|Bill Allombert on Thu, 12 Dec 2002 14:00:21 +0100|
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|Re: How to eliminate the big-oh|
On Thu, Dec 12, 2002 at 12:26:44PM +0100, Franck MICHEL wrote: > Thank you, it works. Certainly a naive question, but: how can we know the > level of priority of variables? Is it possible to change it? The rule is: x has always the highest priority, then priorities are assigned to variable as soon as they are introduced. The customary way to avoid problem is to enter x;t;z as the start of a gp session, so that we have x >> t >> z > >fortunately there is a simpler solution, convert your polynomial to a > vector: > > > >Pol(truncate(Vec(taylor((1-x)/(1-t),t)))) > > It's a nicest solution, unfortunately it does not work for other expressions. > For example, if we slightly modify (1-x)/(1-t) and consider > > truncate(taylor((1-x)/(x-t),t)), we get -1+O(t^16) > > Pol(truncate(Vec(taylor((1-x)/(x-t),t)))) gives the same bad answer Of course, because it is a rational function not a polynomial. The answer is correct, since truncate() apply to the highest priority variable, that is x, and (1-x)/x=x^-1 - 1 + O(x^15) > but subst(truncate(subst(taylor((1-x)/(x-t),t),x,z)),z,x) gives the good > expansion. > If we ask for the type of taylor(1/(1-t),t), we get "SER"; for > taylor((1-x)/(1-t),t) we get "POL"; and for taylor((1-x)/(x-t),t) we get > "RFRAC". When we have x and t, the type is determined with respect to x. It > is determined with respect to t after changing z in x as you have > suggested. If we have to deal with a quotient with multiple variables (x, > y, z, etc.., and t), I presume all the variables above the level of > priority of t would have to be substituted by variables below the level of > priority of t. But it is not very convenient, the determination of levels > of priority of variables is a little bit mysterious for me and I am > wondering if there would be a better solution than using substitutions with > low-level variables. I agree, this system is confusing, but we don't have any idea to make it better. I suppose we should extend truncate to take the variable we want to truncate as an extra parameters. Cheers, Bill.