I realize that there is less than a month left for the application deadline and it has already been a month since I posted this thread. So, I need to come up with design details fast. I have written some details about using sets as output for solvers in this PR https://github.com/sympy/sympy/pull/2948/files. PR because I feel it is better platform to facilitate this discussion than the mailing list. Please have a look.
On 16 February 2014 07:15, Jigar Mistry <jigarmistr...@gmail.com> wrote: > i am also interested in solvers module. how can i contribute to simpy using > this solvers module.Plz help me.... > > > On Tuesday, 21 January 2014 16:25:13 UTC+5:30, Harsh Gupta wrote: >> >> Hi, I'm Harsh Gupta I will be GSOC applicant this year. I want to discuss >> the solvers idea given on the Idea's >> page.https://github.com/sympy/sympy/wiki/GSoC-2014-Ideas#solvers >> >> Some of the aspect of the idea are discussed at >> https://groups.google.com/forum/?fromgroups=#!starred/sympy/8TM8cnuzkG8. >> >> >> Aaron Meurer said: >> >>> I think with TransformationSet we can do quite a bit. That handles >>> sets like {f(x) | x in A}. I think what is missing is the basic set >>> builder {x | P(x)}, where P(x) is a boolean predicate. >> >> >> >> Matthew Rocklin said: >> >>>> > Real issue here - how to represent some solutions (e.g. sin(x)==0). >>> >>> In sets we would represent this with >>> In [1]: imageset(k, pi*k, S.Integers) >>> Out[1]: {π⋅k | k ∊ ℤ} >> >> >> Implementing a general set builder will be very useful, we will need to >> define basic set operations like union >> and intersection on them. We might use a syntax like `BuildSet(expr, >> sym_in_inputset, cond)` >> >> In [1]: BuildSet(pi*k, (k, S.Integers), True).intersect(0, 10) >> Out[1]: {pi, 2*pi, 3*pi} >> >> >> Matthew Rocklin said: >> >>> It sounds like maybe solve should return a Set. >> >> >> I think it will be necessary to return set if we want to represent the >> solution of expressions like `floor(x) - 5`. >> See https://code.google.com/p/sympy/issues/detail?id=3975. >> One problem I see with returning sets is that it can break a lot of >> existing code. >> >> >> As mentioned in the idea page we need to have a method to check if solve >> returns all the solutions. For polynomials or expressions which are >> solved by converting to polynomials we can compare the degree of the >> polynomial to the number of solutions returned. >> >> Other method can be verifying the number of the solutions by using the >> derivative of the function. Say we are given a *continuous* and >> *differentiable* function f(x) and it's derivative w.r.t x is g(x), >> then if g(x) has n solutions then f(x) cannot have more than n + 1 >> solutions. So, if the solve returns n + 1 solutions for f(x) then we are >> guaranteed that we have found all the solutions. >> For this we will need a discontinuity finder and we will also have to make >> sure that we have found all the solutions for g(x), i.e., the derivative of >> f(x), which can be done recursively or by using other methods. >> >> A third way can be using numerical solver. Say we use solve to find the >> solution of f(x) for some interval [a, b] then we can also run the numerical >> solver for f(x) on [a, b] >> if the number of solutions by numerical solver and symbolic solve matches >> then we can be pretty sure that we have found out all the solutions of f(x) >> in [a, b]. >> >> -- >> 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. 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.
