On Friday 26 January 2007 16:14, David Harvey wrote: > On Jan 26, 2007, at 3:39 PM, Joel B. Mohler wrote: > > The integer object method "valuation" computes the p-Adic > > valuation, but the > > polynomial object method "valuation" computes a different sort of > > valuation. > > It seems to me that they could be more analogous, but maybe there's > > something > > I'm not seeing. > > It looks like the valuation function is basically returning the > number of times f(x) is divisible by the linear polynomial x. So it's > like a p-adic valuation, but only testing divisibility at a certain > point. I guess it would make more sense for it to return the times > number f is divisible by a linear factor (x - y), for arbitrary y. > But that discriminates a bit against non-linear irreducible > factors... so perhaps you want f.valuation(p), where p is an > irreducible polynomial? What if it's not a UFD? If the base ring is a > field, then I have no problems with that at all.
I wanted it for any irreducible polynomial, p. Yes, I didn't think about UFD issues. The context I was dealing with certainly had unique factorization. I guess you could execute the same computation with-out unique factorization, but it seems it would likely be a strange thing to do. > > I also don't really think that valuation is the best term to use > > for the > > integer method. I think it would be better named "ord", but I > > don't know if > > that term is quite common enough. > > I prefer valuation, but having ord as a synonym couldn't hurt. Maybe I should have been more clear. I would tend to use the word valuation for this: http://planetmath.org/encyclopedia/PAdicValuation.html The "ord" is the integer required to compute that valuation, but it's being a bit picky perhaps. -- Joel --~--~---------~--~----~------------~-------~--~----~ To post to this group, send email to [email protected] To unsubscribe from this group, send email to [EMAIL PROTECTED] For more options, visit this group at http://groups.google.com/group/sage-devel URLs: http://sage.scipy.org/sage/ and http://modular.math.washington.edu/sage/ -~----------~----~----~----~------~----~------~--~---
