Re: Mysterious type t_RFRAC and denominator function

[Bill Allombert <Bill.Allombert@math.u-bordeaux.fr>]

On Mon, Jul 09, 2018 at 08:58:25PM +0000, Jacques Gélinas wrote:
> What is "t_RFRAC" or a denominator exactly ?

A t_RFRAC is a rational function.

> # type(a/b)
> %1 = "t_POL"
> # type(b/a)
> %2 = "t_RFRAC"
> # denominator(a/b)
> %3 = 1
> # denominator(b/a)
> %4 = a
> 
> Can one conclude that the symbol "a' is treated differently than the symbol "b" ?

No. Variables have priorities, which depends in which order they are
created by GP.
In your example a is introduced before b so has higher priority.
so you are computing in Q(b)(a) and not Q(a)(b).
So a/b is a polynomial in a while b/a is a rational function in a.
It follows that the denominators are 1 and a respectively.

This is documented in 
??"Variable priorities, multivariate objects"@2

Cheers,
Bill