Merge pull request #15 from macocci7/dev_#1

#1: create base functions: done.

Author: macocci7

README.md

@@ -4,10 +4,19 @@ Math library of Integer:
 
 PHP-Math-Integer treats the subjects of number theory (only natural number).
 
+## Contents
+
+- [Requirements](#requirements)
+- [Installation](#installation)
+- [Usage](#usage)
+- [Functions](#functions)
+- [Examples](#examples)
+- [LICENSE](#license)
+
 ## Requirements
 
 - PHP 8.0.0 (CLI) or later
-- Composer
+- [Composer](https://getcomposer.org/)
 
 ## Installation
 
@@ -17,24 +26,100 @@ composer require macocci7/php-math-integer
 
 ## Usage
 
+See [Examples](#examples).
+
 ## Functions
 
-- Number
-- Prime
-- Divisor
-- Multiple
-- Euclid (Euclidean Algorithm)
-- Fraction
-- Bezout (Bezout's Equation)
+- Number: treats basic matters of numbers
+  - isInt(): judges if the param is integer or not
+  - isIntAll(): judges if all of the param are integer or not
+  - isNatural(): judges if the param is natural number or not
+  - isNaturalAll(): judges if all of the param are natural number or not
+  - isFloat(): judges if the param is float or not
+  - isFloatAll(): judges if all of the param are float or not
+  - isNumber(): judges if the param is number or not (different from is_numeric())
+  - isNumberAll(): judges if all of the param are number or not
+  - isFraction(): judges if the param is decimal fraction or not
+  - isFractionAll(): judges if all of the param are fraction or not
+  - sign(): returns the sign of the param as one of -1, 0 or 1
+  - int(): returns the integral part of the param
+  - fraction(): returns the fractional part of the param
+  - nthDigit(): returns the nth digit of the param
+  - numberOfDigits(): returns the number of digits of the param
+  - numberOfFractionalDigits(): returns the number of fractional digits of the param
+
+- Prime: treats matters of primes
+  - isPrime(): judges if the param is prime or not
+  - isPrimeAll(): judges if all of the param are prime or not
+  - next(): returns a prime next to the param
+  - between(): returns array of primes between the params
+  - factorize(): factorize the param and returns the process as an array
+  - factors(): returns the factorized factors of the param as an array
+  - factorizedFormula(): returns the factorized formula as an array
+
+- Divisor: treats matters of divisors
+  - count(): returns the number of divisors of the param
+  - value(): converts the factorized array into an integer and returns it
+  - formula(): returns the factorized formula as strings
+  - list(): returns all of divisors of the param as an array
+  - commonFactors(): returns common factors of the params as an array
+  - greatestCommonFactor(): returns the greatest common factor of the params
+  - commonDivisors(): returns all of common divisors of the param as an array
+  - reduceFraction(): returns reduced fraction consisting of the params as an array
+
+- Multiple: treats matters of multiples
+  - leastCommonMultiple(): returns the least common multiple of the params
+
+- Euclid (Euclidean Algorithm): treats matters of Euclidean Algorithm
+  - run(): runs the Euclidean Algorithm and returns the result as an array
+  - gcd(): returns the greatest common divisor of the params
+  - isGcdOf(): judges if the first param is gcd of the other params or not
+  - isCoprime(): judges if the params are coprime or not
+
+- Fraction: treats matters of Fractions
+  - set(): sets the properties of the fraction specified by the param
+  - isReduced(): judges if the fraction is reduced or not
+  - isProper(): judges if the fraction is a proper fraction or not
+  - isImproper(): judges if the fraction is a improper fraction or not
+  - isMixed(): judges if the fraction is a mixed fraction or not
+  - reduce(): reduces the fraction
+  - toCommonDenominator(): converts the fractions into a common denominator
+  - add(): adds the param to the fraction
+  - substruct(): substructs the param from the fraction
+  - multiply(): multiplies the fraction by the param
+  - divide(): divide the fraction by the param
+  - improper(): converts the fraction into a improper fraction
+  - mixed(): converts the fraction into a mixed fraction
+  - int(): returns the value of the fraction as an integer
+  - float(): returns the value of the fraction as an float
+  - text(): returns the fraction as one-line-text
+
+- Bezout (Bezout's Equation): treats matters of Bezout's Equations
+  - set(): sets the properties of a Bezout's Equation from the param
+  - clear(): clears the properties of the Bezout's Equation
+  - equation(): returns the Bezout's Equation as one-line-text
+  - isSolvable(): judges if the Bezout's Equation is solvable or not
+  - solution(): returns a set of solution as an array
+  - generalSolution(): returns the general solution as an array
+
+## Examples
+
+- [UseNumber.php](example/UseNumber.php) results in >> [UseNumber.txt](example/UseNumber.txt)
+- [UsePrime.php](example/UsePrime.php) results in >> [UsePrime.txt](example/UsePrime.txt)
+- [UseDivisor.php](example/UseDivisor.php) results in >> [UseDivisor.txt](example/UseDivisor.txt)
+- [UseMultiple.php](example/UseMultiple.php) results in >> [UseMultiple.txt](example/UseMultiple.txt)
+- [UseFraction.php](example/UseFraction.php) results in >> [UseFraction.txt](example/UseFraction.txt)
+- [UseEuclid.php](example/UseEuclid.php) results in >> [UseEuclid.txt](example/UseEuclid.txt)
+- [UseBezout.php](example/UseBezout.php) results in >> [UseBezout.txt](example/UseBezout.txt)
 
-## License
+## LICENSE
 
 [MIT](LICENSE)
 
 ***
 
 *Document Created: 2023/10/19*
 
-*Document Updated: 2023/11/04*
+*Document Updated: 2023/11/07*
 
 Copyright 2023 macocci7

composer.json

@@ -1,4 +1,21 @@
 {
+    "name": "macocci7/php-math-integer",
+    "version": "1.0.0",
+    "description": "PHP Math Library of the subjects of number theory(only natural number).",
+    "type": "library",
+    "license": "MIT",
+    "autoload": {
+        "psr-4": {
+            "Macocci7\\PhpMathInteger\\": "src/"
+        }
+    },
+    "authors": [
+        {
+            "name": "macocci7",
+            "email": "macocci7@yahoo.co.jp"
+        }
+    ],
+    "minimum-stability": "stable",
     "require-dev": {
         "squizlabs/php_codesniffer": "^3.7"
     }

composer.lock

@@ -0,0 +1,25 @@
+<?php
+
+/**
+ * Examples of operation with
+ * Macocci7\PhpMathInteger\Bezout
+ */
+
+require_once('../src/loader.php');
+
+use Macocci7\PhpMathInteger\Bezout;
+
+// Bezout's Equation: 3x + 4y = 1
+$b = new Bezout([3, 4, 1, ]);
+echo sprintf("Bezout's Equation: %s\n", $b->equation());
+
+// Solvable or not
+echo sprintf("Is it solvable? - %s.\n", ($b->isSolvable() ? 'Yes' : 'No'));
+
+// A solution set
+$s = $b->solution()['solution'];
+echo sprintf("A solutionset: (x, y) = (%d, %d)\n", $s['x'], $s['y']);
+
+// General solution
+$g = $b->generalSolution()['generalSolution']['formula'];
+echo sprintf("General solution:\n\t%s\n\t%s\n", $g['x'], $g['y']);

example/UseBezout.php

@@ -0,0 +1,6 @@
+Bezout's Equation: 3x + 4y = 1
+Is it solvable? - Yes.
+A solutionset: (x, y) = (-1, 1)
+General solution:
+	x = 4k - 1
+	y = 3k + 1

example/UseBezout.txt

@@ -26,7 +26,7 @@
 
 // Euclidean Algorithm
 $r = $e->run($a, $b);
-echo "Euclidean Algorrith:\n";
+echo "Euclidean Algorithm:\n";
 foreach ($r['processText'] as $t) {
     echo $t . "\n";
 }

example/UseEuclid.php

@@ -1,5 +1,5 @@
 Is 39 GCD(390, 273)? - Yes.
-Euclidean Algorrith:
+Euclidean Algorithm:
 390 = 273 * 1 + 117
 273 = 117 * 2 + 39
 117 = 39 * 3 + 0

example/UseEuclid.txt

@@ -12,20 +12,20 @@
 $n = new Number();
 
 var_dump(
-    $n->isInt(1),
-    $n->isIntAll([ 1, 2, 3, ]),
-    $n->isNatural(1),
-    $n->isNaturalAll([ 1, 2, 3, ]),
-    $n->isFloat(1.2),
-    $n->isFloatAll([ -2.1, 0.0, 1.2, ]),
-    $n->isNumber(1.2),
-    $n->isNumberAll([ -2, 0.1, 3, ]),
-    $n->isFraction(0.1),
-    $n->isFractionAll([ -0.99, 0.1, 0.99]),
-    $n->sign(-2.5),
-    $n->int(3.14),
-    $n->fraction(3.14),
-    $n->nthDigit(-3, 123.456),
-    $n->numberOfDigits(-123.4567),
-    $n->numberOfFractionalDigits(-12.3456),
+    $n->isInt(1), // true
+    $n->isIntAll([ 1, 2, 3, ]), // true
+    $n->isNatural(1), // true
+    $n->isNaturalAll([ 1, 2, 3, ]), // true
+    $n->isFloat(1.2), // true
+    $n->isFloatAll([ -2.1, 0.0, 1.2, ]), // true
+    $n->isNumber(1.2), // true
+    $n->isNumberAll([ -2, 0.1, 3, ]), // true
+    $n->isFraction(0.1), // true
+    $n->isFractionAll([ -0.99, 0.1, 0.99]), // true
+    $n->sign(-2.5), // -1
+    $n->int(3.14), // 3
+    $n->fraction(3.14), // 0.1400...
+    $n->nthDigit(-3, 123.456), // 6
+    $n->numberOfDigits(-123.4567), // 3
+    $n->numberOfFractionalDigits(-12.3456), // 4
 );

example/UseNumber.php

@@ -11,17 +11,35 @@
 
 $p = new Prime();
 
-var_dump(
-    $p->isPrime(3),
-    $p->isPrimeAll([ 2, 3, 5, ]),
-    $p->next(5),
-    $p->between(6, 14),
-    $p->factors(12), // = 2 * 2 * 3
-    $p->countSameElements($p->factors(72)), // = (2 ** 3) * (3 ** 2)
+// judge if $n is prime or not
+$n = 3;
+echo sprintf("Is %d prime? - %s.\n", $n, $p->isPrime($n) ? 'Yes' : 'No');
+
+// judge if all of $n are prime or not
+$n = [ 2, 3, 5, ];
+echo sprintf(
+    "Are all of [%s] prime? - %s.\n",
+    implode(', ', $n),
+    $p->isPrimeAll($n) ? 'Yes' : 'No'
+);
+
+// a prime next to $n
+$n = 5;
+echo sprintf("A prime next to %d is %d.\n", $n, $p->next($n));
+
+// primes between $a and $b
+$a = 6;
+$b = 14;
+echo sprintf(
+    "Primes between %d and %d are [%s].\n",
+    $a,
+    $b,
+    implode(', ', $p->between($a, $b))
 );
 
 // factorize
 $n = 1234567890;
+echo sprintf("Factorize %d:\n", $n);
 $r = $p->factorize($n);
 $l1 = $p->numberOfDigits(max(array_column($r, 0)));
 $l2 = $p->numberOfDigits(max(array_column($r, 1)));
@@ -35,4 +53,5 @@
     );
 }
 
+// Factorized formula
 echo $n . " = " . $p->factorizedFormula($n)['formula'] . "\n";

example/UsePrime.php

@@ -1,28 +1,8 @@
-bool(true)
-bool(true)
-int(7)
-array(3) {
-  [0]=>
-  int(7)
-  [1]=>
-  int(11)
-  [2]=>
-  int(13)
-}
-array(3) {
-  [0]=>
-  int(2)
-  [1]=>
-  int(2)
-  [2]=>
-  int(3)
-}
-array(2) {
-  [2]=>
-  int(3)
-  [3]=>
-  int(2)
-}
+Is 3 prime? - Yes.
+Are all of [2, 3, 5] prime? - Yes.
+A prime next to 5 is 7.
+Primes between 6 and 14 are [7, 11, 13].
+Factorize 1234567890:
    2)1234567890
      ----------
    3) 617283945