We saw last week that there was a plethora of algorithms to integrate
where **p** and **q** were polynomials in **x**.

- Classical (real and complex versions), based on complete factorization
- Hermite or Horowitz reduction to
where is square-free, and we do the last integral by the
Rothstein-Trager algorithm:
where the are the distinct roots of and the are computed by . This algorithm is

*very*impressive.

And they get worse in the elementary function case. In some sense we
are going to see that the Hermite reduction/ Rothstein-Trager algorithm
generalizes nicely to the elementary function case, and this is good in
the sense that we will have an * algorithm*, but it is bad in the
sense that we will inherit all the branch cut problems.

Thu Nov 23 10:59:42 PST 1995