The Maple implementation of mathematical functions reviewed.

Edgardo Cheb-Terrab, CECM

Generally speaking, this project is about completing, strengthening and making
flexible the implementation of the mathematical language in the Maple system.

The first step in this project is the implementation of a computational network
of mathematical relations between elementary transcendental and special
functions. All possible connections are being targeted and the network computes
taking into account user assumptions (if any) on the domain of the function
parameters. Taking into account that the number of Maple mathematical functions
is close to 100, a featured and flexible implementation of these goals is a non
obvious computational project.

The second step includes the strengthening of the implementation of each
mathematical function and related routines (simplification, series, etc.), as
well as completing the set with Mathieu functions and a few others that are
missing. Concerning flexibility, the idea is to allow users to set Maple to work
according to their computational needs with respect to the way each function
computes. Possible choices are: returning inert, or, when possible, returning a
constant value, or a rational form, or an expression in terms of elementary
transcendental functions.