Re: Laurent polynomials instead of fractions

[Dirk Laurie <dirk.laurie@gmail.com>]

2017-07-15 9:12 GMT+02:00 Karim Belabas <Karim.Belabas@math.u-bordeaux.fr>:

> ? [v = valuation(f,xi), Vec(f) / xi^v]
> %4 = [-2, [xi^3 - 2*xi^2 + xi, -2*xi^4 + 8*xi^3 - 12*xi^2 + 8*xi - 2]]
>
> (I'm displaying both the valuation and the renormalized coeffs here). With
> this technique, there is no real need to convert to a vector, you can stick
> to the power series
>
> ? f / xi^v
> %5 = (xi^3 - 2*xi^2 + xi) + (-2*xi^4 + 8*xi^3 - 12*xi^2 + 8*xi - 2)*q + O(q^2)

I didn't know 'valuation', was it been in Pari-GP in about 2005 when I
learnt it?
The help is no more informative than the name:

?valuation
valuation(x,p): valuation of x with respect to p.

I gather that it means the number of times a factor divides the numerator
(positive) or denominator (negative) of a rational. Is that good enough for
practical purposes?