From 6135fced52f5c2e0d86333f1216d15fbe8a10a96 Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?=C3=89milie=20Feral?= <emilie.feral@numworks.com>
Date: Wed, 13 Nov 2019 14:49:44 +0100
Subject: [PATCH] [poincare] Power: always reduce (a^b)^(-1)

---
 poincare/src/power.cpp           | 14 +++++++++-----
 poincare/test/simplification.cpp |  1 +
 2 files changed, 10 insertions(+), 5 deletions(-)

diff --git a/poincare/src/power.cpp b/poincare/src/power.cpp
index e5ffc985a..77bba4c05 100644
--- a/poincare/src/power.cpp
+++ b/poincare/src/power.cpp
@@ -625,18 +625,22 @@ Expression Power::shallowReduce(ExpressionNode::ReductionContext reductionContex
    *                     --> tan(2)+tan(2)*[tan(2)^1/2]^(-1)/tan(2)
    *                     --> tan(2)^(3/2)+tan(2)^(3/2)*[tan(2)^1/2]^(-1)/tan(2)^3/2
    *                     --> ...
-   * Indeed, we have to apply the rule (a^b)^c -> a^(b*c) as soon as c is an
-   * integer.
+   * Indeed, we have to apply the rule (a^b)^c -> a^(b*c) as soon as c is -1.
    */
   if (baseType == ExpressionNode::Type::Power) {
     Power powerBase = static_cast<Power &>(base);
 
+    bool cInteger = indexType == ExpressionNode::Type::Rational && static_cast<Rational &>(index).isInteger();
     bool applyRule = powerBase.childAtIndex(0).sign(reductionContext.context()) == ExpressionNode::Sign::Positive // a > 0
-                     || (indexType == ExpressionNode::Type::Rational && static_cast<Rational &>(index).isInteger()); // c integer
+                     || cInteger; // c integer
+    bool cMinusOne = cInteger && static_cast<Rational &>(index).isMinusOne();
     /* If the complexFormat is real, we check that the inner power is defined
      * before applying the rule (a^b)^c -> a^(b*c). Otherwise, we return
-     * 'unreal' or we do nothing. */
-    if (reductionContext.complexFormat() == Preferences::ComplexFormat::Real) {
+     * 'unreal' or we do nothing.
+     * We escape this additional check if c = -1 for two reasons:
+     * - (a^b)^(-1) has to be reduced to avoid infinite loop discussed above;
+     * - if a^b is unreal, a^(-b) also. */
+    if (!cMinusOne && reductionContext.complexFormat() == Preferences::ComplexFormat::Real) {
       Expression approximation = powerBase.approximate<float>(reductionContext.context(), reductionContext.complexFormat(), reductionContext.angleUnit());
       if (approximation.type() == ExpressionNode::Type::Unreal) {
         // The inner power is unreal, return "unreal"
diff --git a/poincare/test/simplification.cpp b/poincare/test/simplification.cpp
index 23e1820aa..2699ddc57 100644
--- a/poincare/test/simplification.cpp
+++ b/poincare/test/simplification.cpp
@@ -107,6 +107,7 @@ QUIZ_CASE(poincare_simplification_infinity) {
 }
 
 QUIZ_CASE(poincare_simplification_addition) {
+  assert_parsed_expression_simplify_to("1/x^2+3", "\u00123×x^2+1\u0013/x^2", User, Radian, Real);
   assert_parsed_expression_simplify_to("1+x", "x+1");
   assert_parsed_expression_simplify_to("1/2+1/3+1/4+1/5+1/6+1/7", "223/140");
   assert_parsed_expression_simplify_to("1+x+4-i-2x", "-i-x+5");