[poincare/derivative] Derivate special numbers

Derivate the numbers Undefined, Unreal, Infinity symbolically :
  Undefined -> Undefined
  Unreal    -> Unreal
  Infinity  -> Undefined

poincare/include/poincare/infinity.h

@@ -37,6 +37,11 @@ public:
   // Layout
   Layout createLayout(Preferences::PrintFloatMode floatDisplayMode, int numberOfSignificantDigits) const override;
   int serialize(char * buffer, int bufferSize, Preferences::PrintFloatMode floatDisplayMode = Preferences::PrintFloatMode::Decimal, int numberOfSignificantDigits = 0) const override;
+
+  /* Derivation
+   * Unlike Numbers that derivate to 0, Infinity derivates to Undefined. */
+  bool derivate(ReductionContext reductionContext, Expression symbol, Expression symbolValue) override;
+
 private:
   // Simplification
   LayoutShape leftLayoutShape() const override { assert(!m_negative); return LayoutShape::MoreLetters; }
@@ -56,6 +61,7 @@ public:
   static int NameSize() {
     return 4;
   }
+  bool derivate(ExpressionNode::ReductionContext reductionContext, Expression symbol, Expression symbolValue);
 private:
   InfinityNode * node() const { return static_cast<InfinityNode *>(Number::node()); }
 };

poincare/include/poincare/undefined.h

@@ -30,8 +30,8 @@ public:
   }
 
   /* Derivation
-   * Overrides NumberNode's derivate to revert to a non-derivable state */
+   * Unlike Numbers that derivate to 0, Undefined derivates to Undefined. */
-  bool derivate(ReductionContext reductionContext, Expression symbol, Expression symbolValue) override { return false; }
+  bool derivate(ReductionContext reductionContext, Expression symbol, Expression symbolValue) override { return true; }
 
   // Layout
   Layout createLayout(Preferences::PrintFloatMode floatDisplayMode, int numberOfSignificantDigits) const override;

poincare/include/poincare/unreal.h

@@ -28,7 +28,7 @@ public:
   }
 
   /* Derivation
-   * Overrides NumberNode's derivate to revert to a non-derivable state */
+   * Unlike Numbers that derivate to 0, Unreal derivates to Unreal. */
   bool derivate(ReductionContext reductionContext, Expression symbol, Expression symbolValue) override { return false; }
 
   // Layout

poincare/src/infinity.cpp

@@ -31,6 +31,10 @@ template<typename T> Evaluation<T> InfinityNode::templatedApproximate() const {
   return Complex<T>::Builder(m_negative ? -INFINITY : INFINITY);
 }
 
+bool InfinityNode::derivate(ReductionContext reductionContext, Expression symbol, Expression symbolValue) {
+  return Infinity(this).derivate(reductionContext, symbol, symbolValue);
+}
+
 Infinity Infinity::Builder(bool negative) {
   void * bufferNode = TreePool::sharedPool()->alloc(sizeof(InfinityNode));
   InfinityNode * node = new (bufferNode) InfinityNode(negative);
@@ -45,6 +49,11 @@ Expression Infinity::setSign(ExpressionNode::Sign s) {
   return result;
 }
 
+bool Infinity::derivate(ExpressionNode::ReductionContext reductionContext, Expression symbol, Expression symbolValue) {
+  replaceWithUndefinedInPlace();
+  return true;
+}
+
 template Evaluation<float> InfinityNode::templatedApproximate<float>() const;
 template Evaluation<double> InfinityNode::templatedApproximate() const;
 }

poincare/test/derivative.cpp

@@ -8,6 +8,9 @@ void assert_reduces_to_formal_expression(const char * expression, const char * r
 }
 
 QUIZ_CASE(poincare_derivative_formal) {
+  assert_reduces_to_formal_expression("diff(undef,x,x)", Undefined::Name());
+  assert_reduces_to_formal_expression("diff(unreal,x,x)", Unreal::Name());
+  assert_reduces_to_formal_expression("diff(inf,x,x)", Undefined::Name());
   assert_reduces_to_formal_expression("diff(1,x,x)", "0");
   assert_reduces_to_formal_expression("diff(π,x,x)", "0");
   assert_reduces_to_formal_expression("diff(y,x,x)", "0");