On Wed, Jun 30, 2010 at 9:37 AM, Niles Johnson <[email protected]> wrote: > Hello all, > > I have a proposal for implementing basic multivariate power series in > sage. Looking through the sage-devel history, I can see that this has > come up before, and that a number of people have thought hard about > this. What I have in mind is something of a stop-gap, but there are > two reasons I think it's valuable; I'd like to see if some others of > you agree: > > 1. I already have working code, and some other code that uses this to > do universal formal group law calculations (relevant for algebraic > topologists) > > 2. William Stein has noted that multivariate power series usually > don't get off the ground because people find out that they can do what > they want with multivariate polynomials. This happened to me, and the > way I handled it has, I believe, the potential to be useful for > everyone else in this position. > > > Here's the proposal: for power series in x,y,z over a base ring R, > use a dummy variable t and the ring > > R[x,y,z] [[t]] > > as a substitute for > > R[[x,y,z]] > > That is, I work with total-degree power series precision, and replace > > \sum a_ijk x^i y^j z^k + O(x,y,z)^n > > with > > \sum a_ijk (x*t)^i (y*t)^j (z*t)^k+ O(t)^n. > > Then most of the operations for multivariable power series can be > reduced to operations for multivariate polynomials or univariate power > series. > > The only thing left to do is build functions which translate nicely > between these different representations, so that multivariate power > series can be constructed and printed without the user having to think > about the dummy variable t. > > > This is probably not a new idea, but I haven't seen it mentioned here > before. I have seen suggestions of using Maxima, Axiom, or something > else to implement multivariate power series . . . I can't deny that > seems like a better way,
I can. > but it has the disadvantage of not being done > already and that I don't know those languages already. Let me know if > the idea above seems worth finishing. It does to me. It would be way better than nothing, which is what we have now. William > -- > To post to this group, send an email to [email protected] > To unsubscribe from this group, send an email to > [email protected] > For more options, visit this group at > http://groups.google.com/group/sage-devel > URL: http://www.sagemath.org > -- William Stein Professor of Mathematics University of Washington http://wstein.org -- To post to this group, send an email to [email protected] To unsubscribe from this group, send an email to [email protected] For more options, visit this group at http://groups.google.com/group/sage-devel URL: http://www.sagemath.org
