> Apparently only for some of them: it does not solve > ``x**5 - 5*x**4 + 30*x**3 - 50*x**2 + 55*x - 21 = 0``
Thanks. Yes, not all of them, Only equations of form x**5 + p*x**3 + q*x**2 + r*x + s, no fourth order terms are solvable. The implementation was added in https://github.com/sympy/sympy/pull/1746. So, there is scope of improvement. I wonder how many of other methods of solving solvable quintics can be implemented without a knowledge of abstract algebra. Aaron Meurer can you guide me on this? On 27 January 2014 13:28, mario <mario.pern...@gmail.com> wrote: > You wrote "Methods to solve solvable quintics are implemented in sympy." > > Apparently only for some of them: it does not solve > ``x**5 - 5*x**4 + 30*x**3 - 50*x**2 + 55*x - 21 = 0`` > > taken from http://en.wikipedia.org/wiki/Quintic_function > > > > > On Monday, January 27, 2014 3:11:37 AM UTC+1, Harsh Gupta wrote: >> >> 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 <asme...@gmail.com> wrote: >> > On Fri, Jan 24, 2014 at 2:02 PM, Harsh Gupta <gupta....@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+un...@googlegroups.com. >> >> To post to this group, send email to sy...@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+un...@googlegroups.com. >> > To post to this group, send email to sy...@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. -- Harsh -- You received this message because you are subscribed to the Google Groups "sympy" group. 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