Can you tell me what algorithms are used to find the roots. I will try digging more about it and see if the problem can be resolved.
On Tue, Mar 27, 2012 at 9:36 PM, Aaron Meurer <asmeu...@gmail.com> wrote: > Numerically calculating the roots is not very useful. If we wanted to > use numerics, we would just compute the integral numerically in the > first place. I suppose a numeric root counting algorithm could be > useful for verifying that you have all the roots. > > You should focus of classes of functions and how you can show that the > roots generated (in some domain) consist of all of them. For example, > this is easy to do for rational functions. For trigonometric > functions, the solver needs to be modified to return all periodic > solutions. > > Aaron Meurer > > On Tue, Mar 27, 2012 at 3:23 AM, arpit goyal <agmp...@gmail.com> wrote: > > This means i have to first of all , modify the solve() and residue() > > function then work on finding the definite integral. > > I have done a course on Numerical Methods and Computation and do studied > > about finding roots of a function . > > But i did not find them very much efficient. > > Please can any one suggest me papers from i can read about to find roots > of > > functions. > > > > Regards > > Arpit Goyal > > > > > > On Tue, Mar 27, 2012 at 1:13 AM, Aaron Meurer <asmeu...@gmail.com> > wrote: > >> > >> I would try Meijer G first because the result is generally going to be > >> better. For example, it will just give you the convergence conditions > >> (they might not be tight, but in my experience they usually are). > >> > >> Also, as Tom noted, residue() is very buggy, in the sense that it > >> often gives just plain wrong answers (see > >> http://code.google.com/p/sympy/issues/detail?id=2555). I think we > >> could employ some smarter heuristics in that function as well before > >> trying series expansion (like if we are able to determine the strength > >> of the pole just from the form of the expression, then we can compute > >> it by just taking derivatives). > >> > >> Also, there's the problem of finding all the poles, which is not > >> currently implemented in residue(). I'm not sure if it's implemented > >> anywhere else, but as far as I know, it's not. Just using solve() > >> will be unreliable, because we need to have a guarantee to find *all* > >> the poles, not just some of them, which is currently the best that > >> solve() can do. So this project would probably implicitly involve > >> improving solve() as well. > >> > >> Aaron Meurer > >> > >> On Sun, Mar 25, 2012 at 10:41 PM, Joachim Durchholz <j...@durchholz.org> > >> wrote: > >> > Am 26.03.2012 03:26, schrieb Aaron Meurer: > >> > > >> >> I think the best way would be to just try the Meijer G code first, > and > >> >> only fall back to residues if that fails. > >> > > >> > > >> > How quickly can the residues code find out whether it will work on a > >> > given > >> > integral? > >> > If that is quick, trying residues first would be faster. (Meijer can > be > >> > excessively slow, particularly in those cases where it fails to find a > >> > solution.) > >> > > >> > > >> > -- > >> > You received this message because you are subscribed to the Google > >> > Groups > >> > "sympy" group. > >> > To post to this group, send email to sympy@googlegroups.com. > >> > To unsubscribe from this group, send email to > >> > sympy+unsubscr...@googlegroups.com. > >> > For more options, visit this group at > >> > http://groups.google.com/group/sympy?hl=en. > >> > > >> > >> -- > >> You received this message because you are subscribed to the Google > Groups > >> "sympy" group. > >> To post to this group, send email to sympy@googlegroups.com. > >> To unsubscribe from this group, send email to > >> sympy+unsubscr...@googlegroups.com. > >> For more options, visit this group at > >> http://groups.google.com/group/sympy?hl=en. > >> > > > > -- > > You received this message because you are subscribed to the Google Groups > > "sympy" group. > > To post to this group, send email to sympy@googlegroups.com. > > To unsubscribe from this group, send email to > > sympy+unsubscr...@googlegroups.com. > > For more options, visit this group at > > http://groups.google.com/group/sympy?hl=en. > > -- > You received this message because you are subscribed to the Google Groups > "sympy" group. > To post to this group, send email to sympy@googlegroups.com. > To unsubscribe from this group, send email to > sympy+unsubscr...@googlegroups.com. > For more options, visit this group at > http://groups.google.com/group/sympy?hl=en. > > -- You received this message because you are subscribed to the Google Groups "sympy" group. To post to this group, send email to sympy@googlegroups.com. To unsubscribe from this group, send email to sympy+unsubscr...@googlegroups.com. For more options, visit this group at http://groups.google.com/group/sympy?hl=en.
