#9263: Some special functions don't work with arbitrary precision
-----------------------------+------------------------------
Reporter: zimmerma | Owner: jason, jkantor
Type: defect | Status: new
Priority: major | Milestone: sage-5.12
Component: numerical | Resolution:
Keywords: | Merged in:
Authors: | Reviewers:
Report Upstream: N/A | Work issues:
Branch: | Commit:
Dependencies: | Stopgaps:
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Description changed by zimmerma:
Old description:
> {{{
> ----------------------------------------------------------------------
> | Sage Version 4.4.2, Release Date: 2010-05-19 |
> | Type notebook() for the GUI, and license() for information. |
> ----------------------------------------------------------------------
> sage: n(airy_ai(1),digits=100)
> 0.1352924163128813861423083153567858971655368804931640625000000000000000000000000000000000000000000000
> }}}
>
> Clearly the last digits are wrong. This is due to Maxima; currently we
> are not giving it bigfloats, and in any case some of the functions don't
> work with arbitrary precision.
>
> The following functions should be changed to a different default backend
> (mpmath probably):
> * `airy_ai` and `airy_bi` (will be fixed with #12455)
> * `spherical_bessel_j` (it also has a SciPy option, but it also truncates
> the precision)
> * `spherical_bessel_y` (same as `spherical_bessel_j`)
> * `spherical_harmonic`
> * the elliptic integrals
> * `spherical_hankel1` and `spherical_hankel2`
> * `hypergeometric_U` (PARI is implemented and works with arbitrary
> precision, but it's not the default)
> * `bessel_K` and `bessel_Y` (will be fixed with #4102)
> * `inverse_jacobi`
New description:
{{{
----------------------------------------------------------------------
| Sage Version 4.4.2, Release Date: 2010-05-19 |
| Type notebook() for the GUI, and license() for information. |
----------------------------------------------------------------------
sage: n(airy_ai(1),digits=100)
0.1352924163128813861423083153567858971655368804931640625000000000000000000000000000000000000000000000
}}}
Clearly the last digits are wrong. This is due to Maxima; currently we are
not giving it bigfloats, and in any case some of the functions don't work
with arbitrary precision.
The following functions should be changed to a different default backend
(mpmath probably):
* `airy_ai` and `airy_bi` (will be fixed with #12455)
* `spherical_bessel_J` (it also has a SciPy option, but it also truncates
the precision)
* `spherical_bessel_Y` (same as `spherical_bessel_j`)
* `spherical_harmonic`
* the elliptic integrals
* `spherical_hankel1` and `spherical_hankel2`
* `hypergeometric_U` (PARI is implemented and works with arbitrary
precision, but it's not the default)
* `bessel_K` and `bessel_Y` (will be fixed with #4102)
* `inverse_jacobi`
--
--
Ticket URL: <http://trac.sagemath.org/ticket/9263#comment:13>
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