Good day, I am Ishan Pandhare, a student of Mathematics and Computing from the Indian Institute of Technology, Varanasi. I saw this project being mentioned on the project idea list, and would like to know about its current status. Being a curious student of both mathematics and Computer science, I would like to take up this project for Gsoc, if available. Following are my areas of study Differential equations - studied for 2 semesters Algebra - including group theory, vector spaces and modules, studied for 3 semesters Graph Theory - theory and implementation, for one semester Probability, statistics, and Mathematical modeling - studied for 2 semester Discrete mathematics - for 1 semester Numerical techniques (involving topics such as the regula-falsi method, Newton-Rhapson method etc.) - for 1 semster Mathematical methods (involving various transformation techniques including Laplace, Fourier, Hankel etc.) - for 2 semester Also, I would be learning complex analysis, number theory and fluid dynamics before summer. I am also good at python, C, C++, Java and R. I have also studied various Algorithms for 2 semesters.
On Thursday, January 23, 2014 at 1:31:25 AM UTC+5:30 asme...@gmail.com wrote: > On Wed, Jan 22, 2014 at 8:30 AM, Anurag Sharma <anur...@gmail.com> wrote: > > Hello everyone. > > > > This post is regarding the gsoc idea of implementing (or continuing ) the > > work of Aaron Meurer and Chetna Gupta on implementation of Risch > Algorithm > > for symbolic integrations. I have gone through the PR mentioned on the > ideas > > page. It seems there has been good progress last summer. > > I have fairly decent background in abstract algebra and universal > algebra. > > Though I haven't formally done anything related to Differential Algebra. > > > > I wished to know the following things: > > > > 1. There are 3 remaining tasks mentioned in the PR. Would it be okay to > > start on one of them ? (Most probably the one which asks to not hard code > > the value of 'a' ) > > Yes, finishing this PR is probably the best place to start. I would > create a new branch based off the PR branch and submit a new PR (we > can close the old one when you do this). > > > > > 2. Has there been any progress other than that mentioned in that PR? > > No. > > > > > 3. I have skimmed through the first chapter of Bronstein's book. > Algebraic > > Preliminaries. Nothing new there. But the second chapter introduces > > algorithms which I have never implemented and some of them I had not even > > heard of. I would be really glad if you could tell me what sort of > > mathematical background is required to contribute efficiently to this > part > > of the project. > > Well really Bronstein's book is self-contained. The unfortunate thing > for you is that half of it is already implemented, so the > prerequisites are really more like "the first half of Bronstein's > book". I think you have a good opportunity to catch up, especially > since you are still early. You should read through chapter 2. This > gives a more algorithmic introduction to abstract algebra than you may > have seen before. Chapter 3 gives a good understanding of the rational > algorithm, but it is not necessary to understand all the algorithms > there, except the Lazard-Rioboo-Trager, which is the one actually > used. This is important because the full algorithm is just an > extension of this algorithm, so understanding the basics of how it > works is important. Chapter 4 is entirely theoretical. You should get > an understanding of differential algebra, but a deep understanding of > chapter 4 is not fully required. Most of it is just there to prove the > theorems, particularly the Liouville theorem. A lot of it is there > only to prove the algebraic case, which is not even described in the > book. It really depends on how you learn, though. If you feel you > learn better by really understanding all the mathematics, then you > should read chapter 4 more carefully. > > Chapter 5 is the most important. This you should read and understand > (with the possible exception of the proof of Liouville's theorem, > assuming I remember correctly that it's in this chapter). This is the > "base" algorithm. Most of it is already implemented, in risch.py. > > Chapters 6, 7, and 8 are nitty-gritty details of the sub-algorithms. > You really don't need to worry so much about the parts that are > already implemented. It depends on what you plan to do in your project > too, but in many cases you can worry about things when you get to them > too. > > Chapter 9 is more heavy on the math than what you really need to know > to implement it. > > I recommend starting with chapter 2. Try to find the implementation in > SymPy of the algorithms as you go through them, and play with them > using your own inputs. This will help you learn SymPy and the polys > module as well (the polys module can be a bit confusing so let us know > if you can't figure stuff out with it). > > You should also try to follow the Risch code, say for some simple > inputs, alongside the pseudocode in Bronstein. Don't worry too much > about the code in DifferentialExtension to start with. > > > > > I would be really glad if you could link me to some literature on net > which > > explains the Risch algorithm and implementation issues. In the meanwhile > > I'll try to procure the mentioned text from my college library. > > Read Bronstein's "symbolic integration tutorial" (you can find it for > free on his website). This gives a broad outline of the full > algorithm. Note that his book only covers about a third of the full > algorithm (namely, just the pure transcendental part), so don't worry > too much if you can't follow the algebraic part parts. > > Beyond that, Bronstein's book really is the best source, so I would > stick to it for the most part. The book is extremely well written, so > you shouldn't have too many issues with it. > > > > > Apart from Aaron Meurer and Chetna Gupta who else has worked on this > part ? > > It would be really nice if I knew more people familiar to this part of > sympy > > so that I wont have to bug Aaron with every little issue :).. I have > tried > > contacting Chetna but I guess she is not much active now. > > Sorry, it's just us. Raoul might be able to tell you a few things too. > I would most likely be the one to mentor the project if it were > accepted, though. You should just keep your communications on this > list, and I will respond. Or if you want to chat you can use IRC or > gitter (https://gitter.im/sympy/sympy). > > Aaron Meurer > > > > > Cheers > > Anurag > > > > > > -- > > You received this message because you are subscribed to the Google Groups > > "sympy" group. > > To unsubscribe from this group and stop receiving emails from it, send an > > email to sympy+un...@googlegroups.com. > > To post to this group, send email to sy...@googlegroups.com. > > Visit this group at http://groups.google.com/group/sympy. > > For more options, visit https://groups.google.com/groups/opt_out. > -- You received this message because you are subscribed to the Google Groups "sympy" group. To unsubscribe from this group and stop receiving emails from it, send an email to sympy+unsubscr...@googlegroups.com. To view this discussion on the web visit https://groups.google.com/d/msgid/sympy/597094c5-8955-4ffe-8431-0a468a8c5a9cn%40googlegroups.com.
