Re: [Axiom-developer] How to do generic sum using aldor?

[Ralf Hemmecke]

> > Since you want to work with Axiom, I guess you are right here.
> well, there is also axiom-math and axiom-mail ... anyways the people who 
> answer seem to be the same:)

Right. There are not so many people anyway. And your question is not 
only related to Math but it goes a bit deeper.

> > I currently rather rely on what is provided in LibAldor+LibAlgebra and 
> > don't take things from LibAxiom, but that is personal taste.
> I wasn't aware that this is possible.
> Using  #include "aldor" and #include "algebra" compiles but won't run:
> (1) -> sum [1,2,3]
>
>    >> System error:
>    AxiomXL file "sal_list" is missing!
>
> how can one mix axiom and libaldor?

I don't mix. You misunderstood. I for my taste find the libraries coming 
with Aldor cleaner. And even though they have much less functionality, 
it is sufficient for me. Sooner or later the Axiom library has to be 
redesigned anyway, because the files should become literate documents 
and all mis-design should go away. But that is a lot of work and 
certainly not finished tomorrow.

Anyway, you have to use

#include "axiom"

if you want to use your things inside an Axiom session (which is not 
primarily my goal).

> > Yep. But sorry to say: Axiom is weak in that respect (at least to my 
> > knowledge).
> ok, at least this is an answer and I shall not try further.

Well, somebody should make Generator available in Axiom. ;-)
Actually, making Generator available is easy, but still that is not 
enough. Axiom does not allow a Generator in a for expression so

g: Generator X := someAldorFunctionThatReturnsAGenerator()
for x in g repeat doSomething(x)

won't work. One can even work around a little as has been demonstrated 
by Martin Rubey...

http://sourceforge.net/mailarchive/message.php?msg_id=37824208

Look into

svn://svn.risc.uni-linz.ac.at/hemmecke/combinat/trunk
directory combinat/src/axiom-compatibility/axcompat*.as.nw

in order to see how Generator is made available.

In fact Aldor-Combinat is developed on libaldor+libalgebra, but by this 
files in "axiom-compatibility" we provide some wrapper function to make 
(nearly) the same code also compiling with libaxiom and thus available 
in Axiom.

> Thus my "SumPackage" includes also
>
>                 sum ( ll: Stream R) : R == {
>                         import from StreamFunctions2(R,R);
>                         last complete scan(0,+, ll);
>                 }
>
> Is it really true that StreamFunctions2 must explicitly be imported?

StreamFunctions2 is a package. How else would the compiler find out that 
you want to use a function from that package?

> The "last complete scan" makes me worry if the stream is really long
> and all intermediate results are stored; or is it optimized away by the 
> compiler?

I don't think the compiler can optimize that away.
But in StreamAggregate you also find the exports

  frst: % -> S
    ++ frst(s) returns the first element of stream s.
    ++ Caution: this function should only be called after a 
\spad{empty?} test
    ++ has been made since there no error check.
  rst: % -> %
    ++ rst(s) returns a pointer to the next node of stream s.
    ++ Caution: this function should only be called after a 
\spad{empty?} test
    ++ has been made since there no error check.

There is also first and rest, but don't ask me which one you should use, 
I have no idea.

> I rather would like the for loop but do not know where to import it from.
> greping the source files is not really helpful in this case ...

Use a while loop a la...

s: R := 0;
while not empty? ll repeat {
  s := s + first ll;
  ll := rest ll;
}

Hope that helps

Ralf