This program demonstrates a process by which we may compute the equinoxes and solstices.  In this case, we will compute the date and time (TT) of March equinox for a random Gregorian year.

To build a program around the equinoxes and solstices module, we simply include the module at the beginning of the program.
// Attach the equinoxes and solstices functions module.

   include("Equinoxes_and_Solstices_Module_v0.php");
For the example, we will select a random Gregorian year in the range from 1600 to 2400 AD.  In this case, the random year is 2291.
// Select random Gregorian year for example in range 1800 to 2400.

   $Y = mt_rand(1800, 2400); // Selected random year = 2291
We will construct a table centering on March 20th of the example year (2291).  To do this, we first compute the JD12 value for March 20th (JD12Central) of the year 2291.

The JD12 range of the table will span a 7-day period starting on JD12Start = JD12Central−3 and ending on JD12End = JD12Central+3

// Compute the JD12 value for central date, 2291 March 20, at 12:00 TT

   $JD12Central = Ymd_HMS_To_JD($Y . "0320 12"); // = 2557909
Now that we have the JD12Central value for our table (2557909), we can construct the 7-day table of geocentric solar declinations vs. JD12 values from 3 days before to 3 days after this JD12Central value.
// Create 7-day solar declination vs JD12 table centered on JD12Central

   $DataTable = "";

   for ($JD12 = $JD12Central-3;   $JD12 <= $JD12Central+3;   $JD12++)
  {
   list($RAHrs, $declination) = preg_split("[ ]", Geocentric_Sun ($JD12));

   $declination = sprintf("%+1.10f", $declination);

   $DataTable .= "$declination $JD12\n";
  }
The above loop generates the following DataTable structure.
$DataTable =
"
-1.3220036392 2557906
-0.9263094389 2557907
-0.5305688748 2557908
-0.1348809991 2557909
+0.2606541991 2557910
+0.6559358797 2557911
+1.0508624503 2557912
";
Given the above data table, we next call the LaGrange interpolation function to compute the JD value for the moment when the apparent geocentric solar declination equates to zero.
// Interpolate JD of event = Moment when solar declination == 0

  $JDofEvent = LaGrange_Interpolate($DataTable, 0); // = 2557909.3409527 
This returns the interpolated JD value for the moment when the solar declination equates to zero.

In this example, JDofEvent = 2557909.3409527

We can then call the inverse JD number function to compute the corresponding integer-encoded date and time string.
  $Ymd_HMSTT = JD_To_Ymd_HMS($JDofEvent); // = "22910320 20:10:58"
Now we can tidy up the date string by replacing the returned month number sub-string, "03", with "March".
// Construct final output date from integer-encoded date/time string.

  $Y_Mmm_dd_HMS = "$Y March " . substr($Ymd_HMSTT, 6, strlen($Ymd_HMSTT));
This finally gives us the date and time (TT) of the March equinox in Gregorian year 2291.
  $Y_Mmm_dd_HMS = "2291 March 20 20:10:58";