PHP gmp_jacobi() Function

The gmp_jacobi() function is a built-in function that takes two GMP numbers, $numbers1 and $numbers2, as input and generates the Jacobi symbol. $numbers2 should be an odd and positive value.

Syntax

The following syntax shows the PHP GMP Jacobi symbol function.

Parameters

The function accepts two mandatory parameters, $number1 and $number2, as shown in the above syntax.
These parameters can be GMP objects in PHP versions 5.6 and above for the gmp_jacobi() function.
They can be numeric strings as long as it is possible to convert the strings to numbers.

Return Values

This function shows a GMP number or a GMP object (PHP 5.6 and above) that is the Jacobi of the numbers.

Examples

The following example shows the Jacobi symbol of the different numbers and GMP parameters.

Example1: the given code shows the Jacobi symbol of the essential and positive values.

<!DOCTYPE html>
<html>
<body>?
<h4> PHP gmp_jacobi() Function </h4>
<?php
echo "<p> Display  Jacobi symbol of the given parameters. </p>";
$value1 = gmp_jacobi(11, 3);
$value2 = gmp_jacobi(128, 7);
$value3 = gmp_jacobi(157, 129);
$value4 = gmp_jacobi(150, 5);
echo "The Jacobi symbol of the GMP numbers: ".$value1."<br>";
echo "<br/>";
echo "The Jacobi symbol of the GMP numbers: ".$value2."<br>";
echo "<br/>";
echo "The Jacobi symbol of the GMP numbers: ".$value3."<br>";
echo "<br/>";
echo "The Jacobi symbol of the GMP numbers: ".$value4."<br>";
?>
</body>
</html>

Output:

The image shows the Jacobi symbol of the given two values.

Example2: the given code shows the Jacobi symbol of the required and negative values. We can see the difference between output values with negative parameters.

<!DOCTYPE html>
<html>
<body>
<h4> PHP gmp_jacobi() Function </h4>
<?php
echo "<p> Display  Jacobi symbol of the given parameters. </p>";
$value1 = gmp_jacobi(-11, 3);
$value2 = gmp_jacobi(128, -7);
$value3 = gmp_jacobi(-157, -129);
$value4 = gmp_jacobi(150, -11);
echo "The Jacobi symbol of the GMP numbers: " .$value1."<br>";
echo "<br/>";
echo "The Jacobi symbol of the GMP numbers:" .$value2."<br>";
echo "<br/>";
echo "The Jacobi symbol of the GMP numbers: " .$value3."<br>";
echo "<br/>";
echo "The Jacobi symbol of the GMP numbers: " .$value4."<br>";
?>
</body>
</html>

Output:

The image shows the Jacobi symbol of the given two values.

Example3: the following example shows the gmp_jacobi() function with variable parameter and its value

<!DOCTYPE html>
<html>
<body>
<h4> PHP gmp_jacobi() Function </h4>
<?php
echo "<p> Display the Jacobi symbol of the given parameters. </p>";
$var_value1 = "11";
$var_value2 = "121";
$var_value3 = "7";
$var_value4 = "131";
$value1 = gmp_jacobi($var_value1, $var_value3);
$value2 = gmp_jacobi($var_value2, $var_value3);
$value3 = gmp_jacobi($var_value4, $var_value2);
echo "The Jacobi symbol of the GMP numbers: " .$value1."<br>";
echo "<br/>";
echo "The Jacobi symbol of the GMP numbers:" .$value2."<br>";
echo "<br/>";
echo "The Jacobi symbol of the GMP numbers: " .$value3."<br>";
?>
</body>
</html>

Output:

The image shows the Jacobi symbol of the given value.

Example4: the following example shows the gmp_jacobi() function with GMP parameter and its value

<!DOCTYPE html>
<html>
<body>
<h4> PHP gmp_jacobi() Function </h4>
<?php
echo "<p> Display the Jacobi symbol of the given parameters. </p>";
$var_value1 = "11";
$var_value2 = "121";
$var_value3 = "7";
$var_value4 = "131";
$gmp_var1 = gmp_abs($var_value1);
$gmp_var2 = gmp_com($var_value3);
$gmp_var3 = gmp_init($var_value3);
$value1 = gmp_jacobi($var_value1, $gmp_var2);
$value2 = gmp_jacobi($var_value2,  $gmp_var1);
$value3 = gmp_jacobi($var_value4,  $gmp_var3);
echo "The Jacobi symbol of the GMP numbers: " .$value1."<br>";
echo "<br/>";
echo "The Jacobi symbol of the GMP numbers:" .$value2."<br>";
echo "<br/>";
echo "The Jacobi symbol of the GMP numbers: " .$value3."<br>";
?>
</body>
</html>

Output:

The image shows the Jacobi symbol of the given value.

Conclusion

The gmp_jacobi() function displays the Jacobi symbol of the given value. The parameter value must be odd to use the function to work the GMP Jacobi operation.

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