Well, my two cylinder brain is rolling on this a little, so I'll throw
some thoughts out there on the uses of this approach, and possible ways
to handle it. Smart people feel free to laugh, tear up ideas, etc.
This is brainstorming.
The initial generated table could become part of the math test suite,
which will hold the complete table of possible problems and solutions.
Then there is the working integral table, the one used in actual day to
day operations. Once it is shown that Maxima can do an integral
correctly using its own interal routines, it is removed from the
working table. Thus, we build a table of just the integrals Maxima
cannot do correctly itself. I don't know if this is the best approach
- maybe for performance it would be better to go to table lookup and
then try the routines. But I like the idea of a minimal working table
because keeping the integration routines in use whenever possible is
the best way to ensure that no bugs pop out of them. The more they are
used, the more chance someone will find any given error in them.
Perhaps some policy could be implimented where integrals which are
found solvable but take relativly long periods of time could be added
to the table. For future consideration.
Then we examine our generated list of non-solvable-by-Maxima integrals,
to see what it shows. Some integrals will not be solvable in closed
form, some may reveal bugs to be fixed in our integration routines or
elsewhere, some may show cases we should be able to calculate and pave
the way for implimenting them. And some will be beyond any current
symbolic computation by computer, or at least any algorithm we have
both knowledge and time to impliment. Those are the ones that become
part of the working table.
The working table will contain the most general form of the result of
the integration. Before the table lookup returns an answer, it
evaluates the raw table answer in the current variable and properties
environments, to reduce it to the proper form given the environment it
is being inserted into.
Have I got (generally, at least) the right idea, or am I missing the
main method/point?
CY
--- Richard Fateman <fateman@cs.berkeley.edu> wrote:
> I have a number of tables that are out of copyright.
> But I suggest that we make extra integral problems by
> making a list of integrand "parts" e.g.
>
> p1=x^2-a^2
> p2=sin(a*x+b)
> p3=exp(a*x+b)
>
> etc/
> Then compose integrands by exhaustion: pi*pj, pi/pj,
> pi^2 etc.
>
> make a table.
>
>
>
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