Don't worry about not being accepted for this reason. If we decide we want the project, we'll find someone to mentor it. It's true that we are limited by how many proposals we accept mostly by how many mentors we have, but the main thing that should concern you is making the proposal high quality. And anyway, this proposal in particular I think almost anyone could mentor should it come down to it. That is really only an issue for proposals that involve very heavy math (like some project in the polys), or some physics (like the quantum or mechanics module), where we need to make sure the mentor understands everything.
Aaron Meurer On Fri, Mar 8, 2013 at 12:35 AM, Manoj Kumar <[email protected]> wrote: > Thanks for your reply. So do I start formally working on my proposal > (Solving first order ODE's using Lie Groups), that is creating a wiki page > for it. And if I do, who is most likely to be my mentor? . Because I've seen > quite a few good proposals not accepted last time, because of a need of a > mentor. > > > On Fri, Mar 8, 2013 at 1:01 PM, Aaron Meurer <[email protected]> wrote: >> >> On Thu, Mar 7, 2013 at 2:58 AM, Manoj Kumar >> <[email protected]> wrote: >> > Hello again. >> > >> > Sorry to bring this post up again, but I thought it would be good to >> > keep >> > all my ideas on a single thread. >> > >> > I've been reading about lie groups and their application in solving >> > differential equations and I believe I've got my concepts right about >> > solving a linear first order differential equation. Maple, (according to >> > the >> > papers cited in the SoC ideas pages), has two separate papers dedicated >> > to >> > solving differential equations of the first and second order using lie >> > groups. I would like to like to code a clone for solving first order >> > differential equations using lie groups in sympy for my SoC proposal. >> > >> > Theory: >> > There are many differential equations that cannot be solved using the >> > present dsolve in ode.py. Suppose there is a differential equation of >> > the >> > form >> > (dr / ds) = f(r), since the slope is independent of s, moving in the s >> > direction would merge one solution into another. The principal aim of >> > using >> > lie groups is to reduce any given differential equation to the above >> > mentioned form. >> > >> > The coordinates r and s are called canonical coordinates because any lie >> > group transformation which leaves the differential equation invariant >> > would >> > transform it into the form (r, s + alpha) where r remains invariant.If >> > we >> > are able to find such coordinates, then the equation becomes separable. >> > >> > The problem is finding these canonical co-ordinates. This can be broken >> > into >> > four steps(This is for first order differential equations) >> > >> > 1. Find η and ξ , the infinitesimals using this partial diffential >> > equation, >> > which >> > are basically the differentials of the transformed co-ordinates with >> > respect >> > to >> > the transformation parameter. >> > >> > ηx - ξy h2 + (ηy - ξx )h - (ξhx + ηhy ) = 0 >> > >> > This should be the toughest part of the project. As you can see solving >> > a >> > linear first order ODE, leads to solving a much more complicated PDE. >> > However in this PDE, some assumptions could be made for the >> > infinitesimals. >> > >> > Maple has 6 separate algorithms just for finding the infinitesimals as >> > described in the paper. Once this is done. >> > >> > 2. rx ξ + ry η = 0, >> > sx ξ + sy η = 1, >> > >> > Solving these two equations would give, r and s , this can be done by. >> > dx / >> > ξ = dy / η = r(x,y) and dx / ξ = ds >> > >> > 3. After this substituting r and s in >> > ds / dr = sx + h(x,y)sy / rx + h(x, y)ry and simplifying in terms of r >> > and s >> > would give a separable form. >> > >> > 4. And after solving the differential equation in terms of r and s, >> > substituting back r and s in terms of x and y. >> > >> > I haven't focussed on the implementation part yet, but I think it should >> > be >> > structured similar to dsolve, or should it be implemented in dsolve. >> > >> > I've focussed on only first order differential equations here, even >> > Maple >> > also has support only upto the second order.I feel this project would be >> > challenging for me and also a addition to the ODE solver of sympy. >> > >> > @Aaron, Stefan, and Smichr Please do give your feedback. >> >> I haven't formally studied Lie groups and their applications to >> solving ODEs, but from my understanding, they are indeed a powerful >> method for doing so. This would definitely be a welcome project for >> GSoC. >> >> Aaron Meurer >> >> > >> > >> > -- >> > 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 [email protected]. >> > To post to this group, send email to [email protected]. >> > Visit this group at http://groups.google.com/group/sympy?hl=en. >> > For more options, visit https://groups.google.com/groups/opt_out. >> > >> > >> >> -- >> You received this message because you are subscribed to a topic in the >> Google Groups "sympy" group. >> To unsubscribe from this topic, visit >> https://groups.google.com/d/topic/sympy/C4btttnGJss/unsubscribe?hl=en. >> To unsubscribe from this group and all its topics, send an email to >> [email protected]. >> >> To post to this group, send email to [email protected]. >> Visit this group at http://groups.google.com/group/sympy?hl=en. >> For more options, visit https://groups.google.com/groups/opt_out. >> >> > > > > -- > Regards, > Manoj Kumar, > Mech Undergrad. > BPGC > Blog > > -- > 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 [email protected]. > To post to this group, send email to [email protected]. > Visit this group at http://groups.google.com/group/sympy?hl=en. > 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. 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