Automatic adjoints

Computers are not only able to perform computations; they can do mathematics. Well known software is Mathematica and Maple. Adjoints can also be done by symbol manipulation. For example Ralf Giering offers a program for converting linear operator programs into their adjoints.

EXERCISES:

1. Suppose a linear operator $\bold F$ has its input in the discrete domain and its output in the continuum. How does the operator resemble a matrix? Describe the operator $\bold F'$ that has its output in the discrete domain and its input in the continuum. To which do you apply the words ``scales and adds some functions,'' and to which do you apply the words ``does a bunch of integrals''? What are the integrands?