s\n\n"
+
+    return counterexpls
+end
+
+def clear
+    if /win32|win64|\.NET|windows|cygwin|mingw32/i.match(RUBY_PLATFORM)
+       system('cls')
+    else
+       system('clear')
+    end
+end
+
+def pause
+    if /win32|win64|\.NET|windows|cygwin|mingw32/i.match(RUBY_PLATFORM)
+        system('pause')
+    else
+        system('read')
+    end
+end
+
+puts "The following script is a simple test for the following conjecture:\n\n"
+puts "Let S: N -> N be the sum of the digits of a positive integer."
+puts "For all A and B in N, S(A + B) = S(A) + S(B) - 9k, where k is an interger.\n\n"
+puts "What value would you like to test the conjecture for?"
+
+user_input = gets
+
+# Check if the input provided by the user in an iteger
+if /^(?:-?[1-9]\d*$)|(?:^0)$/.match(user_input)
+    max = user_input.to_i()
+    counterexpls = get_counterexpls(max)
+
+    if counterexpls.length == 0
+        puts "The conjecture is proved for all natural numbers smaller or equals to #{max}!"
+    else
+        puts "The conjecture is disproved! Here are the counter examples:"
+
+        counterexpls_str = ""
+        for pair in counterexpls
+            counterexpls_str = "#{counterexpls_str}, (#{pair[0]}, #{pair[1]})"
+        end
+
+        puts counterexpls_str
+    end
+else
+    puts "'#{user_input.chomp}' isn't an iteger!"
+end
+
+puts ""
+pause()+
\ No newline at end of file
diff --git a/script.ts b/script.ts
@@ -0,0 +1,140 @@
+// The following script is a simple test for the following conjecture:
+
+// Let S: N -> N be the sum of the digits of a positive integer.
+// For all A and B in N, S(A + B) = S(A) + S(B) - 9k, where k is an interger.
+
+const readline = require('readline');
+
+class Int {
+    private val: number;
+
+    private constructor(n: number) {
+        this.val = n;
+    }
+
+    public add(n: Int): Int {
+        return new Int(this.val + n.val);
+    }
+
+    public subtrack(n: Int): Int {
+        return new Int(this.val - n.val);
+    }
+
+    public multiply(n: Int): Int {
+        return new Int(this.val * n.val);
+    }
+
+    public divide(n: Int): Int {
+        return new Int(Math.floor(this.val / n.val));
+    }
+
+    public incrementBy(n: Int) {
+        this.val += n.val;
+    }
+
+    public divides(n: Int): boolean {
+        return (n.val / this.val) % 1 == 0;
+    }
+
+    public getDigits(): Int[] {
+        return Array.from(this.val.toString()).map(char => Int.from(char));
+    }
+
+    public sumDigits(): Int {
+        let sum = Int.zero();
+        const digits = this.getDigits();
+
+        for (const n of digits)
+            sum.incrementBy(n);
+
+        return sum;
+    }
+
+    public toString(): string {
+        return `${this.val}`;
+    }
+
+    static from(a: number | string): Int {
+        return new Int(Math.round(Number(a)));
+    }
+
+    static getRange(a: Int, b: Int): Int[] {
+        const start = a.val, end = b.val, range: Int[] = [];
+
+        for (let i = start; i < end; i++) {
+            range.push(Int.from(i));
+        }
+
+        return range;
+    }
+
+    static zero(): Int {
+        return new Int(0);
+    }
+
+    static one(): Int {
+        return new Int(1);
+    }
+}
+
+function askQuestion(query: string) {
+    const rl = readline.createInterface({
+        input: process.stdin,
+        output: process.stdout,
+    });
+
+    return new Promise((resolve: (value?: string | PromiseLike<string>) => void) => rl.question(query, (ans: string) => {
+        rl.close();
+        resolve(ans);
+    }));
+}
+
+function getCounterExp(max: Int) {
+    const starTime = new Date(), counterexmpls: [Int, Int][] = [], nine = Int.from(9);
+    let loadBar = Int.zero();
+
+    for (const a of Int.getRange(Int.one(), max)) {
+
+        const newLoadBar = a.multiply(Int.from(100)).divide(max);
+        if (loadBar != newLoadBar) {
+            console.clear();
+            loadBar = newLoadBar;
+            console.log(`LOADING. . . ${loadBar}%`);
+        }
+
+        for (const b of Int.getRange(a, max)) {
+            // Check if the difference between S(a + b) and (S(a) + S(b)) is a multiple of 9
+            const conjectureHolds = nine.divides(a.add(b).sumDigits().subtrack(a.sumDigits().add(b.sumDigits())));
+            if (!conjectureHolds) counterexmpls.push([a, b]);
+        }
+    }
+
+    const elepsedTime = (new Date().getTime() - starTime.getTime()) / 1000;
+    console.clear();
+    console.log(`LOADED. . . ${loadBar}% in ${elepsedTime}s\n`);
+    return counterexmpls;
+}
+
+console.log(`This script is a simple test for the following conjecture:
+    
+Let S: N -> N be the sum of the digits of a positive integer.
+For all A and B in N, S(A + B) = S(A) + S(B) - 9k, where k is an interger.
+`);
+
+askQuestion("What value would you like to test the conjecture for? ").then(ans => {
+    if (!isNaN(Number(ans))) {
+        const max = Int.from(ans), counterexmpls = getCounterExp(max);
+
+        if (counterexmpls.length == 0)
+            console.log(`The conjecture is proved for all natural numbers smaller or equals to ${max}!`);
+        else {
+            console.log("The conjecture is disproved! Here are the counter examples:");
+
+            let counterexmplsStr = "";
+            for (const pair of counterexmpls)
+                counterexmplsStr = `${counterexmplsStr}, (${pair[0]}, ${pair[1]})`;
+            
+            console.log(counterexmplsStr);
+        }
+    } else console.log(`'${ans}' is not an interger!`);
+}).catch(console.error);+
\ No newline at end of file
diff --git a/script.ts.js b/script.ts.js
@@ -0,0 +1 @@
+const e=require("readline");class t{constructor(e){this.val=e}add(e){return new t(this.val+e.val)}subtrack(e){return new t(this.val-e.val)}multiply(e){return new t(this.val*e.val)}divide(e){return new t(Math.floor(this.val/e.val))}incrementBy(e){this.val+=e.val}divides(e){return e.val/this.val%1==0}getDigits(){return Array.from(this.val.toString()).map(e=>t.from(e))}sumDigits(){let e=t.zero();const o=this.getDigits();for(const t of o)e.incrementBy(t);return e}toString(){return`${this.val}`}static from(e){return new t(Math.round(Number(e)))}static getRange(e,o){const r=e.val,n=o.val,s=[];for(let e=r;e<n;e++)s.push(t.from(e));return s}static zero(){return new t(0)}static one(){return new t(1)}}console.log("This script is a simple test for the following conjecture:\n    \nLet S: N -> N be the sum of the digits of a positive integer.\nFor all A and B in N, S(A + B) = S(A) + S(B) - 9k, where k is an interger.\n"),function(t){const o=e.createInterface({input:process.stdin,output:process.stdout});return new Promise(e=>o.question(t,t=>{o.close(),e(t)}))}("What value would you like to test the conjecture for? ").then(e=>{if(isNaN(Number(e)))console.log(`'${e}' is not an interger!`);else{const o=t.from(e),r=function(e){const o=new Date,r=[],n=t.from(9);let s=t.zero();for(const o of t.getRange(t.one(),e)){const i=o.multiply(t.from(100)).divide(e);s!=i&&(console.clear(),s=i,console.log(`LOADING. . . ${s}%`));for(const s of t.getRange(o,e))n.divides(o.add(s).sumDigits().subtrack(o.sumDigits().add(s.sumDigits())))||r.push([o,s])}const i=((new Date).getTime()-o.getTime())/1e3;return console.clear(),console.log(`LOADED. . . ${s}% in ${i}s\n`),r}(o);if(0==r.length)console.log(`The conjecture is proved for all natural numbers smaller or equals to ${o}!`);else{console.log("The conjecture is disproved! Here are the counter examples:");let e="";for(const t of r)e=`${e}, (${t[0]}, ${t[1]})`;console.log(e)}}}).catch(console.error);+
\ No newline at end of file