Hi,
 
> And even if we implement all of Bronstein's book, there is a lot of
> further potential work. Bronstein's book only covers the
> transcendental case, but there are also the algebraic and mixed cases.

For the mixed case one maybe should look at:

  "Mixed Transcendental and Algebraic Extensions for the Risch-Norman 
Algorithm""

by Stefan Böttner. However I could not obtain a copy of this work yet.

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