On Mon, Feb 3, 2014 at 4:11 PM, someone <[email protected]> wrote: >> We can already solve that one using LambertW (but we need to implement >> all the branches, >> https://code.google.com/p/sympy/issues/detail?id=4006). > > Oh, that was just an example. In this case on can > simplify the TransRootOf object. > > >> Can these work with trig functions (via equivalence from complex >> exponentials)? > > Without going to the details, yes. But it depends on > the arguments, things with infinitely many oscillations > will cause heavy difficulties. In fact the definition > of "tame expression" is > > "An elementary expression is tame if the arguments > of its trigonometric subexpressions are bounded." > > See def 1.5 and example 1.6 from "Real Root Isolation > for Tame Elementary Functions" for the details. > > >> A more classic example of a root that can't be >> expressed in closed-form is cos(x) = x. > > Except if we define another special function > for that ;-) It depends all the time on what > exactly "closed form" means.
The real solution to this is called the Dottie Number (http://mathworld.wolfram.com/DottieNumber.html), but it's not a heavily used constant. So I don't know if it makes sense to add it. Aaron Meurer > > The integral of exp(-x**2) can be done in closed > form but the form is not elementary as you know. > > -- > 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.
