I do not know how to simplify these roots. On Tuesday, January 28, 2014 1:57:45 AM UTC+1, Aaron Meurer wrote: > > Ah, apparently the paper > ( > http://www.ams.org/journals/mcom/1991-57-195/S0025-5718-1991-1079014-X/S0025-5718-1991-1079014-X.pdf > > ("Solving solvable quintics", D. S. Dummit)), glosses over this, > because of this fact. What is the algorithm to eliminate the fourth > order term? > > How can we simplify the roots. Will the more advanced sqrtdenest > algorithms help (https://code.google.com/p/sympy/issues/detail?id=93)? > > Aaron Meurer > > On Mon, Jan 27, 2014 at 10:59 AM, mario <[email protected] <javascript:>> > wrote: > > > > One can always eliminate the fourth order by a translation, in this case > by > > one; one obtains then > > ``x**5 + 20*x**3 + 20*x**2 + 30*x + 10``, which is solved by SymPy; it > would > > be useful to automatize this step. > > > > However the real solution is not simplified, it has ``count_ops = 267``, > vs > > ``count_ops=11`` for the simplified > > real solution ``S('2^(1/5) - 4^(1/5) + 8^(1/5) - 16^(1/5)')`` > > > > > > > > > > > > On Monday, January 27, 2014 11:42:03 AM UTC+1, Harsh Gupta wrote: > >> > >> > 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 <[email protected]> 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 <[email protected]> wrote: > >> >> > On Fri, Jan 24, 2014 at 2:02 PM, Harsh Gupta <[email protected]> > > >> >> > 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 [email protected]. > >> >> >> To post to this group, send email to [email protected]. > >> >> >> 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 [email protected]. > >> >> > To post to this group, send email to [email protected]. > >> >> > 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 [email protected]. > >> > To post to this group, send email to [email protected]. > >> > 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 [email protected] <javascript:>. > > To post to this group, send email to [email protected]<javascript:>. > > > 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 [email protected]. To post to this group, send email to [email protected]. Visit this group at http://groups.google.com/group/sympy. For more options, visit https://groups.google.com/groups/opt_out.
