From ced136f8432be73612ef544898d462b54a233147 Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?=C3=89milie=20Feral?= <emilie.feral@numworks.com>
Date: Fri, 14 Dec 2018 12:14:17 +0100
Subject: [PATCH] [poincare] Fix ComplexCartesian::powerInteger to handle pure
 imaginary complex

---
 poincare/src/complex_cartesian.cpp | 20 ++++++++++++++++++++
 poincare/src/power.cpp             |  2 +-
 2 files changed, 21 insertions(+), 1 deletion(-)

diff --git a/poincare/src/complex_cartesian.cpp b/poincare/src/complex_cartesian.cpp
index 44d826e20..3446484cf 100644
--- a/poincare/src/complex_cartesian.cpp
+++ b/poincare/src/complex_cartesian.cpp
@@ -177,6 +177,26 @@ ComplexCartesian ComplexCartesian::powerInteger(int n, Context & context, Prefer
   Expression a = real();
   Expression b = imag();
   assert(n > 0);
+  assert(!b.isRationalZero());
+
+  // Special case: a == 0 (otherwise, we are going to introduce undefined expressions - a^0 = NAN)
+  // (b*i)^n = b^n*i^n with i^n == i, -i, 1 or -1
+  if (a.isRationalZero()) {
+    ComplexCartesian result;
+    Expression bpow = Power(b, Rational(n));
+    if (n/2%2 == 1) {
+      Expression temp = Multiplication(Rational(-1), bpow);
+      bpow.shallowReduce(context, angleUnit, target);
+      bpow = temp;
+    }
+    if (n%2 == 0) {
+      result = ComplexCartesian(bpow, Rational(0));
+    } else {
+      result = ComplexCartesian(Rational(0), bpow);
+    }
+    bpow.shallowReduce(context, angleUnit, target);
+    return result;
+  }
   // (a+ib) = a^n+i*b*a^(n-1)+(-1)*b^2*a^(n-2)+(-i)*b^3*a^(n-3)+b^3*a^(n-4)+...
   // Real part: A = a^n+(-1)*b^2*a^(n-2)+...
   // Imaginary part: B = b*a^(n-1)
diff --git a/poincare/src/power.cpp b/poincare/src/power.cpp
index 2b65816db..cfd0076c0 100644
--- a/poincare/src/power.cpp
+++ b/poincare/src/power.cpp
@@ -384,7 +384,7 @@ Expression Power::shallowReduce(Context & context, Preferences::AngleUnit angleU
   Expression base = childAtIndex(0);
   Expression index = childAtIndex(1);
   /* Step 0: if both children are true unresolved complexes, the result is not simplified. TODO? */
-  if (!base.isReal(context, angleUnit) && !index.isReal(context, angleUnit)) {
+  if (!base.isReal(context, angleUnit) && base.type() != ExpressionNode::Type::ComplexCartesian && !index.isReal(context, angleUnit) && index.type() != ExpressionNode::Type::ComplexCartesian) {
     return *this;
   }