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Re: Re: How to declare Integers?

Sean Ross wrote:
> Carlos Wexler wrote:
> >
> > How can one declare a variable to be integer in Mathematica?
> > Let me just give an example:
> >
> >         Integrate[Sin[m x]/Sin[x], {x,0,Pi}]
> >
> > Other examples include evaluation of Sin[m Pi], etc...
>       In short, you can't.  There is no variable typing in mathematica.  The
> only way are work around patern matchings and transformation rules that
> are specific to each problem.  For example, you can define n/;Sin[n
> x]==0 and similar ideas.  This doesn't mean that the problems are
> insoluble, it just means that you will have to specify via
> transformation rules the behavior of an integer expression.
>       There are several of us that have been trying to explain to Wolfram
> people what object oriented variable typing means, but they just play
> dense and claim that the whole area is so vague that they can't do it.
> Certainly the variable typing that you (and I) are after is radically
> different from the variable typing done by Fortran or C++, which is for
> purposes of memory allocation and interpretation.

I am sorry that you have been disappointed by the response to your
suggestions about variable typing.

There is a substantial research and development effort at Wolfram
Research in this area, and has been for several years.  Some of the
results of that effort are present in Version 3.0, and significant
additional functionality will be included in the next few releases. 
Many of the latest developments were discussed at the recent
Mathematica conference.  If you are concerned that the developers of
Mathematica do not appreciate the value of this functionality, I can
assure you that this is not the case.

If your concern is instead that you don't feel that your suggestions in
this area have received adequate consideration, then we sincerly
apologize if we have done anything to give you that impression.  We are
always interested in new ideas, and if you think that you have useful
insights that have eluded the people at Wolfram Research, I would
encourage you to send a clear description of your ideas to Wolfram

Since I haven't seen your suggestions, I can't comment directly on the
merit of your ideas.  This problem does admit a variety of partial
solutions (some of which are implemented in other systems) that suffer
from various practical or fundamental deficiencies -- deficiencies that
often show up only after careful analysis -- but your ideas may be an
exception.  If you think you have a truly innovative approach, you
might also consider publishing your discoveries for the next ISSAC or

Dave Withoff
Wolfram Research

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