on the code of genus = 3 KP equation

[kh-abd-kh]

Hi,

In
Computing Riemann theta functions in Sage with applications by: Christopher Swierczewski , Bernard Deconinck

we read "Computing genus 3 solutions to KP is an example of an application of Riemann theta functions in Sage, and serves as additional verification that the Riemann theta function algorithm is correctly implemented. The code is too long to be shown here in its entirety. (Approximately 40 lines, not including the code to compute values of the Riemann theta function and its derivatives.) "

i) it shall be nice if they release the code, we don't have explicit g=3 solitonic solution in the public domain not to mentio for the KP ii) I would like a summary of the problems, so we can make this project an active soliton project. iii) in one on his file Computing with Riemann Surfaces and Abelian Functions General Examination by Chris Swierczewski

chris set up very long term points 4 Future Work page 34 • Provide solutions to non-linear, integrable, partial differential equations. • Provide a framework for constructing and computing rational functions on Riemann surfaces with prescribed poles and zeros. • Efficiently compute linear matrix representations of plane algebraic curves.

it shall be nice if chris can expand on these give some reference or be more specific if he has some concrete examples.

also if there is anything in the direction of the 4.2 The Schottky–Klein Prime Form <<<----- i have never seen any code in public for the klein form.

[kh-abd-kh]

OK, To make life easier, here my own evaluation and please correct me,

1- you have taken over Patterson thesis in python and that is good a- Maple alg_curve doesn't have a standard Abel-Map or Riemann Constant Vector. b- Being in maple it is limited by maple, for example multithreading is terrible in maple. c- Being in python/sage, it opens up many new prespective. cpu/gpu mutlithreading and even better algorithms using Singular Maxima-Pari-GAP-... d- There is now nils bruin package in sage faster in calculation the period matix (using single thread Singular). and moreover it has a Rieamm Theta with Siegel Reduction. e- So far the big advantage is an implementation of the Abel-Map and Riemann Constant Vector whatever it is slow, it needs some multithreading or whatever. f- You are very close to the Akhiezer-Baker Theta and its solns to non-linear pdes. >>>>> what remains are the frequencies. 2- It shall be nice if you have done something with solitons to make it available, you know we live what we leave not what we lived. 3- may be now, you have a real job and making some good money. I am happy for you. But shall be sad to see this ~10 years work gone.

So, the problems is to make it faster and to start the real applications.

[kh-abd-kh]

After many testing; your Riemann Theta is the fastest for higher genus g > 5. i used it with many g =7 calculations. I used with parallel in sage and it works fine. and the Theta works fine with sage 10.1. I hope to offload the cpu and gpu together. it calculates g=7 in less than 2 sec. while nbruin takes 2 mins. julia theta fails with g=7.