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2010-10-01 18:58:55 +0200 | marked best answer | generating series First, I'll mention that I prefer LazyPowerSeriesRing to PowerSeriesRing. Here is an example of using it. It's an unfortunate fact the interface here is a little bit flaky. For example, using gives an error. Even worse is that I only know to define f=1/(1-t) with the following sequence of commands. However, this does has a facility for dealing with infinite products. For example, the generating functions for partitions is the infinite product \prod_{i \ge 1} 1/(1-t^i). We can do this in sage as follows. First we define a function that will return any given factor. Now we define a generator that represents the infinite product without needing to compute it. Now we can define what we want. As I said, there are definitely problems with the interface here, but the structure is quite powerful. Please ask for more specific help if this answer isn't enough for you to solve your problem. |
2010-09-22 17:00:37 +0200 | answered a question | generating series Thanks for the response! Actually, part of my problem (which I forgot to state above) is how to represent the infinite product. To be honest, I've used Sage for about a year, but have not programmed more than a one-line function. So most of the use has been extremely rudimentary. Is there a way to represent an infinite product? Naively, I expected something like prod(P(t,k) for k >= 1) == sum(a(k)*t^k for k >= 0) and then be able to read off the a(k) somehow. |
2010-09-22 16:32:42 +0200 | asked a question | generating series Hi. I want to create a function which will pick out the coefficients of a generating series. In particular, I have a generating series $\sum_{k=0}^\infty a_kt^k$ defined by an infinite product $\prod_{k=1}^\infty P_k(t)$. How do I just pick out the coefficients a_k? I'm using Sage 4.5.3 on Mac OS X 10.6.4. Thanks for the help!!!!!!!!! |