Ralf Hemmecke <[email protected]> writes: > On 07/07/2010 12:25 PM, Martin Rubey wrote: >> I'm off for a lecture, and I accept the criticism. A quick and >> incomplete answer is the article: >> >> http://arxiv.org/abs/math/0702086 > > Oho. So why don't you at least put a pointer to this paper into the > documentation? > > However, > > Page 5: > > guessADE [1,1,2,9/2,32/3,625/24,324/5,117649/720,131072/315, > 4782969/4480] > > returns > > [[x^n]f(x) : -xf'(x) + f(x)^3 - f(x)^2 = 0, f(0) = 1, f'(0) = 1]. > > ??? > > Nowhere is actually explained what that notation means. :-(
OK, thanks for the hint, and for discovering this inconsistency in the article. > Is this a common notation? Can you please give a definition for that > notation? Hm, I thought so, but possibly it's only notation common in combinatorics. [[x^n]f(x) : -xf'(x) + f(x)^3 - f(x)^2 = 0, f(0) = 1, f'(0) = 1]. means: the expression equal to the coefficient of x^n in f(x), where f(x) is given by the differential equation -xf'(x) + f(x)^3 - f(x)^2 = 0 and initial values f(0)=1 and f'(0)=1. I have to admit that sometimes the equation doesn't actually determine the sequence, even with initial values given. (see Section 3.1, description of guessRec) > Let me guess... The sequence that is written after guessADE is obtained by > > [coefficient(f(x), n) for f in F | > -xf'(x) + f(x)^3 - f(x)^2 = 0 and f(0) = 1 and f'(0) = 1] well, this rather looks like we would be iterating over all f in F... > where F is the space of all (differentiable) functions? Oh, no, F is > K[[x]], right? Yes, for guessADE, guessHolo, guessAlg, guessPade, guessFE we consider the given sequence as the first few terms of a formal power series. > PS: You probably don't want me as a reviewer of that paper. ;-) Not so: such comments can actually be very helpful! Only, I would hope that a reviewer does not base his decision on such shortcomings, but rather requests that they are repaired. Martin -- You received this message because you are subscribed to the Google Groups "FriCAS - computer algebra system" group. 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/fricas-devel?hl=en.
