PHP gmp_legendre() Function

PHP language uses function called gmp_legendre() for the mathematical operation. This function figures out the Legendre symbol of two GMP numbers. The function needs two parameters, and the second parameter takes a value that is both odd and positive.

Syntax

The following syntax shows gmp_legendre() function and its operation.

Examples

The following example shows the Legendre symbol of different numbers and GMP parameters. According to the input value, the symbol shows in a 1, 0, and -1 format.

Example1: the given example uses the gmp_legendre() with the essential values.

<!DOCTYPE html>
<html>
<body>
<h4> PHP gmp_legendre() Function </h4>
<?php
echo "<p> Display legendre symbol of the given parameters. </p>";
$value1 = gmp_legendre(11, 3);
$value2 = gmp_legendre(121, 7);
$value3 = gmp_legendre(157, 129);
$value4 = gmp_legendre(150, 5);
echo "The Legendre symbol of the GMP numbers: ".$value1;
echo "<br/>";
echo "The Legendre symbol of the GMP numbers:".$value2;
echo "<br/>";
echo "The Legendre symbol of the GMP numbers: ".$value3;
echo "<br/>";
echo "The Legendre symbol of the GMP numbers: ".$value4;
?>
</body>
</html>

Output:

The image shows the "Legendre symbol" of the given two values.

Example2: the given example uses the gmp_legendre() with the positive and negative values.

<!DOCTYPE html>
<html>
<body>
<h4> PHP gmp_legendre() Function </h4>
<?php
echo "<p> Display legendre symbol of the given parameters. </p>";
$value1 = gmp_legendre(-11, 3);
$value2 = gmp_legendre(121, 7);
$value3 = gmp_legendre(-150, -11);
$value4 = gmp_legendre(150, -7);
echo "The Legendre symbol of the GMP numbers: " .$value1;
echo "<br/>";
echo "The Legendre symbol  of the GMP numbers:" .$value2;
echo "<br/>";
echo "The Legendre symbol  of the GMP numbers: " .$value3;
echo "<br/>";
echo "The Legendre symbol  of the GMP numbers: " .$value4;
?>
</body>
</html>

Output:

The image shows the "Legendre symbol" of the given two values.

Example3: the given an example uses the gmp_legendre() with the variable values.

<!DOCTYPE html>
<html>
<body>
<h4> PHP gmp_legendre() Function </h4>
<?php
echo "<p> Display legendre symbol of the given parameters. </p>";
$var_value1 = "11";
$var_value2 = "28";
$var_value3 = "7";
$var_value4 = "131";
$value1 = gmp_legendre($var_value1, $var_value3);
$value2 = gmp_legendre($var_value2, $var_value3);
$value3 = gmp_legendre($var_value4, $var_value1);
echo "The Legendre symbol  of the GMP numbers: " .$value1;
echo "<br/>";
echo "The Legendre symbol  of the GMP numbers: " .$value2;
echo "<br/>";
echo "The Legendre symbol  of the GMP numbers: " .$value3;
?>
</body>
</html>

Output:

The image shows the "Legendre symbol" of the given two values.

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

<!DOCTYPE html>
<html>
<body>
<h4> PHP gmp_legendre() Function </h4>
<?php
echo "<p> Display the Legendre symbol of the given parameters. </p>";
$var_value1 = "-11";
$var_value2 = "127";
$var_value3 = "-7";
$var_value4 = "131";
$gmp_var1 = gmp_abs($var_value1);
$gmp_var2 = gmp_com($var_value3);
$gmp_var3 = gmp_abs($var_value3);
$value1 = gmp_legendre($var_value4, $gmp_var2);
$value2 = gmp_legendre($var_value2,  $gmp_var1);
$value3 = gmp_legendre($var_value4,  $gmp_var3);
echo "The Legendre symbol of the GMP numbers: " .$value1;
echo "<br/>";
echo "The Legendre symbol of the GMP numbers:" .$value2;
echo "<br/>";
echo "The Legendre symbol of the GMP numbers: " .$value3;
?>
</body>
</html>

Output:

The image shows the "Legendre symbol" of the given two values.

Conclusion

According to the input data, the gmp_legendre() function shows the Legendre value. It shows 1, 0, and -1 values without need of complex mathematical operations and lengthy processes.

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