# What is a polynomial in x?

Roberto Bagnara bagnara at cs.unipr.it
Thu Mar 7 13:51:07 CET 2002

```Christian Bauer wrote:
> Hi!
>
> On Thu, Mar 07, 2002 at 12:58:59PM +0100, Roberto Bagnara wrote:
>
>>     if (is_a_polynomial(e, x)) {
>>
>
>   if (e.info(info_flags::polynomial)) {
>
> (there's also info_flags::integer_polynomial and a couple of others; the
> complete list is in the GiNaC tutorial)

Hmmm...
the notion of polynomial in x that is implemented by degree,
ldegree, and so forth, is more general (and rightly so, we believe).
For instance,

sqrt(2)*x

is a polynomial in x of degree 1 accordind to degree(), whereas the info()
methods would simply classify is as a non-polynomial.
I see two possibilities (but I may be wrong, of course):

1) it is illegal to say degree(sqrt(2)*x) and the fact that now this evaluates
to the sensible value 1 is just an accident: it may stop working at any time.
In other words, degree() and friends would be granted to work only for
expressions e such that e.info(info_flags::polynomial) is true.

2) It is legal to say degree(sqrt(2)*x).  But then it would be useful to
precisely characterize the class of expressions e and x such that
degree(e, x) is well defined.

Am I missing something?
Thanks a lot

Roberto

--
Prof. Roberto Bagnara
Computer Science Group
Department of Mathematics, University of Parma, Italy
http://www.cs.unipr.it/~bagnara/
mailto:bagnara at cs.unipr.it

```