Hi everyone, I'd just like to say thanks for creating Sage, it's a wonderful bit of software that has been very useful to me.
I am an undergrad maths student, and over the past 8 weeks I have been working on a summer project developing code related to Sage. Along with my supervisor, we have been looking at Kontsevich's theorem giving an explicit formula for defining an associative star product on a Poisson algebra ( arXiv:q-alg/9709040 <https://arxiv.org/abs/q-alg/9709040>). The formula for the product is a power series in an indeterminate h; each term involves calculating a sum over a set of graphs, with each term in the sum being formed of a weight and a differential operator. Both of these are derived from what are referred to as "admissible graphs". The weight can be calculated by performing an integral of an integrand defined based on the form of the graph. However, these integrals are in general not easy to compute, taking from a few seconds to a few hours depending on the order of the graph. Further, at a given order, there are (n*(n+1))**n graphs to be considered. We have created a poisson module, with some classes to aid in the calculation of these terms. These include: - A PoissonBracket class to represent a Poisson bracket - A KontsevichGraph class which represents an admissible graph and can calculate its weight and differential operator - A KontsevichGraphList class which generates a list of graphs of a given order - A StarProduct class which, given a PoissonBracket and an indeterminate h, can calculate the star product of two expressions I would like for these classes to be made available publicly so that others can use them and investigate their results. I've been following the general conventions and "Coding in Python for Sage" documents on how to comment the code etc. I have a few design questions about what the best way of implementing some of these features in Sage would be: - The class KontsevichGraph is a subclass of DiGraph; however, it would only ever be used in calculating the Star product of a Poisson bracket. Should it live in the new poisson module or in the graphs module? - The list of graphs generated by KontsevichGraphList has no particularly natural ordering defined on it. It also uses a list of regular graphs (which currently is loaded from an external file). Should both of these generators be added to the digraph_generators module? There is also a little bit more work to be done before the code is fully ready to be integrated into Sage. Once this is done I will look at making the code available. Best, Peter Banks -- You received this message because you are subscribed to the Google Groups "sage-devel" group. To unsubscribe from this group and stop receiving emails from it, send an email to sage-devel+unsubscr...@googlegroups.com. To post to this group, send email to sage-devel@googlegroups.com. Visit this group at https://groups.google.com/group/sage-devel. For more options, visit https://groups.google.com/d/optout.
