The idea presented in this paper is rather simple. I wish I had known about it when I wrote separatevars. It would take about a day to implement, at most (plus review time). It's not suggested that a project focus on just this method, but rather that it can be part of a larger project on ODEs. By the way, you can find the paper online if you Google for the title.
I think it generalizes to n variables. The condition would be that f(x1', ..., xn')**(n - 1)*f(x1, ..., xn) = f(x1, ..., xn')*...*f(x1', ..., xn) (I use prime for the "constant", the a0 and b0 in the paper. Here and throughout, ... means all the intermediate variables are primed, except for f(x1, ..., xn), which means all variables are not primed). For the proof, let phi_i(xi) = f(x1', ..., xi, ..., xn')/f(x1', ..., xn') for i = 1, ..., n - 1 and let phi_n(xn) = f(x1', ..., xn). Then phi_1(x1)*...*phi_n(xn) = f(x1, ..., xn')*...*f(x1', ..., xn)/f(x1', ..., xn')**(n - 1) = f(x1', ..., xn')**(n - 1)*f(x1, ..., xn)/f(x1, ..., xn')**(n - 1) = f(x1, ..., xn). The other direction is still obvious, because the "power" of each variable (primed or not) of f on both sides is the same, so if you split both sides into phi_i's, they will both be the same. The implementation would be the same too, as far as I can tell. There might be some cleverness needed to choose the correct variable to not divide by f(x1', ..., xn')**(n - 1) (even in the two variable case), though I think the only difference will be how nice the result looks modulo what constants are put on what terms. By the way, the implementation of this would go in separatevars(), which is in simplify.py. Aaron Meurer On Mon, Apr 22, 2013 at 9:49 AM, Paanini Navilekar <paanini.navile...@gmail.com> wrote: > Hi, > > I would like to work on the ODE module, particularly on the topic of > separation of a differential equation using the method outlined in the > paper, "A simple method to find out when an ordinary differential equation > is separable" by José ́Ángel Cid. > > The GSoC 2013 ideas page doesn't go into much detail about what the project > entails, so I'd like some more details about the problem. What exactly would > the project entail? Would it require an implementation of the theorum > described in the paper, to determine whether or not a particular ODE is > separable? Furthermore, can this theorum be extended to ODEs containing more > than 2 variables? > > Any help on this matter would be greatly appreciated. > > Thanking You, > Paanini Navilekar > > -- > 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 post to this group, send email to sympy@googlegroups.com. > Visit this group at http://groups.google.com/group/sympy?hl=en-US. > 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 post to this group, send email to sympy@googlegroups.com. Visit this group at http://groups.google.com/group/sympy?hl=en-US. For more options, visit https://groups.google.com/groups/opt_out.
