Initial data commit

Task/Arithmetic-Rational/Lua/arithmetic-rational.lua

@@ -0,0 +1,58 @@
+function gcd(a,b) return a == 0 and b or gcd(b % a, a) end
+
+do
+  local function coerce(a, b)
+    if type(a) == "number" then return rational(a, 1), b end
+    if type(b) == "number" then return a, rational(b, 1) end
+    return a, b
+  end
+  rational = setmetatable({
+  __add = function(a, b)
+      local a, b = coerce(a, b)
+      return rational(a.num * b.den + a.den * b.num, a.den * b.den)
+    end,
+  __sub = function(a, b)
+      local a, b = coerce(a, b)
+      return rational(a.num * b.den - a.den * b.num, a.den * b.den)
+    end,
+  __mul = function(a, b)
+      local a, b = coerce(a, b)
+      return rational(a.num * b.num, a.den * b.den)
+    end,
+  __div = function(a, b)
+      local a, b = coerce(a, b)
+      return rational(a.num * b.den, a.den * b.num)
+    end,
+  __pow = function(a, b)
+      if type(a) == "number" then return a ^ (b.num / b.den) end
+      return rational(a.num ^ b, a.den ^ b) --runs into a problem if these aren't integers
+    end,
+  __concat = function(a, b)
+      if getmetatable(a) == rational then return a.num .. "/" .. a.den .. b end
+      return a .. b.num .. "/" .. b.den
+    end,
+  __unm = function(a) return rational(-a.num, -a.den) end}, {
+  __call = function(z, a, b) return setmetatable({num = a / gcd(a, b),den = b / gcd(a, b)}, z) end} )
+end
+
+print(rational(2, 3) + rational(3, 5) - rational(1, 10) .. "") --> 7/6
+print((rational(4, 5) * rational(5, 9)) ^ rational(1, 2) .. "") --> 2/3
+print(rational(45, 60) / rational(5, 2) .. "") --> 3/10
+print(5 + rational(1, 3) .. "") --> 16/3
+
+function findperfs(n)
+  local ret = {}
+  for i = 1, n do
+    sum = rational(1, i)
+    for fac = 2, i^.5 do
+      if i % fac == 0 then
+        sum = sum + rational(1, fac) + rational(fac, i)
+      end
+    end
+    if sum.den == sum.num then
+      ret[#ret + 1] = i
+    end
+  end
+  return table.concat(ret, '\n')
+end
+print(findperfs(2^19))