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 1890.
// Select random Gregorian year for example in range 1800 to 2400.

   $Y = mt_rand(1800, 2400); // Selected random year = 1890
We will construct a table centering on March 20th of the example year (1890).  To do this, we first compute the JD12 value for March 20th (JD12Central) of the year 1890.

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, 1890 March 20, at 12:00 TT

   $JD12Central = Ymd_HMS_To_JD($Y . "0320 12"); // = 2411447
Now that we have the JD12Central value for our table (2411447), 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 =
"
-1.2465787379 2411444
-0.8512725097 2411445
-0.4559537707 2411446
-0.0607290069 2411447
+0.3342957696 2411448
+0.7290148266 2411449
+1.1233225437 2411450
";
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); // = 2411447.1536951 
This returns the interpolated JD value for the moment when the solar declination equates to zero.

In this example, JDofEvent = 2411447.1536951

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); // = "18900320 15:41:19"
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 1890.
  $Y_Mmm_dd_HMS = "1890 March 20 15:41:19";