This mapping class is a usable example of a "sophisticated" symbolic
mapping class in C++. Bascially it allows you to do things like :

  // X will be the "identity mapping"
  Mapping X = Mapping::X;
  // A undefined mapping
  Mapping f;
  // Now contains some complex stuff
  f = sin(X * X - (X * 3.0) + 0.5);
  // Display it
  cout << f*f << endl;
  // fp will be the first derivative
  Mapping fp = f.derivative();
  // fs the second derivative
  Mapping fs = fp.derivative();
  // Compute the second derivative at 5
  cout << fs(5.0) << endl;

The best is to check the mappings.h to look at what functions and
operators are available. It will be pretty easy to add your own
operators.

The memory management is done in such a way that spurious copies are
avoided and intermediate results will be deallocated correctly. So far
I never traced a memory leak, but feel free to report it if you find
one.

Francois Fleuret
May 2001
Modified 2005, 2007, 2011