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[Axiom-developer] Re: integration
From: |
Martin Rubey |
Subject: |
[Axiom-developer] Re: integration |
Date: |
Fri, 19 Aug 2005 15:54:21 +0200 |
C Y writes:
> Re: fixing bug - Well, I can give it a shot if it's simple to find...
Well, what you need to find out is how the Risch algorithm would handle
sin(x^2). Maybe it is simply handled by pattern matching, as exp(-x^2) is... In
this case, fixing it would be easy. Mathematica also has a representation for
sin(x^n), but I don't know whether it is "useful". (It's in terms of incomplete
Gamma functions)
> 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...
Note that Axioms source is very nicely split into two parts: the "Algebra",
implementing its mathematical capabilities, and the rest (compiler,
interpreter, display, graphics, ...)
> 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.
If you are interested, it's certainly worth the effort.
> > 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.
With some luck (and brains), the lesser become great that way.
> 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?
Output is easy.
)sh OUTFORM
tells you everything you want to know about it.
Pattern matching is there too.
)sh PATMATCH
or rather, use HyperDoc.
Martin
- [Axiom-developer] Re: integration, Martin Rubey, 2005/08/19
- [Axiom-developer] Re: integration, Martin Rubey, 2005/08/19
- [Axiom-developer] Re: integration, C Y, 2005/08/19
- [Axiom-developer] Re: integration,
Martin Rubey <=
- [Axiom-developer] Re: integration, C Y, 2005/08/19
- [Axiom-developer] Unit package question, C Y, 2005/08/19
- RE: [Axiom-developer] Unit package question, Bill Page, 2005/08/19
- RE: [Axiom-developer] Unit package question, C Y, 2005/08/19
- Re: [Axiom-developer] Unit package question, Ralf Hemmecke, 2005/08/22
- Re: [Axiom-developer] Unit package question, Martin Rubey, 2005/08/22
- Re: [Axiom-developer] Unit package question, C Y, 2005/08/23
- Re: [Axiom-developer] Unit package question, Ralf Hemmecke, 2005/08/23
- Re: [Axiom-developer] Unit package question, C Y, 2005/08/23
- Re: [Axiom-developer] Unit package question, Ralf Hemmecke, 2005/08/23