Re: [fricas-devel] Re: [Axiom-mail] A simple question

[Bill Page]

On 01 Feb 2008 22:59:26 +0100, Martin Rubey wrote:
>
>  Alasdair McAndrew writes:
>
> > Sorry about this; I'm a bit out of practice:
> >
> > for n in 10..30 repeat output [n, factor(2^n-1)]
>
> > This gives the first n in factored form which I don't want.
> >  How can I obtain the first n in unfactored form?
>
> ...
>  (8) -> for n in 10..13 repeat output([n, factor(2^n-1)]$List ANY)
>    [10,3 11 31]
>    [11,23 89]
>         2
>    [12,3 5 7 13]
>    [13,8191]
>                                                                    Type: Void
>
>  Just to make sure: what happens is that the interpreter sees
>  the list constructor [], and tries to find a Type as simple as
>  possible. List FR INT is simpler than List ANY.
>

Wow, the result of Alasdair's innocent command:

  for n in 10..30 repeat output [n, factor(2^n-1)]

is certainly obtuse! Even though I understand the cause as Martin
explains it, this still makes me smile :-)  - perhaps more with
embarrassment than anything else! I might have suggested another
solution:

   for n in 10..30 repeat output((n::String)." =", factor(2^n-1))

but really this is not much better and not so obvious. There should be
a better and more obvious way to do arbitrary output in Axiom - maybe
more like Aldor's << operator.

I think this is a little prettier:

(1) -> _<_< (x,y) == hconcat(x,y)$OutputForm
                                                              Type: Void

(2) -> for n in 10..30 repeat output(n << " = "::Symbol << factor(2^n-1))

   Compiling function << with type (PositiveInteger,Symbol) ->
      OutputForm

   Compiling function << with type (OutputForm,Factored Integer) ->
      OutputForm

   10 = 3 11 31
   11 = 23 89
         2
   12 = 3 5 7 13
...
   29 = 233 1103 2089
         2
   30 = 3 7 11 31 151 331
                                                                   Type: Void
(3) ->

Here, once the concept of << is understood, the only obscure notation
is probably

  " = "::Symbol

which is just a way to avoid printing the quotation marks " around the string.

Regards,
Bill Page.