Data commit

Task/Metallic-ratios/Jq/metallic-ratios.jq

@@ -0,0 +1,38 @@
+include "rational" {search: "."};  the defs at  [[Arithmetic/Rational#jq]]
+
+def names:
+  ["Platinum", "Golden", "Silver", "Bronze", "Copper","Nickel", "Aluminium", "Iron", "Tin", "Lead"];
+
+def lucas($b):
+   [1,1] | recurse( [last, first + $b*last] ) | first;
+
+def lucas($b; $n):
+  "Lucas sequence for \(names[$b]) ratio, where b = \($b):",
+  "First \(n) elements: ",
+  [limit($n; lucas($b))];
+
+# dp = integer (degrees of precision)
+def metallic(b; dp):
+  { x0: 1,
+    x1: 1,
+    x2: 0,
+    ratio: r(1; 1),
+    iters: 0 }
+  | .prev = (.ratio|r_to_decimal(dp))  # a string
+  | until(.emit;
+      .iters += 1
+      | .x2 = .b * .x1 + .x0
+      | .ratio = r(.x2; .x1)
+      | .curr = (.ratio|r_to_decimal(dp))  # a string
+      | if .prev == .curr
+        then (if (.iters == 1) then " " else "s" end) as $plural
+        | .emit = "Value to \(dp) dp after \(.iters) iteration\($plural): \(.curr)\n"
+        else .prev = .curr
+        | .x0 = .x1
+        | .x1 = .x2
+	end )
+  | .emit;
+
+(range( 0;10) | lucas(.; 15), metallic(.; 32)),
+
+"Golden ratio, where b = 1:",  metallic(1; 256)