Le lundi 29 février 2016 17:22:33 UTC+1, Jason Merrill a écrit :
>
> The first page of google results didn't give me a good clue about what a
> Recurrence Vector is, and I also couldn't infer this from quickly skimming
> the package README.
>
> Taking a guess, it's something like the coefficients a_i of a1*x_{n} +
> a2*x_{n-1} + a3*x_{n-2} + ... = 0
>
> Is this accurate?
>
Yes, this is exactly that; I iwll add it in the README file.
> It might be nice to show some examples of operating on these coefficients
> once you have obtained them (e.g. finding the generating function of the
> sum or product of two generating functions, or something like that). And
> maybe hooking them up to the Clenshaw Algorithm (
> https://en.wikipedia.org/wiki/Clenshaw_algorithm)?
>
> I'm kind of just guessing here, though; how do you envision that this
> package will be used?
>
Such function is used in "concrete mathematics" for studying integer (or
rational) sequences of "empirically" found numbers. This is how I have been
using it myself with various software; I coded the very same function in
Lisp for Maxima and in Python for Sympy (see the submodule
https://github.com/sympy/sympy/blob/master/sympy/concrete/guess.py written
by myself). It directly leads to the generating function of a sequence
(coefficients are coefficients of the denominator of the generating
function and finding the numerator is the matter of a last and basic
convolution between the initial sequence and the vector returned by my
function). Anyway, I think that the main usage is in the field of
arithmetic. Regards, tb.
