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.

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 1839.
// Select random Gregorian year for example in range 1800 to 2400.

   $Y = mt_rand(1800, 2400); // Selected random year = 1839
We will construct a table centering on March 20th of the example year (1839).  To do this, we first compute the JD12 value for March 20th (JD12Central) of the year 1839.

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, 1839 March 20, at 12:00 TT

   $JD12Central = Ymd_HMS_To_JD($Y . "0320 12"); // = 2392819
Now that we have the JD12Central value for our table (2392819), 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 =
-1.4983858335 2392816
-1.1031057101 2392817
-0.7077919363 2392818
-0.3125533197 2392819
+0.0825030299 2392820
+0.4772725795 2392821
+0.8716538277 2392822
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); // = 2392819.7911101 
This returns the interpolated JD value for the moment when the solar declination equates to zero.

In this example, JDofEvent = 2392819.7911101

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); // = "18390321 06:59:12"
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 1839.
  $Y_Mmm_dd_HMS = "1839 March 21 06:59:12";