On Mon, Aug 25, 2008 at 5:56 AM, Jason Merrill <[EMAIL PROTECTED]> wrote:
>
> On Aug 25, 7:46 am, "Ondrej Certik" <[EMAIL PROTECTED]> wrote:
>> On Mon, Aug 25, 2008 at 12:55 AM, Jason Merrill <[EMAIL PROTECTED]> wrote:
>>
>> > In hopes that it may be a useful reference during the current work on
>> > symbolics, I wrote a toy Mathematica program for transforming a single
>> > higher order ODE into a system of first order ODEs. Most of the free
>> > numerical differential equation solvers I've seen want input in the
>> > form y'[x] == f(y,x), so the purpose of a program like this is to take
>> > more general input and turn it into something suitable for those
>> > routines.
>
> <snip>
>
>> Thanks for doing this. It is indeed very useful, I always wondered how
>> things like this are done in Mathematica.
>>
>> Any ideas how this could be nicely translated to Python?
>>
>> Ondrej
>
> I thought you were going to tell me that sympy already does this. I
> believe I saw an example somewhere in the docs about matching
> derivatives, but I couldn't immediately find it again.
>
The new pynac code referred to elsewhere does this. See the example below:
sage: from sage.symbolic.function import function
sage: var('r,kappa', ns=1)
(r, kappa)
sage: psi = function('psi', 1)(r); psi
psi(r)
sage: g = 1/r^2*(2*r*psi.diff(r,1) + r^2*psi.diff(r,2)); g
(2*psi(1,r)*r + psi(2,r)*r^2)*r^(-2)
sage: g.expand()
psi(2,r) + 2*psi(1,r)*r^(-1)
sage: g.coeff(psi.diff(r,2))
1
sage: g.coeff(psi.diff(r,1))
2*r^(-1)
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