Elliptic curve arithmetic: Difference between revisions

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 P+Q-S (0.000000000000000 : 1.00000000000000 : 0.000000000000000) ## Zero
 P*12345 (10.7585721817304 : 35.3874428812067 : 1.00000000000000)
+</pre>
+=={{header|Sidef}}==
+{{trans|Perl 6}}
+<lang ruby>module EC {
+    var A = 0
+    var B = 7
+    class Horizon {
+        method to_s {
+            "EC Point at horizon"
+        }
+        method *(_) {
+            self
+        }
+        method -(_) {
+            self
+        }
+    }
+    class Point(Number x, Number y) {
+        method to_s {
+            "EC Point at x=#{x}, y=#{y}"
+        }
+        method neg {
+            Point(x, -y)
+        }
+        method -(Point p) {
+            self + -p
+        }
+        method +(Point p) {
+            if (x == p.x) {
+                return (y == p.y ? self*2 : Horizon())
+            }
+            else {
+                var slope = (p.y - y)/(p.x - x)
+                var x2 = (slope**2 - x - p.x)
+                var y2 = (slope * (x - x2) - y)
+                Point(x2, y2)
+            }
+        }
+        method +(Horizon _) {
+            self
+        }
+        method *((0)) {
+            Horizon()
+        }
+        method *((1)) {
+            self
+        }
+        method *((2)) {
+            var l = (3 * x**2 + A)/(2 * y)
+            var x2 = (l**2 - 2*x)
+            var y2 = (l * (x - x2) - y)
+            Point(x2, y2)
+        }
+        method *(Number n) {
+*(self * (n>>1)) + self*(n % 2)
+        }
+    }
+    class Horizon {
+        method +(Point p) {
+            p
+        }
+    }
+    class Number {
+        method +(Point p) {
+            p + self
+        }
+        method *(Point p) {
+            p * self
+        }
+        method *(Horizon h) {
+            h
+        }
+        method -(Point p) {
+            -p + self
+        }
+    }
+}
+say var p = with(1) {|v| EC::Point(v, sqrt(abs(1 - v**3 - EC::A*v - EC::B))) }
+say var q = with(2) {|v| EC::Point(v, sqrt(abs(1 - v**3 - EC::A*v - EC::B))) }
+say var s = (p + q)
+say ("checking alignment:  ", abs((p.x - q.x)*(-s.y - q.y) - (p.y - q.y)*(s.x - q.x)) < 1e-20)</lang>
+{{out}}
+<pre>
+EC Point at x=1, y=2.64575131106459059050161575363926042571025918308
+EC Point at x=2, y=3.74165738677394138558374873231654930175601980778
+EC Point at x=-1.79898987322333068322364213893577309997540625528, y=0.421678696849803028974882458314430376814790014487
+checking alignment:  true
 </pre>