Thanks for your proposals,
First of all, I should precise I'm new to sage ...
I would like, as a first step, and with a sage script , define h as a
fonctional of f and variables t and s, as
h = function('hilbert',function(f),t,s); somewhat like :
sage: t,eps,s=var('t,eps,s')
sage: f=function('f',t)
sage: assume(eps>0)
sage: assume((s-eps)**2+1 >0) # (why ?)
sage: h(s)=limit(integral((f(s+t)-f(s-t))/t,t,eps,Infinity),eps=0)
I don't know how to define h(s) as a fonction of f(t).
Claude
On May 16, 12:32 am, Maurizio <[email protected]> wrote:
> 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,
> > Burcinsage:
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