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

[Martin Rubey]

Dear Alasdair,

(redirecting to axiom-math, where usage questions belong)

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

yes. Or, if you prefer

reduce(+, [ez*ew for ez in z for ew in w])

or, if you are really thinking of the standard inner product

dot(z, w)

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.

For a (very long) explanation see

http://wiki.axiom-developer.org/IndexedVariables

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.

Hope that helps,

Martin

[Bill Page]

Post by Martin Rubey
(redirecting to axiom-math, where usage questions belong)

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.

[Gabriel Dos Reis]

"Bill Page" <***@synthesis.anikast.ca> writes:

[...]

| 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

Do you need a macro there or do you want the syntax to have less
restrictions there?

-- Gaby