First, thank you for the quick replies. I did read the document at http://modular.math.washington.edu/sage/doc/html/ref/module-sage.functions.special.html before posting, but it didn't make it clear to me. I understood that pari was the default, and that is fine with me. I realize now that conventions were confusing me.
OK, I see what is going on. I was wondering if argument order was playing a role and I was instead calculating J(nu,x) nu=0..5 instead of J(nu,x) x=0..5 I did indead do the plots you showed above that show zeroes. Why is the position of x different in your last exampe? What is very confusing and non-intuitive to me at least is why the conventions of the default bessel/pari and the 'maxima' option bessel are reversed and are contradicted by the documentation. Bear with me: We know from tables or independant sources the Bessel J of order n=3.0 has a value of 0 at z=0 and a value of 0.128 and z=2.0 The documentation cited above says: bessel_J( nu, z, [alg=53], [prec=pari]) where alg='maxima' or 'pari' Now look at the following values from sage: bessel_J(2.,3) #default is pari 0.12894324947440206 bessel_J(2.,3,'maxima') 0.48609126058589119 bessel_J(2.,3,'pari') 0.12894324947440206 #this verfies default is pari Note that 0.128.. is the expected value for J(nu=2,z=3.) so the maxima value is 'wrong' see below bessel_J(3,2.,) 0.48609126058589108 #same as maxima answer with reversed args #i.e. this is bessel J (nu=2, z=3) bessel_J(3,2.,'maxima') 0.12894324947440211 #now we have the right answer Therefore the argument order is reversed for 'maxima' option and if fact, the default bessel has an order differenct from the documentation or am I missing something elsewhere? bessel_J(0.,3) 0.00000000000000000 #right bessel_J(0.,3,'maxima') -0.26005195490193339 #'wrong' bessel_J(3,0.,'maxima') 0.00000000000000000 #right So, the argument order given in the linked documentation is consistent with maxima form but not with the default or with 'pari' option. In fact, the examples in that documentation: " sage: bessel_J(2,1.1) # last few digits are random 0.136564153956658000 sage: bessel_J(0,1.1) # last few digits are random 0.719622018527510801 sage: bessel_J(0,1) # last few digits are random 0.765197686557966605 " Do not work unless you reverse the order of the arguments or add the "maxima" option. This is in fact what led me to believe a bug had been introduced. So the question is, is it intended that the default(Pari) bessel functions (I've only looked at J in detail, I don't know if this is a problem with the other bessel functions) have a different argument convention than the ''maxima" option, and if so, the documentation should describe this differences. As it stands now, something is inconsistent. Sorry for the long post, I hope I've at least made my confusion clear. -john --~--~---------~--~----~------------~-------~--~----~ 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 URLs: http://sage.math.washington.edu/sage/ and http://sage.scipy.org/sage/ -~----------~----~----~----~------~----~------~--~---
