Michel Talon wrote:
> Hello,
>
> i have seen a web site where symbolic integration using reduction to
> standard forms via pattern maching is presented in a very favourable light
> compared to using systematic algorithms like Risch algorithm. See
> http://www.apmaths.uwo.ca/~arich/
> This could be of interest for maxima.
> For example the "algebraic function highlights" here:
> http://www.apmaths.uwo.ca/~arich/TestResultHighlights/AlgebraicFunctionHighlights.pdf#pagemode=bookmarks
> show very interesting examples, notably the last one (which my version of
> maxima is not able to integrate at all).
>
>
Unfortunately, as written, Albert Rich's pattern matching program (Rubi)
run on top of Mathematica.
It would be possible to use the MockMMA pattern matcher to run the
patterns (converted automatically to Lisp).
I have read a huge gob of the rules into MockMMA without incident (I
had to remove excess blank lines which
MockMMA took to be end-of-expression markers, first).
However, Rubi also uses various tools in Mathematica for simplification
and transformation, and perhaps there
is not quite an equivalent in Maxima for some of these. FullSimplify
for example.
Assuming that we can find near equivalents of this, the rules+programs
could be done for Maxima, but not trivially.
And yes, there are undoubtedly problems that Rubi can do which cannot be
done by any other system.
These may have more to do with heuristics for factoring over algebraic
number fields, simplification of messy forms,
etc. than with integration per se.
RJF