It would be great to have Puiseux series in Sage. Hierarchically it seems it might make sense as a seperate module in rings/polynomial, just as laurent_series_ring.py. It seems a little categorically confusing (but perhaps convenient?) to add these as a method to polynomials.
Are you reusing any of the Laurent series code for this? My impression (which might be out of date) is that Laurent series need to be cleaned up and improved a bit before building anything on top of them. -Marshall On Apr 30, 1:37 pm, Chris Swierczewski <cswie...@gmail.com> wrote: > Hello, > > I recently implemented Puiseux series expansions in Sage and I would like to > make this available in Sage to everyone. However, I was hoping for some > suggestions as to where to place this code before I go any further. > > First of all, Puiseux series > (wiki<http://en.wikipedia.org/wiki/Puiseux_series>) > are power series that allow for fractional exponents. They're useful in the > theory of algebraic curves. On a smooth point on a (complex) algebraic curve > f(x,y)=0 we can represent y=y(x) locally by a power series. We cannot > represent y(x) as a power series at a branch point / singular point of the > curve but we can do so with a, or several, Puiseux series. > > These local representations have applications in computing integral bases > and the basis of the cohomology of the Riemann surface corresponding to the > algebraic curve. These, amongst other applications, are things that I'm > working on implementing into Sage for my research. > > I'm interested in Puiseux expansions only for algebraic curve so one > possible location for this code is as a method under s > age.rings.polynomial.multi_polynomial_libsingular.MPolynomialRing_libsingular. > When > constructing a multi- > variate polynomial over QQ[x,y] using PolynomialRing or when taking a > symbolic expression in two variables and using the > Expression.polynomial() method this is the type received in return. > > Another possibility is just writing puiseux as a module-level function. > Suggestions as to where to place this is welcome. > > -- > Chris Swierczewski > University of Washington > Department of Applied Mathematicshttp://www.cswiercz.info -- 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
