Interesting... it seems that every transform (Laplace, Fourier, Hilbert, etc.) are evaluated trying lookup table method first (in combination with partial decomposition or factorization probably), and only if this method fails, the integration engine takes place. I'm wondering whether this solution is the same adopted by mathematica et al. I know this is certainly the best for speed, which is wonderful! It seems it's also possible in maple to disable the integration if the lookup method fails. According to this, it seems that implementing transforms is just a matter of providing a vast lookup table, provided that you have a powerful enough pattern engine, gcd (probably the toughest one), factorization and other basic stuff... Hopefully (most of) these are coming with pynac, right?
Regards Maurizio On 15 Mag, 17:26, Burcin Erocal <[email protected]> wrote: > Hi Claude, > > On Fri, 15 May 2009 06:41:14 -0700 (PDT) > > Claude <[email protected]> wrote: > > > Hi All, > > Could somebody help me in programming, for example, the Hilbert > > transform, or Mellin transform, taking Laplace one as a guideline. > > Thanks in advance. > > The documentation of both Hilbert and Mellin transform functions in > Maple seem to suggest that they use table lookups: > > http://www.maplesoft.com/support/help/view.aspx?path=inttrans/hilbert > > http://www.maplesoft.com/support/help/view.aspx?path=inttrans/mellin > > In the Description section of the pages above, see item 4 in the first > link and 3 in the second one. > > The pattern matching capabilities of the new symbolics will be useful > here. For some documentation and examples you can try: > > sage: var('x,y',ns=1) > sage: x.subs? > > Taking the documentation in the above links as a guideline, such a > function might: > > - transform the given expression to a normal form, using some > simplification rules > > - use the relevant lookup table to do the necessary substitutions > > For now, it will be enough to come up with simplification rules that > apply only to expressions you're interested in. The lookup table can > also be restricted in this way. Do you have access to a table of > Hilbert/Mellin transforms relevant for you application? > > Can you give examples of expected input and output for the transform > you want to implement? > > Cheers, > Burcin --~--~---------~--~----~------------~-------~--~----~ 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/sage-support URLs: http://www.sagemath.org -~----------~----~----~----~------~----~------~--~---
