Since the functions in both your examples do not have poles at t=0, certainly the Larurent series has no negative powers and is a power series. You cannot expect Sage to guess that you mean "about t=1" -- you did not tell it.
If you look at the docs you see that f.laurent_series() does nothing expect convert the type of f to that of a Laurent series. What you want is a functions which does "expand this as a Laurent series about a point t_0". On 24 May 2016 at 17:03, saad khalid <[email protected]> wrote: > Hey everyone: > > So, I have the following function: > (2t^3+1)/((t^2+t+1)^2(t-1)^2) > > I want to take get the Laurent series expansion of it. It can be seen > through Wolfram Alpha here: > http://www.wolframalpha.com/input/?i=laurent+series+expansion+of+%282t^3%2B1%29%2F%28%28t^2%2Bt%2B1%29^2%28t-1%29^2%29 > > From my understanding, it's just the taylor series expansion at t = 1. I try > using the laurent_series function on sage as follows: > > k.<t> = QQ[[]] > f = (2t^3+1)/((t^2+t+1)^2(t-1)^2) > g = f.laurent_series(); g > > > What I get as an output is this: > > 1 + 4*t^3 + 7*t^6 + 10*t^9 + 13*t^12 + 16*t^15 + 19*t^18 + O(t^20) > > This isn't the Laurent Series, this is just the taylor series at t=0. > Similarly, even in the example in the Sage docs, the laurent series of the > power series in the example > simply outputs the power series it started with. > > sage: k.<w> = QQ[[]] > sage: f = 1+17*w+15*w^3+O(w^5) > sage: parent(f) > Power Series Ring in w over Rational Field > sage: g = f.laurent_series(); g > 1 + 17*w + 15*w^3 + O(w^5) > > > Now, I know I can get the output I want by asking for the taylor series > expansion about the point 1, however I was wondering why this function > wasn't working. Or, am I not understanding this correctly. Thank you! > > -- > You received this message because you are subscribed to the Google Groups > "sage-support" group. > To unsubscribe from this group and stop receiving emails from it, send an > email to [email protected]. > To post to this group, send email to [email protected]. > Visit this group at https://groups.google.com/group/sage-support. > For more options, visit https://groups.google.com/d/optout. -- You received this message because you are subscribed to the Google Groups "sage-support" group. To unsubscribe from this group and stop receiving emails from it, send an email to [email protected]. To post to this group, send email to [email protected]. Visit this group at https://groups.google.com/group/sage-support. For more options, visit https://groups.google.com/d/optout.
