[Axiom-developer] Re: integration

[C Y]

--- Martin Rubey <address@hidden> wrote:

> Thank you!
> 
> C Y writes:
>  > Well, I tried :-).  Formatting is a hash, I'm afraid - is there a
> way
>  > to paste formatted text I missed?
> 
> Yes, just look at the edited text. "::" + indented text is our
> friend.

Ah :-).

> and thanks again for spotting the bug. Now: go ahead and fix it :-)

No problem - I'm beginning to think Axiom is where the most interesting
work on CAS will occur.  I suspect you came to this conclusion long
ago, but I'm beginning to think the Maxima source code will require
such a determined effort to improve to a decent point that it might be
best to just impliment all the features it has that Axiom doesn't in
Axiom.  I'm finding myself posting suggestions that look remarkably
like the ones you were making early on, and at some point after that
(IIRC) you popped up on the Axiom lists :-).  I sense a pattern... 
although I must say I prefer Maxima's ASCII display to Axiom's, at
least for easy reading.  I wonder how hard that would be to impliment?

Re: fixing bug - Well, I can give it a shot if it's simple to find... 
I've got some learning to do though.  Me thinks the Risch algorithm
would be a rather ambitious way to try getting the hang of the Axiom
source code...

> A starting point might be the following:
> 
> )tr FSCINT )math
> )tr  INTEF )math
> )tr INTTR )math
> )tr INTAF )math
> )tr INTPM )math
> )tr INTALG  )math
> 
> integrate(sin(x^2),x)
> 
> If you know the Risch algorithm, you can certainly spot the point
> where it should have done something but didn't do :-)

Ah, yes - the Risch algorithm.  Do you happen to know if the full
algorithm is described online anywhere?  Ideally both Risch's algorithm
and the extensions by Cherry et. al. for special functions would be
formally implimented (or documented since a fair part of it must
already be present.)  Apparently nobody impliments the full algorithm
due to complexity?:  http://mathworld.wolfram.com/RischAlgorithm.html  
I wonder if it's too complex for the Axiom system, given the structure
it has in place.  I've never studied it, but given how critical it is
to both systems it's high time I learned about it.

> Unfortunately Manuel Bronstein died. I don't know anybody who would
> be able to document these routines.

Well, when the great fall the lesser must pick up the torch.  I need to
get ahold of some basic materials (Bronstein's books would be useful,
I'd wager :-) and get as much up to speed as my brain allows.  I need
to learn Axiom's guts anyway and this sounds like a possibly useful
way.  Maybe I could warm up by implimenting a physical units domain in
Axiom, although lord knows how I'd convince it to display things in the
form (numbers and variables)*units, or recognize Newtons out of
a*kg*b*s^-2*c*m.  Does Axiom have provisions for non-standard display
conventions and substitution like that?

Cheers,
CY

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