[Beowulf] Teaching Scientific Computation (looking fo the perfect text)

[Florent Calvayrac]

Robert G. Brown a écrit :
> On Wed, 21 Nov 2007, David Mathog wrote:
>
>>
>> A = B + C <VecX>  D
>>
>> triple = A <dot> B <vecX> C
>>
>> For all I know operator definition does exist in C++ now - the
>> language is humongous and I certainly am not familiar with some of
>> the more obscure corners.
>
> (one or two last ones while I clear mail:-).  Actually a really, really
> interesting idea, but one does have a whole new class of typing errors.
> If you go with either tensor products or graded algebra products, you
> have to think carefully about what happens when you multiply e.g. real
> times quaternion, complex times quaternion, etc.  Some of these are as
> ambiguous as multiplying a 2D vector by a 4D vector without specifying
> the embedding or that their is one -- is the result a scalar, a vector,
> or a tensor?
>
> But it still is a really good idea.  There is a generalized algebra of
> dyad, triad, inner and outer products, and so on.  It would be really
> interesting to define a compiler that could cope.  Even symbolic
> manipulation languages tend to have to work at it and maybe have
> complex and quaternions but rarely anything else.
>
>

the TAO language used on the APE family of SIMD computers (lot of 
acronyms here)
does exactly that thanks to a good macro preprocessor. It is mainly used 
for QCD but
I found it very nice for other uses ;  pity it only compiles on those 
machines.




-- 
Florent Calvayrac  | 
Professeur Universite du Maine
Lab. de Physique de l'Etat Condense UMR-CNRS 6087 
Inst. de Rech. en Ingenierie Molec. et Matx Fonctionnels  FR CNRS 2575