Hi Martin, Here is my ztrans.input file in its current diabolical form - all the cleverness is yours and Themos's; the extra hack work is my own. It does forward transforms pretty well (of powers, exponential functions and mixtures thereof), but inverse transforms are less well handled. For example,
ex:=ztrans(n^5,n,z) produces a formidable polynomial quotient; to invert it you need to apply partial fractions to ex/z, and apply the inverse transform to each individual fractional term multiplied by z. This is not happening right now. As well, I need to implement shifts: ztrans(f(n-k),n,z) == z^(-b)*ztrans(f(n),n,z) and for f(n+k). My own thoughts for difference equations were much more modest than yours: linear equations with constant coefficients, and equations which can be transformed into linear equations. I can't imagine it would be too hard? Of course, if I get the z-ztransforms working, that can be used.... cheers, Alasdair On 05 Jun 2007 11:53:24 +0200, Martin Rubey <[EMAIL PROTECTED]> wrote:
"Alasdair McAndrew" <[EMAIL PROTECTED]> writes: > but does anybody actually use Axiom for mathematics: teaching, research, or > even fun? I am. For example, I wrote a tiny script to spit out all set partitions in (Coxeter-) Type B and D and counted the first few terms, then entered them into Sloane's database, to find the reference Ruedi Suter. I also used Axiom to check a conjecture on Jeu de Taquin. To this end I implemented growth diagrams by Fomin, but I am unable to pursue this project on my own. Last year I used the (in my opinion) formidable graphics to show students how a saddle point and a tangential plane looks like. Gorgeous! > Is anybody out there adding further mathematical functionality to Axiom - > numerical routines, difference equation solvers, discrete mathematics etc > etc? I added the guessing package (currently state of the art), and together with Ralf a project to deal with combinatorial species. Concerning difference equations, you might know that my favorite would-be project is a hierarchy covering functions satisfying algebraic diffential equations, holonomic functions, algebraic functions, rational functions polynomials on one hand and "admissible" recurrence relations D-finite recurrence relations recurrence relations with constant coefficients on the other hand. But I could not find a collaborator so far -- unfortunately, Antoine Hersen gave up. (One needs to know a bit about Ore-algebras, AKA skew-polynomial rings.) > FWIW, as Martin well knows, I've been banging my head over pattern matching > and z-transforms lately. I have a file which works to about 75%; the last > bit, which involves partial fractions, is still giving me gyp. Try to formulate a question, then I can try to answer it. > And on the meta-mathematical side, has anybody got an emacs mode to work > with *.input files? Francois Maltey sent me some files, but I am unable to incorporate them into my emacs mode (which I use myself meanwhile), for lack of time. Martin
ztrans.input
Description: Binary data
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