From 376d9ef9a227519dec4fb3aed51c96edde8b5e1c Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?=C3=89milie=20Feral?= <emilie.feral@numworks.com>
Date: Fri, 20 Apr 2018 11:46:31 +0200
Subject: [PATCH] [poincare] Improve the transformation from complex to
 expression to avoid complex(1, 0) -> Addition(Decimal(1),
 Multiplcation(Decimal(0), Symbol(I)))

---
 poincare/src/expression.cpp | 63 +++++++++++++++++++++++++++++++++++--
 1 file changed, 61 insertions(+), 2 deletions(-)

diff --git a/poincare/src/expression.cpp b/poincare/src/expression.cpp
index 8c8363134..60f90babb 100644
--- a/poincare/src/expression.cpp
+++ b/poincare/src/expression.cpp
@@ -15,7 +15,9 @@
 #include <poincare/ieee754.h>
 #include <poincare/addition.h>
 #include <poincare/multiplication.h>
+#include <poincare/subtraction.h>
 #include <poincare/power.h>
+#include <poincare/opposite.h>
 #include <ion.h>
 #include <cmath>
 #include <float.h>
@@ -836,12 +838,69 @@ template<typename T> Expression * Expression::complexToExpression(std::complex<T
   if (complexFormat == ComplexFormat::Default) {
     complexFormat = Preferences::sharedPreferences()->complexFormat();
   }
+  if (std::isnan(c.real()) || std::isnan(c.imag()) || std::isinf(c.real()) || std::isinf(c.imag())) {
+    return new Undefined();
+  }
+
   switch (complexFormat) {
     case ComplexFormat::Cartesian:
-      return new Addition(CreateDecimal(c.real()), new Multiplication(new Symbol(Ion::Charset::IComplex), CreateDecimal(c.imag()), false), false);
+    {
+      Expression * real = nullptr;
+      Expression * imag = nullptr;
+      if (c.real() != 0 || c.imag() == 0) {
+        real = CreateDecimal(c.real());
+      }
+      if (c.imag() != 0) {
+        if (c.imag() == 1.0 || c.imag() == -1) {
+          imag = new Symbol(Ion::Charset::IComplex);
+        } else if (c.imag() > 0) {
+          imag = new Multiplication(CreateDecimal(c.imag()), new Symbol(Ion::Charset::IComplex), false);
+        } else {
+          imag = new Multiplication(CreateDecimal(-c.imag()), new Symbol(Ion::Charset::IComplex), false);
+        }
+      }
+      if (imag == nullptr) {
+        return real;
+      } else if (real == nullptr) {
+        if (c.imag() > 0) {
+          return imag;
+        } else {
+          return new Opposite(imag, false);
+        }
+        return imag;
+      } else if (c.imag() > 0) {
+        return new Addition(real, imag, false);
+      } else {
+        return new Subtraction(real, imag, false);
+      }
+    }
     default:
+    {
       assert(complexFormat == ComplexFormat::Polar);
-      return new Multiplication(CreateDecimal(std::abs(c)), new Power(new Symbol(Ion::Charset::Exponential), new Multiplication(new Symbol(Ion::Charset::IComplex), CreateDecimal(std::arg(c)), false), false), false);
+      Expression * norm = nullptr;
+      Expression * exp = nullptr;
+      T r = std::abs(c);
+      T th = std::arg(c);
+      if (r != 1 || th == 0) {
+        norm = CreateDecimal(r);
+      }
+      if (r != 0 && th != 0) {
+        Expression * arg = nullptr;
+        if (th > 0) {
+          arg = new Multiplication(CreateDecimal(th), new Symbol(Ion::Charset::IComplex), false);
+        } else {
+          arg = new Opposite(new Multiplication(CreateDecimal(-th), new Symbol(Ion::Charset::IComplex), false), false);
+        }
+        exp = new Power(new Symbol(Ion::Charset::Exponential), arg, false);
+      }
+      if (exp == nullptr) {
+        return norm;
+      } else if (norm == nullptr) {
+        return exp;
+      } else {
+        return new Multiplication(norm, exp, false);
+      }
+    }
   }
 }