dilog is lame

[williamstein]

dilog on almost all input gives NotImplementedError:

sage: dilog(-1)
---------------------------------------------------------------------------
<type 'exceptions.NotImplementedError'>   Traceback (most recent call last)

/home/was/Desktop/<ipython console> in <module>()

/home/was/s/local/lib/python2.5/site-packages/sage/functions/special.py in dilog(t)
    743         return t.dilog()
    744     except AttributeError:
--> 745         raise NotImplementedError
    746
    747 def lngamma(t):

<type 'exceptions.NotImplementedError'>:
sage:                                     

Should add dilog to RDF, RR, CDF, CC elements, when it makes sense.

This does work:

sage: dilog(pari(2))
2.4674011002723396547086227499690377838 - 2.1775860903036021305006888982376139473*I

See also this from pari-dev (which I don't agree with):

Component: basic arithmetic

Author: Mike Hansen

Reviewer: Paul Zimmermann

Merged: sage-4.6.alpha1

Issue created by migration from https://trac.sagemath.org/ticket/783

[williamstein]

comment:1

Vincent Lefevre <[email protected]> 	
to pari-dev
	
show details
	 1:08 am (5 hours ago) 
Hi,

With Pari 2.3.2:

? dilog(-1)
%1 = -0.8224670334241132182362075834 + 9.136285398175292265776793780 E-29*I

but the value should be a real number. I suppose that the imaginary
term is due to a rounding error, in which case it should be zeroed
if one knows that the mathematical result is a real number.

Note that due to this problem, the plot function fails with:
 *** plot: impossible assignment t_COMPLEX --> t_REAL.

[aghitza]

comment:2

Attachment: 783-dilog_lame.patch.gz

But polylog is implemented to a more serious extent, in calculus.py. I think we should just have dilog(z) be an alias for polylog(2, z).

I've put up a patch making this change.

[mwhansen]

comment:3

Looks good to me.

[sagetrac-mabshoff]

comment:4

The hunk

diff -r 631bb7b11fe9 -r 2829ba5e615e sage/functions/all.py
--- a/sage/functions/all.py     Tue Apr 15 04:19:13 2008 -0700
+++ b/sage/functions/all.py     Sat Apr 19 10:33:01 2008 -0400
@@ -16,7 +16,7 @@ from special    import (bessel_I, bessel
                         spherical_bessel_J, spherical_bessel_Y,
                         spherical_hankel1, spherical_hankel2,
                         spherical_harmonic, jacobi,
-                        inverse_jacobi, dilog,
+                        inverse_jacobi,
                         lngamma, exp_int, error_fcn)

 from orthogonal_polys import (chebyshev_T,

conflicts with one of the other patches in 3.0.1.alpha0, so I am merging that one manually.

Cheers,

Michael

[sagetrac-mabshoff]

comment:5

Merged in Sage 3.0.1.alpha0

[zimmermann6]

comment:6

I'd like to reopen this ticket, since the fix only corrected integer input (here with Sage 4.3.1):

sage: dilog(-1.1)
ERROR: An unexpected error occurred while tokenizing input
The following traceback may be corrupted or invalid
The error message is: ('EOF in multi-line statement', (2251, 0))

---------------------------------------------------------------------------
NotImplementedError                       Traceback (most recent call last

Pari knows how to compute this:

sage: gp.dilog(-1.1)
-0.89083809026228267332015894927022713036

[mwhansen]

Author: Mike Hansen

[zimmermann6]

comment:9

There is something strange in the examples added:

sage: from sage.symbolic.pynac import py_li2_for_doctests as py_li2 
sage: py_li2(-1.1)
---------------------------------------------------------------------------
TypeError                                 Traceback (most recent call last)

/users/caramel/zimmerma/Adm/Stages/10/Prest/<ipython console> in <module>()

/usr/local/sage-core2/local/lib/python2.6/site-packages/sage/symbolic/pynac.so in sage.symbolic.pynac.py_li2_for_doctests (sage/symbolic/pynac.cpp:15450)()

TypeError: py_li2_for_doctests() takes exactly 2 positional arguments (1 given)

Shouldn't py_li2 take two arguments?

Also I've noticed the following, which maybe should be in a different ticket:

sage: dilog(+Infinity)
dilog(+Infinity)
sage: dilog(-Infinity)
dilog(-Infinity)
sage: limit(dilog(x),x=+Infinity)
Infinity
sage: limit(dilog(x),x=-Infinity)
-Infinity

Maybe dilog(+Infinity) and dilog(-Infinity) should return the corresponding limits?

[mwhansen]

comment:10

The patch had some typos so I uploaded a correct version. The +Infinity/-Infinity thing should probably be a new ticket as it's something that should be done in a manner consistent for all functions.

[zimmermann6]

comment:11

good work, Mike!

[zimmermann6]

Reviewer: Paul Zimmermann

[burcin]

comment:12

The function syntactically_equal() in attachment: trac_783.patch doesn't contain doctests. I don't see how the changes to sage/symbolic/expression.pyx in that patch are relevant to this ticket. Perhaps these should be on a different ticket.

[zimmermann6]

comment:13

Replying to @burcin:

The function syntactically_equal() in attachment: trac_783.patch doesn't contain doctests. I don't see how the changes to sage/symbolic/expression.pyx in that patch are relevant to this ticket. Perhaps these should be on a different ticket.

you are perfectly right, Burcin. Mike, please could you remove that unused code from the patch?
Paul

[mwhansen]

Attachment: trac_783.patch.gz

[mwhansen]

comment:14

Sorry about that -- I'm not sure how those changes snuck into that patch.

[zimmermann6]

comment:15

Sorry about that -- I'm not sure how those changes snuck into that patch.

I'm sorry I didn't see that during my review. Anyway I confirm all doctests still pass
(tested with Sage 4.5.2).

Paul

[qed777]

Merged: sage-4.6.alpha1