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, 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. -Niles -- To post to this group, send an email to sage-devel@googlegroups.com To unsubscribe from this group, send an email to sage-devel+unsubscr...@googlegroups.com For more options, visit this group at http://groups.google.com/group/sage-devel URL: http://www.sagemath.org
