Php/docs/function.gmp-gcdext

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gmp_gcdext

(PHP 4 >= 4.0.4, PHP 5, PHP 7)

gmp_gcdextCalculate GCD and multipliers


说明

gmp_gcdext ( GMP $a , GMP $b ) : array

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]


参数

a
PHP 5.5 之前为 GMP 数值资源,PHP 5.6 之后为 GMP 对象或数字,或可以转为数字的字符串。
b
PHP 5.5 之前为 GMP 数值资源,PHP 5.6 之后为 GMP 对象或数字,或可以转为数字的字符串。


返回值

An array of GMP numbers.


范例

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?>