gmp_gcdext

(PHP 4 >= 4.0.4, PHP 5)

gmp_gcdext — Calculate GCD and multipliers

说明

array gmp_gcdext ( resource $a , resource $b )

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 » "Diophantine Equation" page at MathWorld

参数

a: It can be either a GMP number resource, or a numeric string given that it is possible to convert the latter to a number.
b: It can be either a GMP number resource, or a numeric string given that it is possible to convert the latter to a number.

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
?>


	PHP5中文手册 gmp_gcd gmp_hamdist GMP PHP Manual gmp_gcdext (PHP 4 >= 4.0.4, PHP 5) gmp_gcdext — Calculate GCD and multipliers 说明 array gmp_gcdext ( resource `$a` , resource `$b` ) Calculates g, s, and t, such that as + bt = 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: ax + by = c. For more information, go to the » "Diophantine Equation" page at MathWorld 参数 `a` It can be either a GMP number resource, or a numeric string given that it is possible to convert the latter to a number. `b` It can be either a GMP number resource, or a numeric string given that it is possible to convert the latter to a number. 返回值 An array of GMP numbers. 范例 Example#1 Solving a linear Diophantine equation <?php // Solve the equation as + bt = 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: 122 + 21-1 = 3 ?> gmp_gcd gmp_hamdist GMP PHP Manual