Hello, On Thu, 24 Feb 2011 15:52:07 +0300 "Alexey U. Gudchenko" <[email protected]> wrote:
> But generally "Laurent series" can contain infinitely number of terms > with negative powers. So it must be reflected in [1], and > distinguished. If there are no objections. I think so, too. > In this case (opposite to "formal Laurent series") there are not > general rules how to multiplicate series with each other. Yes. To my (limited) understanding, in this case one cannot speak of a field or ring structure, as both require a multiplication. > By the way in [1]: > "K[[X]] and has a ring structure." > "K((X)) and has a field structure." > > I do not understand the difference about ring structure or field > structure. (Is it misprint?) IIRC, a ring is basically a field minus the division and subtraction operation. However, algebraic structures are certainly "none of my business". I want to add one more keyword to the discussion: Google just taught me about Puiseux series (http://en.wikipedia.org/wiki/Puiseux_series), which seem to be series with rational exponents on the base functions. > Also, as number of terms with positive powers in "Laurent series" can > be infinitely too with the same time as negative ones, it's > interesting in this case what to do with O() when consider some > asymptotic expansion from this series or does sense of it exists, and > what sort of if it does. I do not know exactly the answer now. Me neither. If this is unclear it is possibly the best options not to provide the order of the remainder terms. Alex -- You received this message because you are subscribed to the Google Groups "sympy" 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/sympy?hl=en.
