Another update from ingydotnet^djgoku

Task/Matrix-arithmetic/PowerShell/matrix-arithmetic.psh

@@ -0,0 +1,44 @@
+function det-perm ($array) {
+    if($array) {
+        $size = $array.Count
+        function prod($A) {
+            $prod = 1
+            if($A) { $A | foreach{$prod *= $_} }
+            $prod
+        }
+        function generate($sign, $n, $A) {
+            if($n -eq 1) {
+                $i = 0
+                $prod = prod @($A | foreach{$array[$i++][$_]})
+                [pscustomobject]@{det = $sign*$prod; perm = $prod}
+            }
+            else{
+                for($i = 0; $i -lt ($n - 1); $i += 1) {
+                    generate $sign ($n - 1) $A
+                    if($n % 2 -eq 0){
+                        $i1, $i2 = $i, ($n-1)
+                        $A[$i1], $A[$i2] = $A[$i2], $A[$i1]
+                    }
+                    else{
+                        $i1, $i2 = 0, ($n-1)
+                        $A[$i1], $A[$i2] = $A[$i2], $A[$i1]
+                    }
+                    $sign *= -1
+                }
+                generate $sign ($n - 1) $A
+            }
+        }
+        $det = $perm = 0
+        generate 1 $size @(0..($size-1)) | foreach{
+            $det += $_.det
+            $perm += $_.perm
+        }
+        [pscustomobject]@{det =  "$det"; perm = "$perm"}
+    } else {Write-Error "empty array"}
+}
+det-perm 5
+det-perm @(@(1,0,0),@(0,1,0),@(0,0,1))
+det-perm @(@(0,0,1),@(0,1,0),@(1,0,0))
+det-perm @(@(4,3),@(2,5))
+det-perm @(@(2,5),@(4,3))
+det-perm @(@(4,4),@(2,2))