determine if expression is polynomial P(x,y/Q(x,y)

Can you give some examples of cases that you run into in your work where
rat or ratsimp is not sufficient?  Perhaps people on this list will have
some ideas, or perhaps it will help  us think of new functionality for
Maxima.

                -s

On Sat, Feb 25, 2012 at 13:53, nijso beishuizen <nijso at hotmail.com> wrote:

>  Thank you for your input. I realize now that it is more difficult than I
> thought, because some input that could be rewritten to P/Q will not be
> recognized in my simple algorithms. Anyway, when the expression is already
> of the form P/Q, then polynomialp will do the trick.
> I will have to think about the cases where the expression can be rewritten
> to P/Q and see if there are other properties that I can use to detect (some
> of) these as well.
>
>
>
> ------------------------------
> Date: Sat, 25 Feb 2012 12:34:43 -0500
> Subject: Re: [Maxima] determine if expression is polynomial P(x,y/Q(x,y)
> From: macrakis at alum.mit.edu
> To: nijso at hotmail.com
> CC: maxima at math.utexas.edu
>
>
> It is very easy to determine whether an expression is *of the form* P(x,y)/Q(x,y),
> where P and Q are polynomials in a given list of variables:
>
> ratfunp(ex,vars) := polynomialp(num(ex),vars) and
> polynomialp(denom(ex),vars)$
>
> If you need them, polynomialp has additional arguments that let you
> specify symbolic parameters etc. so that you can consider (a*x+1)/(b*y-1) a
> polynomial in variables x and y, with parameters a and b.
>
> Other people's solutions test whether an expression *can be written* in
> the form P(x,y)/Q(x,y) -- a problem which is in the general case
> unsolvable, but in many practical cases perfectly tractable.  But beware of
> things like trigonometric identities (as RJF says), radicals, etc.
>
>               -s
>
> On Sat, Feb 25, 2012 at 09:02, nijso beishuizen <nijso at hotmail.com> wrote:
>
>  Dear all,
>
> The problem I am dealing with now is related to my previous question about
> determining if an expression is polynomial. I now want to determine if an
> expression is of the form P(x,y)/Q(x,y), where P and Q are bivariate
> polynomials in x and y. Like my previous problem, it should also accept
> expressions that contain e.g. sin(x) but then return something meaningful
> when it is not a polynomial.
>
> I think this can be done by putting the expression in CRE form and
> determine the numerator and denominator using Q:ratdenom(expr) and
> P:ratnumer(expr).
> If I call showratvars(Q), will Q then always be a polynomial in x and y if
> it returns [x,y]?
>
>
> Regards,
> Nyso
>
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