On Saturday, March 31, 2012 10:07:15 PM UTC+5:30, Stefan Krastanov wrote: > > > If the integral can be simplified to an expression that contains the > > functions > > I implement in interval arithmetic, then it can be handled. > > But many do not simplify. And when an expression is hard to understand > (a complicated integral for example) one tries to plot it to get more > information. It is not only integrals, there are also nsolve > expressions, infinite sums and so many other thing that are not > restricted to the small number of mpmath functions. > > >> > >> A simple linear or quadratic interpolation should do the trick in most > >> cases. > >> > > > > For gamma/ bessel functions we can use interval arithmetic based on their > > series expansions. As the recursion goes from a larger block to a smaller > > block, it is impossible without knowing how the function behaves to do > > interval > > arithmetic. A linear/ quadratic interpolation is equivalent to series > > expansion and > > hence can be done, though it has to be atleast quadratic to get decent > > results. > > > > If you are saying that interpolations (not power series expansions as > they are not the same thing in the general case) are good enough, then > why not use them also for integrals and all the other complicated > expressions that can not be expressed in mpi? > I think most of the explicit equations can be handled by your implementation. I don't think the implicit equations involving such expressions can be plotted even in mathematica / Matlab.( haven't verified it though). Plotting using interpolation is possible, but it might lead to erroneous plots and hence it is better not to implement a interpolating plots for such functions.
It will be possible to add support to almost all the functions which can be expressed as union of piecewise functions, which are either monotonic or periodic. > I may very well be mistaken, but to me it seems like you will try to > extend mpmath a bit and then be forced to redo all this in sympy using > interpolations for all the expressions that can not be translated to > mpmath. > -- You received this message because you are subscribed to the Google Groups "sympy" group. To view this discussion on the web visit https://groups.google.com/d/msg/sympy/-/C6uFqDX-BxoJ. To post to this group, send email to [email protected]. To unsubscribe from this group, send email to [email protected]. For more options, visit this group at http://groups.google.com/group/sympy?hl=en.
