Merge pull request RobotLocomotion#5213 from soonho-tri/pr-add-expres…

…sion-expand

Add symbolic::Expression::Expand()

drake/common/BUILD

@@ -426,6 +426,15 @@ drake_cc_googletest(
     ],
 )
 
+drake_cc_googletest(
+    name = "symbolic_expansion_test",
+    deps = [
+        ":common",
+        ":symbolic",
+        ":symbolic_test_util",
+    ],
+)
+
 drake_cc_googletest(
     name = "symbolic_expression_test",
     deps = [

drake/common/symbolic_expression.cc

@@ -156,10 +156,15 @@ double Expression::Evaluate(const Environment& env) const {
   return ptr_->Evaluate(env);
 }
 
+Expression Expression::Expand() const {
+  DRAKE_ASSERT(ptr_ != nullptr);
+  return ptr_->Expand();
+}
+
 Expression Expression::Substitute(const Variable& var,
                                   const Expression& e) const {
   DRAKE_ASSERT(ptr_ != nullptr);
-  return Expression{ptr_->Substitute({{var, e}})};
+  return ptr_->Substitute({{var, e}});
 }
 
 Expression Expression::Substitute(const Substitution& s) const {

drake/common/symbolic_expression.h

@@ -198,6 +198,15 @@ class Expression {
    */
   double Evaluate(const Environment& env = Environment{}) const;
 
+  /** Expands out products and positive integer powers in expression. For
+   * example, <tt>(x + 1) * (x - 1)</tt> is expanded to <tt>x^2 - 1</tt> and
+   * <tt>(x + y)^2</tt> is expanded to <tt>x^2 + 2xy + y^2</tt>. Note that
+   * Expand applies recursively to sub-expressions. For instance, <tt>sin(2 * (x
+   * + y))</tt> is expanded to <tt>sin(2x + 2y)</tt>.
+   * @throws std::runtime_error if NaN is detected during expansion.
+   */
+  Expression Expand() const;
+
   /** Returns a copy of this expression replacing all occurrences of @p var
    * with @p e.
    * @throws std::runtime_error if NaN is detected during substitution.