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## [Axiom-developer] evaluator for functional equations / CHALLENGE!

 From: Martin Rubey Subject: [Axiom-developer] evaluator for functional equations / CHALLENGE! Date: 11 Sep 2006 12:04:25 +0200 User-agent: Gnus/5.09 (Gnus v5.9.0) Emacs/21.3

Dear all!

next week I'm going to present my guessing package at MathInfo 06. It works
quite well meanwhile :-)

Hower, there is one thing I don't really want to program - in fact, I won't -
although it would be really really useful. Maybe somebody else can do it. I
offer a price, ok?

The challenge is as follows:

I need an operation evalADE that takes a functional equation of the form

f(x) = g(f(x), D(f(x),x), D(f(x),x,2),...),

where g is any "nice" expression, some initial values, and an integer n.

The result of the operation should be the n-th coefficient of the taylor
expansion of f, if it exists.

Even more important, suppose that the functional equation is of the form

p(f(x), D(f(x),x), D(f(x),x,2), ...)

where p is a polynomial. These f are called differentially algebraic.

The algorithm does not need to be especially fast, but it would be nice to be a
able to compute the first fifty to hundred coefficients in a reasonable time.

Note that Axiom provides an operation seriesSolve, which provides a partial
solution. However, it is very buggy and gives up even for certain algebraic
equations.

Price is negotiable.

Martin