Php/docs/function.gmp-gcdext
gmp_gcdext
(PHP 4 >= 4.0.4, PHP 5, PHP 7)
gmp_gcdext — Calculate GCD and multipliers
Description
Calculates g, s, and t, such that a*s + b*t = g = gcd(a,b), where gcd is the greatest common divisor. Returns
an array with respective elements g, s and t.
This function can be used to solve linear Diophantine equations in two
variables. These are equations that allow only integer solutions and have the form:
a*x + b*y = c.
For more information, go to the [http://mathworld.wolfram.com/DiophantineEquation.html » "Diophantine
Equation" page at MathWorld]
Parameters
a- Either a GMP number resource in PHP 5.5 and earlier, a GMP object in PHP 5.6 and later, or a numeric string provided that it is possible to convert the latter to a number.
b- Either a GMP number resource in PHP 5.5 and earlier, a GMP object in PHP 5.6 and later, or a numeric string provided that it is possible to convert the latter to a number.
Return Values
An array of GMP numbers.
Examples
Example #1 Solving a linear Diophantine equation
<?php// Solve the equation a*s + b*t = g// where a = 12, b = 21, g = gcd(12, 21) = 3$a = gmp_init(12);$b = gmp_init(21);$g = gmp_gcd($a, $b);$r = gmp_gcdext($a, $b);$check_gcd = (gmp_strval($g) == gmp_strval($r['g']));$eq_res = gmp_add(gmp_mul($a, $r['s']), gmp_mul($b, $r['t']));$check_res = (gmp_strval($g) == gmp_strval($eq_res));if ($check_gcd && $check_res) { $fmt = "Solution: %d*%d + %d*%d = %d\n"; printf($fmt, gmp_strval($a), gmp_strval($r['s']), gmp_strval($b), gmp_strval($r['t']), gmp_strval($r['g']));} else { echo "Error while solving the equation\n";}// output: Solution: 12*2 + 21*-1 = 3?>
