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## ACA 2017 - Differential Algebra for an extended domain

I'm back from presenting work in the "23rd Conference on Applications of Computer Algebra - 2017" . It was a very interesting event. This second presentation, about "Differential algebra with mathematical functions, symbolic powers and anticommutative variables", describes a project I started working in 1997 and that is at the root of Maple's dsolve and pdsolve performance with systems of equations. It is a unique approach. Not yet emulated in any other computer algebra system.

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

Differential algebra with mathematical functions,

symbolic powers and anticommutative variables

Edgardo S. Cheb-Terrab

Physics, Differential Equations and Mathematical Functions, Maplesoft

Abstract:
Computer algebra implementations of Differential Algebra typically require that the systems of equations to be tackled be rational in the independent and dependent variables and their partial derivatives, and of course that , everything is commutative.

It is possible, however, to extend this computational domain and apply Differential Algebra techniques to systems of equations that involve arbitrary compositions of mathematical functions (elementary or special), fractional and symbolic powers, as well as anticommutative variables and functions. This is the subject of this presentation, with examples of the implementation of these ideas in the Maple computer algebra system and its ODE and PDE solvers.

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 Differential polynomial forms for mathematical functions (basic)
 Differential polynomial forms for compositions of mathematical functions
 Generalization to many variables
 Arbitrary functions of algebraic expressions
 Examples of the use of this extension to include mathematical functions
 Differential Algebra with anticommutative variables