I'm reading and understanding the solvers code. I have started documenting it here https://github.com/sympy/sympy/wiki/solvers.
@Matthew For implementing and dealing with infinite sets I've found a draft by Richard Fateman http://www.cs.berkeley.edu/~fateman/papers/sets.pdf I have skimmed through it and it appears all of the techniques described there are implementable in sympy. On 25 January 2014 06:28, Aaron Meurer <asmeu...@gmail.com> wrote: > On Fri, Jan 24, 2014 at 2:02 PM, Harsh Gupta <gupta.hars...@gmail.com> wrote: >>>> Great to hear it. As noted on the ideas page, this one will require a >>>> good deal of thought to be done in the application, so let's start >>>> discussing. >> >> Thanks a lot, and sorry for the late reply >> >>>> Another thing I'd like to know is if there's literature on solving >>>> algorithms, particularly solving transcendental equations, and very >>>> particularly on if there are any complete algorithms out there for >>>> some class of equations. >> >> I found a old paper called "SOLVING SYMBOLIC EQUATIONS WITH PRESS" >> http://www.research.ed.ac.uk/portal/files/413486/Solving_Symbolic_Equations_%20with_PRESS.pdf >> >>>> Do we know how other computer algebra systems solve this problem? How >>>> robust are the algorithms behind wolframalpha.com ? >> >> I have found another paper "A Review of Symbolic Solvers" >> http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.44.9444&rep=rep1&type=pdf >> and according to it Mathematica performs performs pretty bad. > > That was in 1996. > > Nonetheless this, along with the Wester paper, should provide some > good test cases so we can see what can be done that we can't do. > > Aaron Meurer > >> >>>> An audit of the current solve code might be in order. In particular, >>>> I'd like to know: >>>> >>>> 1. what are the different "solvers"? (if we split solve into "hints" >>>> like with dsolve, these would be the different hints), and >>>> 2. which are algorithmically complete (i.e., we know they will give >>>> all solutions, or they can detect somehow if they may have missed >>>> one)? >>>> >>>> And this may raise auxiliary questions, like: >>>> >>>> - to what degree can the different solvers be separated? For instance, >>>> one solver (I'm not sure if it's actually implemented) would use >>>> decompose() to solve recursively. How would such "recursive solvers" >>>> look in a hints system? >>>> >>>> - of those that are heuristic (not algorithmically complete), can they >>>> be improved? >> >> I'm going through the solvers code and will answer these questions soon. >> >> -- >> You received this message because you are subscribed to the Google Groups >> "sympy" group. >> To unsubscribe from this group and stop receiving emails from it, send an >> email to sympy+unsubscr...@googlegroups.com. >> To post to this group, send email to sympy@googlegroups.com. >> Visit this group at http://groups.google.com/group/sympy. >> For more options, visit https://groups.google.com/groups/opt_out. > > -- > You received this message because you are subscribed to the Google Groups > "sympy" group. > To unsubscribe from this group and stop receiving emails from it, send an > email to sympy+unsubscr...@googlegroups.com. > To post to this group, send email to sympy@googlegroups.com. > Visit this group at http://groups.google.com/group/sympy. > For more options, visit https://groups.google.com/groups/opt_out. -- Harsh -- You received this message because you are subscribed to the Google Groups "sympy" group. To unsubscribe from this group and stop receiving emails from it, send an email to sympy+unsubscr...@googlegroups.com. To post to this group, send email to sympy@googlegroups.com. Visit this group at http://groups.google.com/group/sympy. For more options, visit https://groups.google.com/groups/opt_out.
