Derive it for j=1 m=0 m'=1 or 1 0. That's what I did. Just put these numbers in all the equations and it is then easy to check if you get the right expression for beta or not.
O. Sent from mobile phone On Jun 17, 2011 2:05 PM, "Sean Vig" <[email protected]> wrote: > On Fri, Jun 17, 2011 at 15:25, Ondrej Certik <[email protected] >wrote: > >> Yes, that's what I had in mind. All these functions (like spherical >> harmonics, Legendre polynomials, ...) should be both symbolic and the >> actual result. >> I think we might be able to use the eval=False option when >> constructing the class, so that it plays well with the sympy >> machinery. >> In any case, this is easy to fix. >> >> The hard part is to actually calculate the correct result. Sean, did >> you make any progress? >> >> I did. Attached find the working version of the Wigner small d >> function. See the comments in the function -- I have found some wrong >> equations in Varshalovich (or my understanding of them is wrong). But >> I have figured out the right ones, see the comments, and I have >> checked them with the tables in Varshalovich, and it agrees, both for >> general beta, and for beta=pi/2. My function returns the trigonometric >> expressions in the form sin(a*beta/2), while Varshalovich uses powers >> of sin(beta/2). But they are equivalent. >> >> If you run the script, it prints the tables, so you can directly >> compare it to Varshalovich. Sean, can you compare the speed of >> evaluation for general beta, using Brian+your fix, versus my >> implementation? Let's use the one, which is faster. >> >> >> Ondrej >> >> -- >> 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. >> >> > I played around a bit with some other equations to get d, and while they > would work, there were still problems getting them to simplify nicely. I'll > work out the equations to make sure I understand what is going on and can > check the speed of the evaluations. > > Sean > > -- > 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. > -- 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.
