#4102: make bessel_J symbolic
----------------------------------+-----------------------------------------
Reporter: jwmerrill | Owner: burcin
Type: enhancement | Status: needs_review
Priority: major | Milestone: sage-5.10
Component: calculus | Resolution:
Keywords: | Work issues:
Report Upstream: N/A | Reviewers: Karl-Dieter Crisman
Authors: Benjamin Jones | Merged in:
Dependencies: | Stopgaps:
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Old description:
> The motivation for this is
>
> {{{
> sage: plot(bessel_J(1, x), (x, 1, 10))
> Traceback (most recent call last):
> ...
> TypeError: Unable to convert x
> (='1-1/8*x^2+1/192*x^4-1/9216*x^6+1/737280*x^8-1/88473600*x^10+1/14863564800*x^12-1/3329438515200*x^14+1/958878292377600*x^16+O(x^17)')
> to real number.
> }}}
>
> The problem is that special functions, or at least {{{bessel_J}}}, can't
> currently be partially evaluated--that is, called with a
> {{{SymbolicExpression}}} as an argument. The model of good behavior is
> {{{polylog}}}, for which the above method produces a perfectly nice plot
>
> {{{
> sage: plot(polylog(1,x),(x,.1,.9)) #makes a fine plot
> }}}
>
> See discussion at http://groups.google.com/group/sage-
> support/browse_thread/thread/1b985b080ba2369e/7dee9eed953857f5#7dee9eed953857f5
New description:
The motivation for this is
{{{
sage: plot(bessel_J(1, x), (x, 1, 10))
Traceback (most recent call last):
...
TypeError: Unable to convert x
(='1-1/8*x^2+1/192*x^4-1/9216*x^6+1/737280*x^8-1/88473600*x^10+1/14863564800*x^12-1/3329438515200*x^14+1/958878292377600*x^16+O(x^17)')
to real number.
}}}
The problem is that special functions, or at least {{{bessel_J}}}, can't
currently be partially evaluated--that is, called with a
{{{SymbolicExpression}}} as an argument. The model of good behavior is
{{{polylog}}}, for which the above method produces a perfectly nice plot
{{{
sage: plot(polylog(1,x),(x,.1,.9)) #makes a fine plot
}}}
See discussion at http://groups.google.com/group/sage-
support/browse_thread/thread/1b985b080ba2369e/7dee9eed953857f5#7dee9eed953857f5
----
Release manager:
Apply: attachment:trac_symbolic_bessel_v6.patch,
attachment:trac_symbolic_bessel_doctests.patch,
attachment:trac_symbolic_bessel_deprecation.patch
--
Comment (by benjaminfjones):
I still have not been able to track down the doctesting issue (described
starting at comment:41). I've tried bisecting the doctest state (delta
debugging) to no avail. The problem seems to be intimately linked to the
doctesting environment. I'm unable to reproduce the doctest failure when
running __all__ the prior doctests which come before in `bessel.py`, in
the right order, by hand, and then running the offending one.
The only thing I can tell for sure is that at some point as the doctests
are run, one of the pynac symbol tables get's modified. This causes the
`bessel_j` vs `bessel_J` problem.
My inclination is to remove the offending doctest and file a new ticket to
resolve the problem. Meanwhile, the bessel function code can be reviewed
and become useful. I've posted a patch `trac_symbolic_bessel_v6` which
removes the offending doctest block.
Comments?
----
Patchbot, apply trac_symbolic_bessel_v6.patch
trac_symbolic_bessel_doctests.patch trac_symbolic_bessel_deprecation.patch
--
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/4102#comment:48>
Sage <http://www.sagemath.org>
Sage: Creating a Viable Open Source Alternative to Magma, Maple, Mathematica,
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