README

1. Features

PHP-Math-Integer is a PHP library which treats the subjects of number theory (only natural number).

Available Subjects:

basic matters of Numbers
basic matters of Primes
basic matters of Divisors
basic matters of Multiples
basic matters of Euclidean Algorithm
basic matters of Common Fractions
basic matters of Bezout's Identities

3. Requirements

PHP 8.1 or later
Composer

4. Installation

composer require macocci7/php-math-integer

5. Usage

5.1. Macocci7\PhpMathInteger\Number
5.2. Macocci7\PhpMathInteger\Prime
5.3. Macocci7\PhpMathInteger\Divisor
5.4. Macocci7\PhpMathInteger\Multiple
5.5. Macocci7\PhpMathInteger\Euclid
5.6. Macocci7\PhpMathInteger\Fraction
5.7. Macocci7\PhpMathInteger\Bezout

5.1. Macocci7\PhpMathInteger\Number

This class treats basic matters of numbers.

PHP:

<?php

require_once __DIR__ . '/../vendor/autoload.php';

use Macocci7\PhpMathInteger\Number;

$n = new Number();

echo "Is 1 int? - " . ($n->isInt(1) ? 'Yes' : 'No') . ".\n";
echo "Are [ 1, 2, 3, ] all int? - " . ($n->isIntAll([ 1, 2, 3, ]) ? 'Yes' : 'No') . ".\n";
echo "Is 1 natural? - " . ($n->isNatural(1) ? 'Yes' : 'No') . ".\n";
echo "Are [ 1, 2, 3, ] all natural? - " . ($n->isNaturalAll([ 1, 2, 3, ]) ? 'Yes' : 'No') . ".\n";
echo "Is 1.2 float? - " . ($n->isFloat(1.2) ? 'Yes' : 'No') . ".\n";
echo "Are [ -2.1, 0.0, 1.2, ] all float? - " . ($n->isFloatAll([ -2.1, 0.0, 1.2, ]) ? 'Yes' : 'No') . ".\n";
echo "Is 1.2 number? - " . ($n->isNumber(1.2) ? 'Yes' : 'No') . ".\n";
echo "Are [ -2, 0.1, 3, ] all number? - " . ($n->isNumberAll([ -2, 0.1, 3, ]) ? 'Yes' : 'No') . ".\n";
echo "Is 0.1 fraction? - " . ($n->isFraction(0.1) ? 'Yes' : 'No') . ".\n";
echo "Are [ -0.99, 0.1, 0.99, ] all fraction? - " . ($n->isFractionAll([ -0.99, 0.1, 0.99, ]) ? 'Yes' : 'No') . ".\n";
echo "Sign of -2.5 is " . $n->sign(-2.5) . ".\n";
echo "Integer part of 3.14 is " . $n->int(3.14) . ".\n";
echo "Fractional part of 3.14 is " . $n->fraction(3.14) . ".\n";
echo "-3th digit of 123.4567 is " . $n->nthDigit(-3, 123.4567) . ".\n";
echo "Number of digits -123.4567 is " . $n->numberOfDigits(-123.4567) . ".\n";
echo "Number of fractional digits -12.3456 is " . $n->numberOfFractionalDigits(-12.3456) . ".\n";

Result:

Is 1 int? - Yes.
Are [ 1, 2, 3, ] all int? - Yes.
Is 1 natural? - Yes.
Are [ 1, 2, 3, ] all natural? - Yes.
Is 1.2 float? - Yes.
Are [ -2.1, 0.0, 1.2, ] all float? - Yes.
Is 1.2 number? - Yes.
Are [ -2, 0.1, 3, ] all number? - Yes.
Is 0.1 fraction? - Yes.
Are [ -0.99, 0.1, 0.99, ] all fraction? - Yes.
Sign of -2.5 is -1.
Integer part of 3.14 is 3.
Fractional part of 3.14 is 0.14.
-3th digit of 123.4567 is 6.
Number of digits -123.4567 is 3.
Number of fractional digits -12.3456 is 4.

Methods:

5.2. Macocci7\PhpMathInteger\Prime

This class treats basic matters of primes.

PHP:

<?php

require_once __DIR__ . '/../vendor/autoload.php';

use Macocci7\PhpMathInteger\Prime;

$p = new Prime();

// 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\n",
    implode(', ', $n),
    $p->isPrimeAll($n) ? 'Yes' : 'No'
);

// a prime previous to $n
$n = 5;
echo sprintf("A prime previous to %d is %d.\n", $n, $p->previous($n));

// a prime next to $n
$n = 5;
echo sprintf("A prime next to %d is %d.\n\n", $n, $p->next($n));

// primes between $a and $b
$a = 6;
$b = 14;
echo sprintf(
    "Primes between %d and %d are [%s].\n\n",
    $a,
    $b,
    implode(', ', $p->between($a, $b))
);

// factorize
$n = 1234567890;
echo sprintf("Factorize %d:\n\n", $n);

$r = $p->factorize($n);
$l1 = $p->numberOfDigits(max(array_column($r, 0)));
$l2 = $p->numberOfDigits(max(array_column($r, 1)));
$s = str_repeat(' ', $l1 + 1);
$b = $s . str_repeat('-', $l2);

foreach ($r as $f) {
    echo (
        $f[0]
        ? sprintf("%" . $l1 . "d)%" . $l2 . "d\n%s\n", $f[0], $f[1], $b)
        : sprintf("%s%" . $l2 . "d\n", $s, $f[1])
    );
}
echo "\n";

// Factorized formula
echo $n . " = " . $p->factorizedFormula($n)['formula'] . "\n";

Result:

Is 3 prime? - Yes.
Are all of [2, 3, 5] prime? - Yes.

A prime previous to 5 is 3.
A prime next to 5 is 7.

Primes between 6 and 14 are [7, 11, 13].

Factorize 1234567890:

  2)1234567890
    ----------
  3) 617283945
    ----------
  3) 205761315
    ----------
  5)  68587105
    ----------
3607)  13717421
    ----------
          3803

1234567890 = 2 * 3 ^ 2 * 5 * 3607 * 3803

Methods:

5.3. Macocci7\PhpMathInteger\Divisor

This class treats basic matters of divisors.

PHP:

<?php

require_once __DIR__ . '/../vendor/autoload.php';

use Macocci7\PhpMathInteger\Divisor;

$d = new Divisor();
$a = 12;
$b = 18;

// Number of divisors
echo sprintf("%d has %d divisors.\n", $a, $d->count($a));

// List of all divisors
echo sprintf("[%s]\n", implode(', ', $d->list($a)));

// Common factors
echo sprintf("%d = %s\n", $a, $d->formula($a));
echo sprintf("%d = %s\n", $b, $d->formula($b));
echo sprintf(
    "common factors : %s\n",
    $d->formula($d->value($d->commonFactors($a, $b)))
);
echo sprintf(
    "common divisors : [%s]\n",
    implode(', ', $d->commonDivisors($a, $b))
);

// greatest common factor (divisor)
echo sprintf(
    "greatest common factor (divisor) : %s\n",
    $d->greatestCommonFactor($a, $b)
);

// Reducing fraction
$r = $d->reduceFraction($a, $b);
$ra = $d->value($r[0]);
$rb = $d->value($r[1]);
echo sprintf("%d/%d reduces to %d/%d\n", $a, $b, $ra, $rb);

Result:

12 has 6 divisors.
[1, 2, 3, 4, 6, 12]
12 = 2 ^ 2 * 3
18 = 2 * 3 ^ 2
common factors : 2 * 3
common divisors : [1, 2, 3, 6]
greatest common factor (divisor) : 6
12/18 reduces to 2/3

Methods:

5.4. Macocci7\PhpMathInteger\Multiple

This class treats basic matters of multiples.

PHP:

<?php

require_once __DIR__ . '/../vendor/autoload.php';

use Macocci7\PhpMathInteger\Multiple;

$m = new Multiple();
$a = 12;
$b = 18;

// least common multiple
echo sprintf(
    "least common multiple of %d and %d is %d\n",
    $a,
    $b,
    $m->leastCommonMultiple($a, $b)
);

Result:

least common multiple of 12 and 18 is 36

Methods:

5.5. Macocci7\PhpMathInteger\Euclid

This class treats basic matters of Euclidean Algorithm.

PHP:

<?php

require_once __DIR__ . '/../vendor/autoload.php';

use Macocci7\PhpMathInteger\Euclid;

// Presets values
$e = new Euclid();
$a = 390;
$b = 273;
$c = 39;

// Judges if $c is GCD($a, $b) or not
echo sprintf(
    "Is %d GCD(%d, %d)? - %s.\n",
    $c,
    $a,
    $b,
    $e->isGcdOf($c, $a, $b) ? 'Yes' : 'No'
);

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

// Formula of remainders
echo "Remainders can be expressed as:\n";
foreach ($r['processData'] as $d) {
    echo sprintf("%d = %d - %d * %d\n", $d['r'], $d['a'], $d['b'], $d['c']);
}

// Judges if $a and $b are coprime or not
echo sprintf(
    "Are %d and %d coprime? - %s.\n",
    $a,
    $b,
    $e->isCoprime($a, $b) ? 'Yes' : 'No'
);

// GCD($a, $b)
echo sprintf(
    "Because the Greatest Common Divisor of %d and %d is %d.\n",
    $a,
    $b,
    $e->gcd($a, $b)
);

Result:

Is 39 GCD(390, 273)? - Yes.
Euclidean Algorithm:
390 = 273 * 1 + 117
273 = 117 * 2 + 39
117 = 39 * 3 + 0
Remainders can be expressed as:
117 = 390 - 273 * 1
39 = 273 - 117 * 2
0 = 117 - 39 * 3
Are 390 and 273 coprime? - No.
Because the Greatest Common Divisor of 390 and 273 is 39.

Methods:

5.6. Macocci7\PhpMathInteger\Fraction

This class treats basic matters of common fractions.

PHP:

<?php

require_once __DIR__ . '/../vendor/autoload.php';

use Macocci7\PhpMathInteger\Fraction;

// prest: 1 and 2/4
$f = new Fraction('1 2/4');

// is reduced or not?
echo $f->text() . " is " . ($f->isReduced() ? '' : 'not ') . "reduced.\n";

// is proper or not?
echo $f->text() . " is " . ($f->isProper() ? '' : 'not ') . "a proper fraction.\n";

// is improper or not?
echo $f->text() . " is " . ($f->isImproper() ? '' : 'not ') . "a improper fraction.\n";

// is mixed or not?
echo $f->text() . " is " . ($f->isMixed() ? '' : 'not ') . "a mixed fraction.\n";

// convert $f into a improper fraction
echo $f->text() . " = " . $f->improper()->text() . "\n";

// convert $f into a mixed fraction
echo $f->text() . " = " . $f->mixed()->text() . "\n";

// reduce fraction
echo $f->text() . " reduces to " . $f->reduce()->text() . "\n";

// integral part
echo "integral part of " . $f->text() . " is " . $f->int() . "\n";

// change into a float
echo $f->text() . " = " . $f->float() . "\n";

// four arithmetic operations
$f1 = new Fraction('1/3');
$f2 = new Fraction('1/6');
echo $f1->text() . ' + ' . $f2->text() . ' = ' . $f1->add($f2)->text() . "\n";
$f1->set('2/3');
$f2->set('1/6');
echo $f1->text() . ' - ' . $f2->text() . ' = ' . $f1->substract($f2)->text() . "\n";
$f1->set('2/3');
$f2->set('1/6');
echo $f1->text() . ' * ' . $f2->text() . ' = ' . $f1->multiply($f2)->text() . "\n";
$f1->set('2/3');
$f2->set('1/6');
echo $f1->text() . ' / ' . $f2->text() . ' = ' . $f1->divide($f2)->text() . "\n";

// reduce fractions to a common denominator
$f1->set('1/3');
$f2->set('2/5');
echo "reduce the fractions of " . $f1->text() . " and " . $f2->text()
    . " to a common denominator:\n";
$f1->toCommonDenominator($f2);
echo $f1->text() . " and " . $f2->text() . "\n";

Result:

1 2/4 is not reduced.
1 2/4 is not a proper fraction.
1 2/4 is not a improper fraction.
1 2/4 is a mixed fraction.
1 2/4 = 6/4
6/4 = 1 2/4
1 2/4 reduces to 1 1/2
integral part of 1 1/2 is 1
1 1/2 = 1.5
1/3 + 1/6 = 1/2
2/3 - 1/6 = 1/2
2/3 * 1/6 = 1/9
2/3 / 1/6 = 4/1
reduce the fractions of 1/3 and 2/5 to a common denominator:
5/15 and 6/15

Methods:

5.7. Macocci7\PhpMathInteger\Bezout

This class treats basic matters of Bezout's Identity.

PHP:

<?php

require_once __DIR__ . '/../vendor/autoload.php';

use Macocci7\PhpMathInteger\Bezout;

// Bezout's Identity: 3x + 4y = 1
$b = new Bezout([3, 4, 1, ]);
echo sprintf("Bezout's Identity: %s\n", $b->identity());

// 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']);

Result:

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

Methods:

6. Examples

UseNumber.php results in >> UseNumber.txt
UsePrime.php results in >> UsePrime.txt
UseDivisor.php results in >> UseDivisor.txt
UseMultiple.php results in >> UseMultiple.txt
UseFraction.php results in >> UseFraction.txt
UseEuclid.php results in >> UseEuclid.txt
UseBezout.php results in >> UseBezout.txt

7. LICENSE

MIT

Document Created: 2023/10/19

Document Updated: 2024/04/18

macocci7 / php-math-integer

Maintainers

Details

README

1. Features

2. Contents

3. Requirements

4. Installation

5. Usage

5.1. Macocci7\PhpMathInteger\Number

5.2. Macocci7\PhpMathInteger\Prime

5.3. Macocci7\PhpMathInteger\Divisor

5.4. Macocci7\PhpMathInteger\Multiple

5.5. Macocci7\PhpMathInteger\Euclid

5.6. Macocci7\PhpMathInteger\Fraction

5.7. Macocci7\PhpMathInteger\Bezout

6. Examples

7. LICENSE