[Rd] Computer algebra in R - would that be an idea??

[simon blomberg]

>  >>>>> "bry" == bry  <bry at xdocs.dk>
>>>>>>      on Fri, 15 Jul 2005 14:16:46 +0200 writes:
>
>     bry> About a year ago there was a discussion about interfacing R 
>with J on the J
>     bry> forum, the best method seemed to be that outlined in this 
>vector article
>     bry> http://www.vector.org.uk/archive/v194/finn194.htm
>
>(which is interesting to see for me,
>  if I had known that my posted functions would make it to an APL
>  workshop...
>  BTW: Does one need special plugins / fonts to properly view
>      the APL symbols ? )
>
>
>     bry> and use J instead of APL
>
>     bry> http://www.jsoftware.com
>
>well, I've learned about J as the ASCII-variant of APL, and APL
>used to be my first `beloved' computer language (in high school!)
>-- but does J really provide computer algebra in the sense of
>Maxima , Maple or yacas... ??

I wonder if at this point it would be useful to think about how a 
symbolic algebra system might be used by R users, and whether that 
would affect the choice of system. For example, Maxima and yacas seem 
to be mostly concerned with "getting the job done", which might be 
all that the data analyst or occasional user needs. However, 
mathematical statisticians might be more concerned with developing 
new mathematics. For example, commutative algebra has been found to 
be very useful in the theory of experimental design (e.g. Pistone, 
Riccomagno, Wynn (2000) Algebraic Statistics: Computational 
Commutative Algebra in Statistics. Chapman & Hall). Now, Maxima can 
already do the necessary calculations (ie Groebner bases of 
polynomials), but as far as I know, yacas cannot. But who knows where 
the next breakthrough will come from? In that case Axiom might be 
more useful and appropriate, as it is largely used by research 
mathematicians. We would then need a mechanism for the development of 
new data structures in R that could potentially match Axiom's rich 
and extensible type system. I guess some mechanism that relies on S4 
classes would be necessary. Of course, there is nothing to stop us 
developing packages for more than one system ("We are R. We will 
assimilate you!"). I have no idea how to do any of this: I'm just 
floating ideas here. :-)

Cheers,

Simon.

>
>(and no, please refrain from flame wars about APL vs .. vs ..,
>  it's hard to refrain for me, too...)
>
>Martin Maechler, ETH Zurich
>
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-- 
Simon Blomberg, B.Sc.(Hons.), Ph.D, M.App.Stat.
Centre for Resource and Environmental Studies
The Australian National University
Canberra ACT 0200
Australia

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