PHP-Math-Integer

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:

Method	Detail
`isInt(mixed $n)`	judges if the param is integer or not
`isIntAll(array $ns)`	judges if all of the param are integer or not
`isNatural(mixed $n)`	judges if the param is natural number or not
`isNaturalAll(array $ns)`	judges if all of the param are natural number or not
`isFloat(mixed $n)`	judges if the param is float or not
`isFloatAll(array $ns)`	judges if all of the param are float or not
`isNumber(mixed $n)`	judges if the param is number or not (different from is_numeric())
`isNumberAll(array $ns)`	judges if all of the param are number or not
`isFraction(mixed $n)`	judges if the param is decimal fraction or not
`isFractionAll(array $ns)`	judges if all of the param are fraction or not
`sign(int\|float\|null $n)`	returns the sign of the param as one of -1, 0 or 1
`int(float $n)`	returns the integral part of the param
`fraction(float $n)`	returns the fractional part of the param
`nthDigit(int $n, int\|float $d)`	returns the nth digit of the param
`numberOfDigits(int\|float $n)`	returns the number of digits of the param
`numberOfFractionalDigits(float $n)`	returns the number of fractional digits of the param

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:

Method	Detail
`isPrime(int $n)`	judges if the param is prime or not
`isPrimeAll(array $elements)`	judges if all of the param are prime or not
`previous(int $n)`	returns a prime previous to the param
`next(int $n)`	returns a prime next to the param
`between(int $a, int $b)`	returns array of primes between the params
`factorize(int $n)`	factorize the param and returns the process as an array
`factors(int $n)`	returns the factorized factors of the param as an array
`factorizedFormula(int $n)`	returns the factorized formula as an array

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:

Method	Detail
`count(int $n)`	returns the number of divisors of the param
`value(array $factors)`	converts the factorized array into an integer and returns it
`formula(int $n)`	returns the factorized formula as strings
`list(int $n)`	returns all of divisors of the param as an array
`commonFactors(int $n1, int $n2)`	returns common factors of the params as an array
`greatestCommonFactor(int $n1, int $n2)`	returns the greatest common factor of the params
`commonDivisors(int $n1, int $n2)`	returns all of common divisors of the param as an array
`reduceFraction(int $n1, int $n2)`	returns reduced fraction consisting of the params as an array

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:

Method Detail

leastCommonMultiple(int $n1, int $n2) returns the least common multiple of the params

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:

Method	Detail
`run(int $n1, int $n2)`	runs the Euclidean Algorithm and returns the result as an array
`gcd(int $a, int $b)`	returns the greatest common divisor of the params
`isGcdOf(int $c, int $a, int $b)`	judges if the first param is gcd of the other params or not
`isCoprime(int $a, int $b)`	judges if the params are coprime or not

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:

Method	Detail
`set(string $s)`	sets the properties of the fraction specified by the param
`isReduced()`	judges if the fraction is reduced or not
`isProper()`	judges if the fraction is a proper fraction or not
`isImproper()`	judges if the fraction is a improper fraction or not
`isMixed()`	judges if the fraction is a mixed fraction or not
`reduce()`	reduces the fraction
`toCommonDenominator(Fraction &$f)`	converts the fractions into a common denominator
`add(Fraction $f)`	adds the param to the fraction
`substract(Fraction $f)`	substracts the param from the fraction
`multiply(Fraction $f)`	multiplies the fraction by the param
`divide(Fraction $f)`	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

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:

Method	Detail
`set(array $c = [])`	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

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

Name		Name	Last commit message	Last commit date
Latest commit History 49 Commits
.github/workflows		.github/workflows
bin		bin
examples		examples
src		src
tests		tests
.gitignore		.gitignore
LICENSE		LICENSE
PHP_VERSIONS		PHP_VERSIONS
README.md		README.md
composer.json		composer.json
phpcs.xml		phpcs.xml
phpmd.xml		phpmd.xml
phpstan.neon		phpstan.neon

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PHP-Math-Integer

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

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