I am really not sure what you are trying to tell us, here. I'm sorry.
On 21.04.2012 01:28, Sai Nikhil wrote:
@Tom Bachmann: I'm waiting for your reply on this thread. Please give a look at it. On 21 April 2012 00:12, Sai Nikhil <tsnleg...@gmail.com <mailto:tsnleg...@gmail.com>> wrote: Hello, I recently started tinkering around with some math function in Maple and viewed the source code of some of the packages. Maple 15(my version) doesn't provide the source code for all packages. Some of the packages are built directly into the terminal. So, its not possible to view source code now. But, finally after rigorous googling, I found the algorithm implemented by Mr. Wolfram Koepf and Mr. Dominik Gruntz and also the implemented source code of the package(algorithm) in earlier version(Maple V, if I'm not wrong). So, we replicated it, to build as sympy code in python. I'm explaining the idea of the algorithm below and the Maple's source code is uploaded on my personal website @ this url <http://www.tsndiffopera.in/gsoc/Formal_Power_Series.mpl.txt> : To understand this algorithm, one has to first know about the Hypergeometric Function and Simple Differential Equation (SimpleDE, a homogeneous linear DE with polynomial coefficients as shown in image below). Inline images 2, where P,Q are obtained from the Hypergeometric series (pFq). Coming to the implementation part, for a function /f/ , we setup the SimpleDE of the form: / / /Inline images 3/, (where Aj is coefficient of the required Formal Power series.) and expand it . Then we collect the coefficients of all the rationally dependent terms and equate them to zero. For testing whether two terms are rationally dependent, we divide one by the other and test whether the quotient is a rational function in x or not. / / //then convert the DE into a recurrence equation of the form, Inline images 4, for the coefficients ak (hypergeometric series), where pj are polynomials in k and M ∈ N if the RE only contains one or two summands then, /f/ is of hypergeometric type and the RE can be solved else if the DE has constant coefficients then, /f/ is of exp-like(exponential) type and even then the RE can be solved. if /f/ ^k (x) (kth derivative of /f/), is a rational function in x, then we can use the rational Algorithm and integrate the result k times to get the FPS. The above explanation can be put in a nut shell as described in the following image(Maple Format): Inline images 5 there are also many cool examples provided for me in the pdf here @ my personal website url <http://www.tsndiffopera.in/gsoc/Formal%20Power%20Series%28W.Koepf%26D.Gruntz%29.pdf> . Many special cases including the exp-like case are also included in the pdf. They are definitely helpful to me to successfully implement the idea . I still have 4 more end-sem examinations and they will be over by the next weekend. I can devote more of my time on coding after that. @ Mr. Christopher Smith and @ Mr. Tom Bachmann , please reply after seeing this e-mail. /-thanks,/ /Sai Nikhil <http://www.tsndiffopera.in>/ / / / / /1/ -- You received this message because you are subscribed to the Google Groups "sympy" group. To post to this group, send email to sympy@googlegroups.com. To unsubscribe from this group, send email to sympy+unsubscr...@googlegroups.com. For more options, visit this group at http://groups.google.com/group/sympy?hl=en.
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