# [Maxima] Bug # 535363 and using polynomialp

Rupert Swarbrick rupert.swarbrick at lineone.net
Fri Sep 21 17:41:01 CDT 2007

On Fri, 21 Sep 2007 09:27:25 -0700
"Richard Fateman" <fateman at cs.berkeley.edu> wrote:

> I'm missing something here..

Or maybe I didn't explain myself very clearly! :P

> A polynomial at any finite point is finite.
> A polynomial at infinity looks like its leading term.
> Why would you use lHopital's rule?

Yes. What I meant was say you have

lim x->a  f(x) / p(x)

where p is a polynomial. This is what R. Toy was suggesting in his post
in the bug report, I think - the example in said report was

lim x->0 e^(1/x) / x^6

So the point is "how zero" the polynomial is!

> As for testing whether something is a polynomial, consider converting
> it to rational form and see
> (1) if the denominator is a constant
> (2) there is only one variable in the list of variables in the header.
>    This would be a 3 line program.  It might take more time but it
> would notice that (x^2-1)/(x+1) was a polynomial.

This makes sense from a mathematical point of view, but I don't
understand how one writes maxima / lisp code to find the list of
variables. Maybe this is trivial - I haven't yet understood the
structure you use to represent expressions and have been using
(displa ) lots!
>
> I don't know what program is in the linear algebra package.
>
> If you want to fix all the bugs in the limit package, I think that
> looking at Gruntz's PhD thesis would give you a guide as to how to
> replace it by something more likelyto work.

I agree that this is definitely what we should do in the long term but
I have lowlier short term goals (!)

But more seriously, working on implementing some of that would be very
interesting.

Rupert
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