#4102: make bessel_J symbolic
----------------------------------+-----------------------------------------
Reporter: jwmerrill | Owner: burcin
Type: enhancement | Status: needs_review
Priority: major | Milestone: sage-5.9
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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Comment (by benjaminfjones):
There is something strange going on. Here is sage-5.9.beta2 with the three
patches applied:
{{{
[bjones@cabbage:devel/sage]% ../../sage
----------------------------------------------------------------------
| Sage Version 5.9.beta2, Release Date: 2013-03-28 |
| Type "notebook()" for the browser-based notebook interface. |
| Type "help()" for help. |
----------------------------------------------------------------------
**********************************************************************
* *
* Warning: this is a prerelease version, and it may be unstable. *
* *
**********************************************************************
sage: y = function('y', x)
sage: diffeq = x^2*diff(y,x,x) + x*diff(y,x) + x^2*y == 0
sage: f = desolve(diffeq, y, [1, 1, 1]); f
(bessel_Y(0, 1) + bessel_Y(1, 1))*bessel_J(0, x)/(bessel_J(0,
1)*bessel_Y(1, 1) - bessel_J(1, 1)*bessel_Y(0, 1)) - (bessel_J(0, 1) +
bessel_J(1, 1))*bessel_Y(0, x)/(bessel_J(0, 1)*bessel_Y(1, 1) -
bessel_J(1, 1)*bessel_Y(0, 1))
}}}
which is exactly what the doctest expects.
Now doctesting `sage/functions/bessel.py` with sage in the exact same
state:
{{{
[bjones@cabbage:devel/sage]% ../../sage -t sage/functions/bessel.py
Running doctests with ID 2013-04-01-21-31-17-4bc246be.
Doctesting 1 file.
sage -t sage/functions/bessel.py
**********************************************************************
File "sage/functions/bessel.py", line 977, in sage.functions.bessel.Bessel
Failed example:
f = desolve(diffeq, y, [1, 1, 1]); f
Expected:
(bessel_J(0, 1) + bessel_J(1, 1))*bessel_Y(0, x)/(bessel_Y(0,
1)*bessel_J(1, 1) - bessel_Y(1, 1)*bessel_J(0, 1)) - (bessel_Y(0, 1) +
bessel_Y(1, 1))*bessel_J(0, x)/(bessel_Y(0, 1)*bessel_J(1, 1) -
bessel_Y(1, 1)*bessel_J(0, 1))
Got:
(bessel_Y(0, 1) + bessel_Y(1, 1))*bessel_j(0, x)/(bessel_j(0,
1)*bessel_Y(1, 1) - bessel_j(1, 1)*bessel_Y(0, 1)) - (bessel_j(0, 1) +
bessel_j(1, 1))*bessel_Y(0, x)/(bessel_j(0, 1)*bessel_Y(1, 1) -
bessel_j(1, 1)*bessel_Y(0, 1))
}}}
The lower cased `bessel_j` is what Maxima returns if you don't register a
conversion to `bessel_J`, the Sage symbolic version of J that these
patches introduce.
What is also strange is that the above output does actually represent a
different form of the correct solution (modulo replacing bessel_j by
bessel_J).
So what is going on here?
FWIW, sage-5.8 with same three patches applied does not exhibit this
behavior.
--
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/4102#comment:41>
Sage <http://www.sagemath.org>
Sage: Creating a Viable Open Source Alternative to Magma, Maple, Mathematica,
and MATLAB
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