[seqfan] Re: Integer Sequence Analysis in Mathematica 7

[Mitch Harris]

On Wed, Nov 19, 2008 at 4:51 PM, Hans Havermann <pxp at rogers.com> wrote:
> This might be of interest to sequence fans:
>
> "Mathematica 7 introduces a new level of systematic integer sequence
> analysis
...
>for the first time

just to be accurate, -in- Mathematica, with built in Mathematica
functions... <cough>combstruct in Maple</cough>

> make it possible to take lists of sequence elements and
> systematically find large classes of closed-form Mathematica formulas

systematically -guess-, right? (for a finite list)

Anyway, it -is- excellent that it has a new guessing function, it will
-considerably- help the experimental process (generate some numbers,
hypothesize a function, check OEIS to see if it's already there and
check the rest of the
sequence).

Sorry to turn back to the negative comments but (maybe Eric can pass
this along to the mma designers), look at that first example for the
determinant of a Hilbert matrix. How would one normally write that?
With products of factorials. But the mma solution uses these special
functions, Glaisher, BarnesG. First time I've -ever- seen these. And
lots of other manipulations that by hand would result in factorials
and binomials, through mma result in opaque Gammas with sqrt(pi)-like
coefficients. I understand that mma might be designed in the direction
of people having more facility with analysis than me, but, hey, if a
summation/product is not closed-form, then replacing it with a special
function name is not really either, and the summation/product will say
more about the combinatorics anyway.

(yes I'm sure there are better forums for a rant, but there it is.
suggestions for other places to discuss?)

-- 
Mitch Harris