From d9c2275a79bd090098e416861ec14d0294ae8c39 Mon Sep 17 00:00:00 2001
From: heav <hheav3@gmail.com>
Date: Thu, 27 Oct 2022 02:22:50 +0000
Subject: tentative complex numbers

---
 czzc/math.lua | 51 +++++++++++++++++++++++++++++++++++++++++++++++++++
 1 file changed, 51 insertions(+)
 create mode 100644 czzc/math.lua

diff --git a/czzc/math.lua b/czzc/math.lua
new file mode 100644
index 0000000..cad47ee
--- /dev/null
+++ b/czzc/math.lua
@@ -0,0 +1,51 @@
+local M = {}
+
+local complex_mt = {
+    __tostring = function(self)
+        if self.im == 0 then
+            return tostring(self.re)
+        elseif self.re == 0 then
+            return (math.abs(self.im) == 1 and (self.im < 0 and "-" or "") or tostring(self.im)) .. "i"
+        elseif self.im > 0 then
+            return tostring(self.re) .. "+" .. (math.abs(self.im) == 1 and "" or tostring(self.im)) .. "i"
+        elseif self.im == 1 then
+            return tostring(self.re) .. "+i"
+        elseif self.im == -1 then
+            return tostring(self.re) .. "-i"
+        else
+            return tostring(self.re) .. tostring(self.im) .. "i"
+        end
+    end,
+    __add = function(z1, z2)
+        if type(z2) == "number" then z2 = M.complex(z2) end
+        return M.complex(z1.re + z2.re, z1.im + z2.im)
+    end,
+    __sub = function(z1, z2)
+        if type(z2) == "number" then z2 = M.complex(z2) end
+        return M.complex(z1.re - z2.re, z1.im - z2.im)
+    end,
+    __mul = function(z1, z2)
+        if type(z2) == "number" then z2 = M.complex(z2) end
+        return M.complex(z1.re * z2.re - z1.im * z2.im,
+                         z1.re * z2.im + z1.im * z2.re)
+    end,
+}
+
+-- makes a new complex number.
+M.complex = function(re, im)
+    local res = {re = re or 0, im = im or 0, type = "complex"}
+    setmetatable(res, complex_mt)
+    return res
+end
+
+M.sqrt = function(n)
+    if type(n) == "number" and n < 0 then
+        return M.complex(0, math.sqrt(-n))
+    else
+        return math.sqrt(n)
+    end
+end
+
+M.i = M.complex(0, 1)
+
+return M
-- 
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