Add Gauss_Easter in Powershell (algorithm-archivists#684)

Co-authored-by: James Schloss <[email protected]>

Author: dovisutu

contents/computus/code/powershell/gauss_easter.ps1

@@ -0,0 +1,60 @@
+function Calculate-Computus([int]$Year, [switch]$Servois) {
+
+    # Year's position on the 19 year metonic cycle
+    $a = $Year % 19
+
+    # Century index
+    $k = [Math]::Floor($Year / 100)
+
+    # Shift of metonic cycle, add a day offset every 300 years
+    $p = [Math]::Floor((13 + 8 * $k) / 25)
+
+    # Correction for non-observed leap days
+    $q = [Math]::Floor($k / 4)
+
+    # Correction to starting point of calculation each century
+    $M = (15 - $p + $k - $q) % 30
+
+    # Number of days from March 21st until the full moon
+    $d = (19 * $a + $M) % 30
+
+    # Returning if user wants value for Servois' table
+    if($Servois) {
+        return ((21 + $d) % 31).ToString()
+    }
+
+    # Finding the next Sunday
+    # Century-based offset in weekly calculation
+    $N = (4 + $k - $q) % 7
+
+    # Correction for leap days
+    $b = $Year % 4
+    $c = $Year % 7
+
+    # Days from d to next Sunday
+    $e = (2 * $b + 4 * $c + 6 * $d + $N) % 7
+
+    # Historical corrections for April 26 and 25
+    if(($d -eq 29 -and $e -eq 6) -or ($d -eq 28 -and $e -eq 6 -and $a -gt 10)) {
+        $e = -1
+    }
+
+    # Determination of the correct month for Easter
+    if(22 + $d + $e -gt 31) {
+        return "April " + ($d + $e - 9)
+    }
+    else {
+        return "March " + (22 + $d + $e)
+    }
+}
+
+
+# Here, we will output the date of the Paschal full moon
+# (using Servois notation), and Easter for 2020-2030
+
+Write-Host "The following are the dates of the Paschal full moon (using Servois",
+           "notation) and the date of Easter for 2020-2030 AD:"
+Write-Host "Year`tServois number`tEaster"
+foreach($year in 2020..2030) {
+    Write-Host "$year`t$(Calculate-Computus $year -Servois)`t`t$(Calculate-Computus $year)"
+}

contents/computus/computus.md

@@ -285,6 +285,8 @@ For now, we have the code outputting a tuple of $$d$$ and $$e$$, so users can us
 [import, lang:"python"](code/python/gauss_easter.py)
 {% sample lang="crystal" %}
 [import, lang:"crystal"](code/crystal/gauss_easter.cr)
+{% sample lang="ps1" %}
+[import, lang:"powershell"](code/powershell/gauss_easter.ps1)
 {% sample lang="c" %}
 [import, lang:"c"](code/c/gauss_easter.c)
 {% sample lang="cpp" %}