I'm aware that the FriCAS package can be called from within Sage / Python, and I don't see any reason to rewrite what's already there, just extend it's current recognition capabilities and put a nice friendly wrapper function around all of these disparate routines. Something like find_sequence_formula([1,1,2,3,5,8,13]) or find_polynomial_generating_function([...], x) would be nice. I'm willing to work on writing the wrapper functions and help with extending the sequence recognition capabilities that are already there. It's been a little while since I've seriously thought about writing this sort of function in Sage, but my intuition is that the FriCAS package can already pick up a lot of what FindSequenceFunction will recognize out of the box.
I can / should put together a long list of sequence test cases that I'd like to see recognized by these routines in Sage. Anything that's in the Wolfram / Mathematica documentation is on the list. Also, sequences involving factors, or polynomial multiples of, special sequences like the Stirling, Bernoulli, and r-order harmonic numbers are something I'd like to see. How much does the existing FriCAS rely on being able to find a homogeneous recurrence for the input sequences? There are a number of examples of sums involving the Stirling and Bernoulli numbers that cannot be expressed this way. Also, Mathematica tends to ignore closed-form sequence expressions involving harmonic numbers (say for known formulas satisfied by the Stirling numbers of the first kind), whereas if we have the FriCAS package's analog to the RISC Guess package along with an OSS version of Sigma and RSolve, these expressions are easy to obtain. These are just some suggestions at a starting point for replacing my having to switch over to Mathematica when I need sequence recognition functions. Maxie On Saturday, November 19, 2016 at 11:30:09 AM UTC-6, Martin R wrote: > > I'd be interested in what output you'd like to have. > > The hard part in the FriCAS package was to get decent speed, changing > output should be relatively straightforward. > > (I guess that you are aware of the possibility of using the package from > within sage) > > Martin > > Am Samstag, 19. November 2016 16:56:42 UTC+1 schrieb Maxie Schmidt: >> >> Hello, >> >> I have been working back and forth between Sage and Mathematica for a >> while now trying to learn how to use Sage to replace Mathematica's core >> functionality in my day to day use of it. One of the (sets of) functions >> haven't yet found a suitable open source alternative for is related to >> guessing formulas and generating functions for an input sequence (as in >> Mathematica's FindSequenceFunction and FindGeneratingFunction). Related >> functions are Mathematica's RSolve ( >> https://reference.wolfram.com/language/ref/RSolve.html?q=RSolve) used to >> solve recurrence relations in closed-form formulas, and the closed-source >> RISC Sigma package ( >> https://www.risc.jku.at/research/combinat/risc/software/Sigma/index.php) >> which is able to generate recurrences for many sums and simplify sums >> involving harmonic numbers. >> >> The closest open source alternative I have come across so far is Rubey's >> software written in FriCAS described at >> http://axiom-wiki.newsynthesis.org/GuessingFormulasForSequences. >> However, looking at the source code for the package leaves quite a bit of >> work to do to reproduce the output of the Mathematica functions mentioned >> above. Is there a better open source alternative to the Mathematica >> functions FindSequenceFunction and RSolve that I'm missing in Sage? >> >> If there isn't a good complete replacement for using Mathematica's >> routines for sequence formula guessing and solving recurrences, I'm >> interested in trying to write functions / packages that will replace >> Mathematica for these tasks. I have already done some work in Sage related >> to guessing formulas for special polynomial sequences in my Master's thesis >> at UIUC posted at https://arxiv.org/abs/1609.07301. Any suggestions or >> links to related open source software are appreciated. >> >> Sincerely, >> >> Maxie >> > -- You received this message because you are subscribed to the Google Groups "sage-devel" group. To unsubscribe from this group and stop receiving emails from it, send an email to sage-devel+unsubscr...@googlegroups.com. To post to this group, send email to sage-devel@googlegroups.com. Visit this group at https://groups.google.com/group/sage-devel. For more options, visit https://groups.google.com/d/optout.
