Hi. On Mar 21, 2011, at 1:10 PM, Yuri Karadzhov wrote: > Hello: > > I am PhD student of the Kiev Institute of Mathematics, National > Academy of Science, Ukraine. I have an honors master's degree in > mathematical physics and computer sciences. > > Currently in applied math department I study the theory of Lie groups > and it's application to the differential equations. The most recent > works however concerned with supersymmetry of Schrödinger-Pauli > equation of arbitrary dimension. The obtained results widely extend > the number of exactly solvable Quantum Mechanic problems as well as > generalize the approach of finding such problems. > > I am interested in participating in Sympy 2011 GsoC project. I have > required mathematical skills as well as good knowledge of different > CAS (Mathematica, Maple, Sage) and experience to write extensions for > them. The proposed ideas were interesting for me and I would be glad > to help with most of them, especially with ones concerned with > integration, series, ordinary and partial differential equation, Lie > groups, supersymmetry and quantum mechanics. > > I would also like to propose my own ideas which I found helpful in my > study. > 1. Implement functions to be able to collect similar members of > expression containing functions and to gather coefficients of linearly > independent members. > > e.g. expression > x*(a+b*y+sin(y))+y*(c+3*x+x^2)+x*sin(y+3)+x*cos(y)+f(x,y,t) > > should be translated to > a*x+(b+c)*y+3*x*y+x^2*y+(1+cos(3))*x*sin(y)+(1+sin(3))*x*cos(y) > +f(x,y,t) > > and functions and coefficients should be gathered > [a, b+c, 3, 1, 1+cos(3), 1+sin(3), 1] > [x, y, x*y, x^2*y, x*sin(y), x*cos(y), f(x,y,t)] > > where x, y are variables and a, b, c, t - unknown constants > That is, to do the same things that collect and coeffs functions do > with polynomials.
This would be useful, but would be very easy to implement. > 2. Implement case wise methods for expressions depending on > parameters. > e.g. Solve ODE containing constant parameters > diff(f(r),r)=a*f(r)+b*r+c > > has two significantly different solutions > f(r)=C1*exp(a*r)-b*r/a-(b+a*c)/a^2 if a != 0 > f(r)=b*r^2/2+c*r+C1 if a = 0 > > where r - independent variable, f - dependent variable, a, b, c - > arbitrary constants > This problems become extremely painful, when we have bunch of more > complex equations and expressions. Unfortunately there are no > solutions in commercial CAS, such as Maple, Mathematica and MatLab as > well as in open source such as Maxima and Sage. Actually Symbolic > Tools Box (former MuPad) in MatLab tried to solve the second problem, > but the solution does not work well. Mentioned problems are connected > with each other and with improvement of pattern matching problem in > Sympy. I have complete solution for Maple and porting it to > Mathematica. I think it won't be a problem to implement this algorithm > in Sympy. This would be useful, I think, though it's a difficult problem to solve in general. But something like this would allow us to solve Sturm-Liouville problems and hence improve the PDE solver too, I think. > > Also I want to concentrate attention on some small problems, solution > of which can improve usability of Sympy > e.g. It is possible to simplify usage of dsolve function in case when > dependent and independent variables are obvious. > The equation > eq=diff(y,x)+a*y+b*x+c > has y as dependent variable and x as independent, so it is better to > write > dsolve(eq) > The solution is complete (as patch for Sage, but it can be easily > adopt to Sympy). This would also be easy to implement. > > I think that it can be interesting to implement this algorithms in > Sympy in terms of the GSoC project. > > If you are interested in my proposal please contact me and I will send > you precise plan and if not, I will be glad to participate in one of > the proposed projects. > > Best regards, > Yuri Karadzhov The first and third item would be useful to have, but they are not really big enough projects for a summer of code. The second one could be, though. I would need to see a more detailed plan on what you plan to implement to see if it is big enough. Aaron Meurer -- You received this message because you are subscribed to the Google Groups "sympy" group. To post to this group, send email to [email protected]. To unsubscribe from this group, send email to [email protected]. For more options, visit this group at http://groups.google.com/group/sympy?hl=en.
