#9263: Maxima-evaluated functions don't work with arbitrary precision
-----------------------------+----------------------------------------------
Reporter: zimmerma | Owner: jason, jkantor
Type: defect | Status: new
Priority: major | Milestone: sage-5.11
Component: numerical | Resolution:
Keywords: | Work issues:
Report Upstream: N/A | Reviewers:
Authors: | Merged in:
Dependencies: | Stopgaps:
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Changes (by eviatarbach):
* owner: AlexGhitza => jason, jkantor
* component: basic arithmetic => numerical
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. It looks like Sage only knows how
> to compute Ai(x) in double precision, and then extended the double
> precision result to 100 digits.
>
> This is a *defect*: an error should be raised if the target precision
> cannot be attained (or Sage should be able to compute
> Ai(x) to arbitrary precision).
>
> I guess this problem concerns other functions than Ai.
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`
* `airy_bi`
* `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`
*
--
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Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/9263#comment:6>
Sage <http://www.sagemath.org>
Sage: Creating a Viable Open Source Alternative to Magma, Maple, Mathematica,
and MATLAB
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