On second thought, I think it would be better to use the airy equation to calculate derivatives or order higher than 1. Like
sage: airy_ai(2,x) x*airy_ai(x) sage: airy_ai(3,x) airy_ai(x)+x*airy_ai_prime(x) sage: diff(airy_ai(x),x,2) x*airy_ai(x) sage: diff(airy_ai(x),x,3) airy_ai(x)+x*airy_ai_prime(x) which is very likey to be the way mpmath calculates higher order derivatives. Integrals however, would be returned as: sage: airy_ai(-1,x) airy_ai(-1,x) sage: integral(airy_ai(x),x) airy_ai(-1,x) what do you think? Oscar On 7 feb, 09:15, Burcin Erocal <[email protected]> wrote: > On Tue, 7 Feb 2012 06:56:30 -0800 (PST) > > > > > > > > > > Oscar Lazo <[email protected]> wrote: > > On 7 feb, 04:48, Burcin Erocal <[email protected]> wrote: > > > I don't think we want to have separate functions for the > > > derivatives in Sage. These might help you get around the printing > > > problem for now, but they are not useful in general. > > I disagree here, Mathematica has got the AiryAiPrime function. And > > mpmath supports calculating derivatives and integrals of arbitrary > > order! I think it would be best if we could do something like: > > > sage: airy_ai(x) > > airy_ai(x) > > sage: airy_ai(x,1) > > airy_ai_prime(x) > > sage: airy_ai(x,-2) > > airy_ai(x,-2) > > > that is, make a single object that returns arbitrary derivatives or > > integrals. > > You're right, I didn't know mpmath supported this. We can have a main > function that takes a single argument and another one with two > arguments to represent the derivatives. This is similar to how maple > implements the airy function: > > http://www.maplesoft.com/support/help/Maple/view.aspx?path=Airy > > The implementation would be similar to that of the psi function: > > http://hg.sagemath.org/sage-main/file/tip/sage/functions/other.py#l810 > > Note that there are two symbolic functions Function_psi1 and > Function_psi2, with a regular python function names psi() that > wraps these. > > You can also put the new functions in a new file sage/functions/airy.py. > > Cheers, > Burcin -- 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/sage-support URL: http://www.sagemath.org
