Waldek Hebisch schrieb:
>
> clicliclic@freenet.de wrote:
> >
> > Rationalizing by substitution belongs to the 18th century (the age
> > of the Bernoullis and Euler), for a Risch integrator it amounts to
> > admitting defeat!
>
> Of course I would like to handle such integrals using general
> code. But when there is rationalizing substitution, then
> execution time is usualy much better compared to full Trager
> procedure. So this is desirable optimization.
>
Your use of the term optimization is futuristic in that it is relative
to a procedure that has been described but not been implemented in
FriCAS or elsewhere.
> >
> > Alternatively, Kauers' Groebner-basis heuristics could be resorted
> > to when an algebraic integral is pronounced ">> ... impossible". He
> > does it in about ten lines of code ...
>
> Ten lines of pseudo code. Real code that only handles very simple
> case is already longer. More complicated cases need code which
> introduces extra variables. The real problem is exection time.
> I could add to FriCAS few lines of code (probably more than 10)
> that will "handle" general case. But ATM there is no hope that
> such code would finish execution in reasonable time. Groebner
> bases do well in simple cases, but may also lead to enormous
> execution time. At least theoretically Trager procedure has
> lower complexity than Groebner bases, so it is not clear if
> adding Groebner bases to the mix helps.
>
And also about ten lines of Mathematica code in the Appendix - but this
line count does not include a separate interface package used to access
Singular on whose Groebner basis engine the code relies (without real
need, I suppose).
So everybody is holding their breath in expectation of a full
implementation of Trager's futuristic procedure in some FriCAS version
1.2.x with 5
|
