Re: [Axiom-math] Re: [Axiom-developer] Summing over a list

[Bill Page]

Quoting Martin Rubey:

> (redirecting to axiom-math, where usage questions belong)
>
> Alasdair McAndrew writes:
>
> > Given two lists,for example:
> >
> > z:=[1,2,3,4,5,6]
> > w:=[1,0,0,1,1,1]
> >
> > it seems that the sum of the pairwise product is obtained by
> >
> > reduce(+,[z.i*w.i for i in 1..6])3B
> ... 
> > which is all very well.  But why doesn't
> >
> > sum(z.i*w.i,i=1..6)
> >
> > work?  I mean, sum(i^2,i=1..6) is fine. 
> ... 
> Short explanation: unlike Mma or Maple, in axiom evaluation is
> extremely simple: first the arguments are evaluated, then the
> function.  So, in your case, first axiom tries to evaluate
>
>   z.i*w.i
>
> and
>
>   i=1..6
>
> but there is no operation elt (which the dot is syntactig sugar
> for)  that takes a list and a symbol -- try to type z.i into the
> interpreter!  To make things clearer, note that there *is* an
> operation "=" that takes a symbol and a segment. 

As I mentioned in another thread on macros in Lisp, there
is a possible way to write the 'sum' operation in Axiom that
avoids this "premature evaluation" by using macros in Spad
or the interpreter:

(1) -> macro Sum(x, j,z) == reduce(+,[x for j in z])
                                                      Type: Void

\(2) -> z:=[1,2,3,4,5,6]

   (2)  [1,2,3,4,5,6]
                                  Type: List PositiveInteger

(3) -> w:=[1,0,0,1,1,1]

   (3)  [1,0,0,1,1,1]
                            Type: List NonNegativeInteger

(4) -> Sum(z.i*w.i, i,1..6)

   (4)  16
                                         Type: PositiveInteger

-------

I would really like to write it like this:

(5) -> macro Sum(x,z) == reduce(+,[x for variable(z) in segment(z)])

  Line   1: macro Sum(x,z) == reduce(+,[x for variable(z) in segment(z)])
           ..........................................A
  Error  A: syntax error at top level
  Error  A: Possibly missing a IN
   2 error(s) parsing

So then I could have written:

  Sum(z.i*w.i,i=1..6)

but Axiom's parser seems a little too strict. I think this
also illustrates a point about Lisp macros that would
presumably allow me to write such a thing (syntax not
withstanding). Maybe something like this?

(5) -> macro Sum(x,z) == (local j; j=:variable(z); _
           reduce(+,[x for j in segment(z)]))
                                                             Type: Void

(6) -> Sum(z.i*w.i , i=1..6)

   There are no library operations named :
      Use HyperDoc Browse or issue
                                  )what op:
      to learn if there is any operation containing ": " in its name. 

   Cannot find a definition or applicable library operation named :
      with argument type(s)
                                   Symbol

      Perhaps you should use "@" to indicate the required return type,
      or "$" to specify which version of the function you need. 

-----

But Axiom's interpreter seems to choke on it. :-(

Regards,
Bill Page.