|Dirk Laurie on Sat, 15 Jul 2017 13:55:39 +0200|
[Date Prev] [Date Next] [Thread Prev] [Thread Next] [Date Index] [Thread Index]
|Re: Laurent polynomials instead of fractions|
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?