[[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.
Oh, I knew the [x^n]f(x) notation, but ...
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...
... you iterate over all n. n lives where exactly? Unspecified. Right?
Well, and my mistake with f in F should actually show you that the
notation is not clear.
Do you always assume that you have full information of f, i.e. f is a
given (analytic) function? (Well, analytic is too much, because you
actually deal with formal power series.)
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.
But your sequence is fully given, i.e. you could compute the coefficient
up to any order n.
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.
I'm particularly picky with shortcomings. Actually, my dream would be if
papers were checked by a computer. Undefined objects would immediately
lead to rejecting the paper, because the computer-prover would be unable
to figure out the meaning of the rest of the paper.
Well, put it in another way, before a human reader sees the paper, it
would have to pass the automated correctness checker as a requirement.
Ralf
--
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.
