Risch Algorithm - Implementation

Implementation

Transforming Risch's theoretical algorithm into an algorithm that can be effectively executed by a computer is a complex task which took a long time.

The case of the purely transcendental functions (which do not involve roots of polynomials) is relatively easy and has been implemented early in most computer algebra systems. The first implementation was done by Joel Moses in Macsyma soon after the publication of Risch's paper.

The case of purely algebraic functions has been solved and implemented in Reduce by James H. Davenport.

The general case has been solved and implemented in Scratchpad, a precursor of Axiom, by Manuel Bronstein.