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## ACA 2017 - The FunctionAdvisor, beyond a database of mathematical information.

Maple

I'm back from presenting work in the "23rd Conference on Applications of Computer Algebra -2017" . It was a very interesting event. This fourth presentation, about "The FunctionAdvisor: extending information on mathematical functions with computer algebra algorithms", describes the FunctionAdvisor project at Maple, a project I started working during 1998, where the key idea I am trying to explore is that we do not need to collect a gazillion of formulas but just core blocks of mathematical information surrounded by clouds of algorithms able to derive extended information from them. In this sense this is also unique piece of software: it can derive properties for rather general algebraic expressions, not just well known tabulated functions. The examples illustrate the idea.

At the end, there is a link to the presentation worksheet, with which one could open the sections and reproduce the presentation examples.

The FunctionAdvisor: extending information on mathematical functions

with computer algebra algorithms

Edgardo S. Cheb-Terrab

Physics, Differential Equations and Mathematical Functions, Maplesoft

Abstract:

A shift in paradigm is happening, from: encoding information into a database, to: encoding essential blocks of information together with algorithms within a computer algebra system. Then, the information is not only searchable but can also be recreated in many different ways and actually used to compute. This talk focuses on this shift in paradigm over a real case example: the digitizing of information regarding mathematical functions as the FunctionAdvisor project of the Maple computer algebra system.

Beyond the concept of a database

 " Mathematical functions, are defined by algebraic expressions. So consider algebraic expressions in general ..."
 Formal power series for algebraic expressions
 Differential polynomial forms for algebraic expressions
 Branch cuts for algebraic expressions
 The nth derivative problem for algebraic expressions
 Conversion network for mathematical and algebraic expressions
 References