Initial data commit

Task/Nth-root/Picat/nth-root.picat

@@ -0,0 +1,30 @@
+go =>
+  L = [[2,2],
+       [34,5],
+       [34**5,5],
+       [7131.5**10],
+       [7,0.5],
+       [1024,10],
+       [5642, 125]
+  ],
+  foreach([A,N] in L)
+    R = nthroot(A,N),
+    printf("nthroot(%8w,%8w) %20w (check: %w)\n",A,N,R,A**(1/N))
+  end,
+  nl.
+
+%
+% x^n = a
+%
+% Given a and n, find x (to Precision)
+%
+nthroot(A,N) = nthroot(A,N,0.000001).
+
+nthroot(A,N,Precision) = X1 =>
+  NF = N * 1.0, % float version of N
+  X0 = A / NF,
+  X1 = 1.0,
+  do
+      X0 := X1,
+      X1 := (1.0 / NF)*((NF - 1.0)*X0 + (A / (X0 ** (NF - 1))))
+  while( abs(X0-X1) > Precision).