On Apr 13, 7:48 pm, ObsessiveMathsFreak <[email protected]> wrote: > On Apr 12, 8:52 pm, ObsessiveMathsFreak > > <[email protected]> wrote: > > On Apr 12, 3:51 am, kcrisman <[email protected]> wrote: > > > > > > Or simply legendre_P, legendre_Q > > > > > Unfortunately, these functions do not support non integer values of n, > > > > i.e. they don't support generalised legendre functions, which is what > > > > I need. > > > > Are gen_legendre_P and gen_legendre_Q okay? These are all used from > > > Maxima, as I recall. > > > > - kcrisman > > > They worked and were a _lot_ faster. Thanks! > > > sage: time plot([lambda x: P(n,0,x), lambda x: Q(n,0,x)], > > (x,-1,1),ymin=-2,ymax=2) > > sage: time plot([gen_legendre_P(n,0,x), gen_legendre_Q(n,0,x)], > > (x,-1,1),ymin=-2,ymax=2) > > Time: CPU 3.79 s, Wall: 3.80 s > > Time: CPU 0.32 s, Wall: 0.41 s > > Actually, it appears I was mistaken. gen_legendre_P does not appear to > work for non integral n at least > > gen_legendre_P(2.1,0,1) > TypeError: Attempt to coerce non-integral RealNumber to Integer > > I think I must have been running the test with integer values for n. > In fact the code for gen_legendre_P explicitly states that it is only > valid for integer values of n.
As currently implemented, the mpmath Legendre functions are likely to be slow for integer parameters and fast (relatively speaking) for noninteger parameters. So you may consider using the Maxima functions (or something else) for integer parameters and the mpmath functions for noninteger parameters. > mpmath still works, but it seems to be a bit awkward to translate the > result from class mpc to a normal sage value. > > float(mpmath.legenp(2.1,0,-2)) > TypeError: float() argument must be a string or a number > > You have to be pretty roundabout with things > > V=mpmath.legenp(2.1,0,-2) > z=float(V.real)+I*float(V.imag) > z > 5.83105230126 + 1.8957900574*I Of course float() won't work when the result is complex. Just use complex(). Alternatively, if you want Sage numbers, check out the functions call, sage_to_mpmath, mpmath_to_sage in sage.libs.mpmath.all. Fredrik -- 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
