CY wrote:
>On Tuesday 20 July 2004 11:51 pm, Richard Fateman wrote:
>
>
>
>>Depends on what you mean by "added functionality". If you add a "new
>>representation" then I think the answer is yes, you have to consider what
>>each command might do, and whether the default for "unknown" stuff is good
>>enough. Added functionality which fits in the standard representation is
>>not so problematical. E.g. adding the Lambert W function which would
>>require a handful of additions:
>>
>>a. how to differentiate
>>b. how to evaluate in floating point
>>c. how to evaluate in bigfloat
>>d. maybe some integration formulas
>>e. some fact about the inverse (for solve)
>>f. maybe some facts about taylor series
>>g. simplification at special arguments.
>>
>>
>
>But if we have more series representations present in the system than just
>taylor do we need to also consider those, for example?
>
It might be possible to have one scheme for essentially "all" series,
but I haven't
thought about it.
> It would be nice
>if, for given types of new additions, we have a checklist of items that
>need to be thought out/documented before the addition is ready for prime
>time.
>
Yes
> (I guess in that sense a lot of Maxima isn't ready for prime time,
>for that matter.) For people wanting to add functions, a standard function
>programmer documentation template addressing various points like the ones
>you listed above would (IMHO anyway) be an excellent policy to implement.
>(And create for what's already there.)
>
>
>
>>None of these requires changing existing programs, but only data, and
>>new programs. some other stuff might need changes, e.g.
>>simplification of expressions around W; e.g. exp(W(x)) would require
>>changes to exp simplifier.
>>
>>
>
>Which is a good illustration of why I think there should be some systematic
>way a programmer could have a checklist - so they can say "Yep, OK, got the
>simplifier rules for exp, foo, bar, ..." even if the decision is no new
>rules are needed.
>
>
>
>>Introduction of new functions is much simpler. It is even simpler
>>if you just define away the function as, for example, if sinh were not
>>there, you could define sinh(x):=(exp(x)-exp(-x))/2 , or if all
>>functions were immediately replaced by their (truncated) taylor series.
>>So not all is quite so desperate.
>>
>>
>
>No, but it would be nice if it were systematic.
>
>
>
>>The point of the Axiom system is, at least in principle, to make use of
>>declarative knowledge about stuff like "polynomials" over "rings" in
>>which case you know that to define such domains, you need to build upon
>>the operations and representations of specific rings, and all these
>>operations and related axioms are listed. So you will in that sense get
>>the job done right in an abstract mathematical sense.
>>
>>
>
>In principle I like the sound of that. How do the feature sets of Maxima
>and Axiom compare for real world use? Axiom seems to be the more "solid"
>of the two systems, but I've always had the impression Maxima was the more
>practical of the two for non mathematical research type work.
>
I think the Axiom people should respond. I do not have any recent
experience with
Axiom. I suspect that Axiom does less, overall. What it does may be
extensible in
abstract domains which are not covered by 3M, but those areas are of
limited interest.
>
>
>
>>The extent to which this can actually work has been an issue. If all
>>you get is "modern algebra" but not analysis, then the result is
>>insufficient for Macsyma, unless you do a lot of faking.
>>If you are less ambitious and are interesting in (say) univariate
>>polynomials over finite fields, then you can be linguistically very clean,
>>and I suspect you could even add new representations in a fairly clean
>>manner.
>>
>>My feeling is that any of the "3M" CAS are too ambitious.
>>
>>
>
>Perhaps, but their success as products indicates that what they do is
>something people find useful. I guess its the old problem that nothing
>worthwhile is easy.
>
The market is not necessarily the best judge. Most sales are to support
calculus labs, I suspect.
RJF
>
>CY
>
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