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.
