incorrect translation of Bessel from Maxima?

[kcrisman]

From this sage-support thread:

But other sums are simply wrong.

k = var('k')
sum(x^(2*k)/factorial(2*k),k,0,oo)

gives

-1/4*sqrt(2)*sqrt(pi)*x^(3/2)

but the answer should be sinh(x). 

Hmm.  That shouldn't be happening, though I wouldn't be surprised if it didn't turn out as easy as that.

(%i1) load(simplify_sum);
(%o1) /Users/.../Sage-5.12-OSX-64bit-10.6.app/Contents/Reso\
urces/sage/local/share/maxima/5.29.1/share/solve_rec/simplify_sum.mac
(%i3) display2d:false;

(%o3) false
(%i4) simplify_sum(sum(x^(2*k)/factorial(2*k),k,0,inf));

(%o4) sqrt(%pi)*bessel_i(-1/2,x)*sqrt(x)/sqrt(2)

So I'm not sure why that would happen - maybe because of incorrect Bessel simplification?

sage: maxima_calculus('bessel_i(-1/2,x)')
bessel_i(-1/2,x)
sage: _._sage_()
sqrt(2)*sqrt(1/(pi*x))*cosh(x)

That gives cosh(x), which I think is what you meant.

I don't know why this would happen, but presumably it should be possible to track down without too much effort.

Component: calculus

Author: Nils Bruin

Branch/Commit: dd3786f

Reviewer: Peter Bruin

Issue created by migration from https://trac.sagemath.org/ticket/16224

[kcrisman]

Description changed:

--- 
+++ 
@@ -1,4 +1,4 @@
-From [https://groups.google.com/forum/#!topic/sage-support/IgC78rcdO7c this sage-suppot thread}:
+From [this sage-support thread](https://groups.google.com/forum/#!topic/sage-support/IgC78rcdO7c):
 
 ```
 But other sums are simply wrong.

[nbruin]

comment:2

It's a problem in the automatic translation learning for max_to_sr. If we force it to learn about Bessel functions beforehand, there's no problem:

sage: var('k')
k
sage: sum(bessel_I(2,x),k,1,10)
10*bessel_I(2, x)
sage: sum(x^(2*k)/factorial(2*k),k,0,oo)
sqrt(pi)*sqrt(x)*sqrt(1/(pi*x))*cosh(x)
sage: from sage.interfaces.maxima_lib import *
sage: sage_op_dict[operator.mul] #as it should be
<ECL: MTIMES>

On the other hand, in a fresh session:

sage: var('k')
k
sage: sum(x^(2*k)/factorial(2*k),k,0,oo)
-1/4*sqrt(2)*sqrt(pi)*x^(3/2)
sage: from sage.interfaces.maxima_lib import *
sage: sage_op_dict[operator.mul]
<ECL: %BESSEL_I>

The problem is that the bessel_I(-1/2,x) gets immediately rewritten to another expression, so the default heuristics for max_to_sr fail. The remedy: initialize the translation of %BESSEL_I. This consists simply of adding the line

    sage.functions.bessel.bessel_I: "%BESSEL_I",

to sage_op_dict in sage/interfaces/maxima_lib.py

[nbruin]

Branch: u/nbruin/ticket/16224

[nbruin]

Commit: 303a30b

[nbruin]

comment:4

OK, this should do the trick. I've also made the routines produce an error rather than corrupt the dictionaries. That should make diagnosing such problems a little easier in the future.

If someone wants to add a doctest for this somewhere, go ahead.

---

New commits:

303a30b

trac 16224: make sure maxima_lib knows about bessel functions.

[nbruin]

Author: Nils Bruin

[nbruin]

comment:5

On second thought we can probably do better than having to register all this in two spots:sage:

sage: bessel_I._maxima_()
bessel_i
sage: tbl=sage.symbolic.pynac.symbol_table['maxima']
sage: tbl['bessel_i']
bessel_I

so the information is there already. We should just let sr_to_max and max_to_sr look in those spots before reverting to just converting strings back and forth and trying to guess the appropriate symbols from that. That would provide an extra level and would mean that functions like bessel_I that are spelled differently in maxima and/or get rewritten can be converted without entering their translations in another spot.

[sagetrac-git]

Changed commit from 303a30b to b7f21d5

[sagetrac-git]

Branch pushed to git repo; I updated commit sha1. New commits:

b7f21d5

trac 16224: make max_to_sr look in sage.symbolic.pynac.symbol_table['maxima']

[nbruin]

comment:7

Replying to @sagetrac-git:

Branch pushed to git repo; I updated commit sha1. New commits:

b7f21d5	trac 16224: make max_to_sr look in sage.symbolic.pynac.symbol_table['maxima']
This should do a much more programmatic and hence more reliable job than forcing people to register the same information in yet another spot.