Related: https://github.com/jverzani/SymPy.jl and http://nemocas.org/
On Wed, Mar 16, 2016 at 5:01 PM, Chris Rackauckas <[email protected]> wrote: > Taking a quick look at the paper you linked makes big use of symbolic > computing algorithms to compute things like a Groebner basis. To get the > infrastructure for what's proposed you would need a whole symbolic > computing library, which is why they used Mathematica. I think implementing > a fast and extendable symbolic computing library in Julia would be great > because of its type system, but this sounds like a lot more than a GSoC > project. > > If you want to put together quantum mechanics and differential > equations, you could look into specialized solvers which are focused on > those types of equations. PDE solvers for Schrodinger's equation and the > like. Helping out with the complex numbers issues could be really > interesting an insightful (see the julia-dev thread, and look up the > issues) and would be required to go forward here. > > However, quantum algorithms may be interesting in Julia, and maybe you > could simulate their actual running (this would likely be a large project > too...), but the quantum algorithm implementations themselves wouldn't be > very useful. > > But yes, I think a lot of people think that ODE is pretty high on the > priority list. I've seen a few of the developers say things along those > lines. There's a lot of very basic and useful things that need to be done. > For sure there should be some tests to show that the algorithms are all > implemented properly, and there should be more stiff solvers and the like. > > On Tuesday, March 15, 2016 at 11:10:26 AM UTC-7, Joseph Obiajulu wrote: >> >> Hello All, >> >> My name is Joseph Obiajulu and I'm a junior studying mathematics and >> computer science at Princeton University. I was looking through the project >> ideas for potential GSoC projects on the Sage page, and I came across a >> project idea concerning "Native Julia solvers for ordinary differential >> equations." I have experience with differential equations from my math >> training, as well as exposure to different numerical computing methods and >> am starting to get my feet wet with coding in Julia, and so thought that I >> might be able to contribute to the project. I wanted to ask on this mailing >> list, especially to those who will mentor this project, where the best >> place to start would be (I have a few ideas, but I wanted to ask those who >> have put more thought into this question for advice). Also, I was wondering >> if this is a high-priority project, or if there is another project that the >> Julia community would rather have someone work on for the summer. >> >> With that said, I also am thinking of proposing two of my own project >> ideas (of course, I would only end up pursuing one over the summer, but I >> figured it doesn't hurt to propose additional ideas). The first is working >> to expand Julia|Quantum>. I have a particular interest in quantum mechanics >> and especially quantum computing, and I thought a cool project would be to >> work on implementing some of the long term JuliaQuantum project goals (see >> these >> goals here >> <https://github.com/JuliaQuantum/Roadmap/blob/master/LongTerm.md>), as >> well as maybe implementing simple quantum computing algorithms, such as >> Shor's and Groover's. This idea is still very much in its infancy, so I'm >> curious to hear what people think of it. >> >> The second is a native julia implementation of holonomic functions >> <https://en.wikipedia.org/wiki/Holonomic_function>. Holonomic functions >> draw their strength from their closure properties, and often can simplify >> some calculations (or at least that's what I've read, I'm still looking >> into it). The following dissertation >> <http://www.risc.jku.at/publications/download/risc_3886/thesisKoutschan.pdf> >> would be something I would work through as I try to implement standard >> operations of holonomic functions (addition, multiplication, integration, >> derivatives, etc). This is more of a 'Blue Sky' project, but I find it >> particularly interesting, because it is probably the most "mathematically >> heavy" one of the three I've proposed, and I that's something that get's me >> excited, especially that it deals with analysis, which is my mathematical >> focus. >> >> I'm eagerly awaiting to hear from the Julia community! >> >> Thanks for the help, >> Joseph >> >
