implement Nielsen Generalized Polylogarithm

[burcin]

Numeric evaluation methods for the Nielsen Generalized Polylogarithm are commented out in the pynac source since it tries to call the CLN library directly. The calls to CLN should be replaced with their MPFR, etc. equivalents and the function made available symbolically in Sage. The Pynac part is pynac/pynac#3

Component: symbolics

Issue created by migration from https://trac.sagemath.org/ticket/10050

[zimmermann6]

comment:1

note that there are issues with the current polylog function:

sage: polylog(2,1.0)
1/6*pi^2
sage: polylog(2,0.9)
polylog(2, 0.900000000000000)

The first command should not evaluate symbolically, since the input 1.0 is a floating-point.
The second command should evaluate numerically, like for example bessel_J(2,0.9).

Should I open a separate ticket?

Paul

[burcin]

comment:2

Replying to @zimmermann6:

note that there are issues with the current polylog function:

sage: polylog(2,1.0)
1/6*pi^2
sage: polylog(2,0.9)
polylog(2, 0.900000000000000)

The first command should not evaluate symbolically, since the input 1.0 is a floating-point.
The second command should evaluate numerically, like for example bessel_J(2,0.9).

Should I open a separate ticket?

I was thinking of the other polylog like functions from ginac/inifcns_nstdsums.cpp when I created this ticket. It seems even the symbolic evaluation code for these is commented out, so this would require quite a bit more work than I thought. I am removing the beginner keyword and changing this ticket to only mention numeric evaluation of polylogs.

[burcin]

Description changed:

--- 
+++ 
@@ -1,5 +1,10 @@
-Ginac includes an implementation of polylogarithms. The numeric methods of this implementation is commented out in the pynac source since it tries to call the `CLN` library directly, but the other parts should work.
+Numeric evaluation methods for the `polylog` function are commented out in the pynac source since it tries to call the `CLN` library directly. The calls to CLN should be replaced with their MPFR, etc. equivalents.
 
-We should expose these functions (with a name other than `Li`).
+```
+sage: polylog(2,1.0)
+1/6*pi^2
+sage: polylog(2,0.9)
+polylog(2, 0.900000000000000)
+```
 
-An example of how this can be done is available in #8864.
+This is also [pynac issue #3](https://bitbucket.org/burcin/pynac/issue/3/)

[rwst]

Description changed:

--- 
+++ 
@@ -7,4 +7,4 @@
 polylog(2, 0.900000000000000)
 ```
 
-This is also [pynac issue #3](https://bitbucket.org/burcin/pynac/issue/3/)
+This is also [pynac issue #3](http://hg.pynac.org/pynac/issue/3/numerical-evaluation-of-polylogarithms)

[rwst]

comment:4

At the moment Pynac calls symbolic/pynac.pyx:py_li() which calls mpmath. It is not clear to me why the outcommented pynac code would be needed, to remove the call overhead? If you replace the CLN dependency, with what MPFR?, how would this be better or faster than mpmath?

Proposed to be invalid. If you agree I would reword this ticket to fix the mentioned bugs only.

[rwst]

comment:5

Ah okay, what was meant in this ticket's description is GiNaC's implementation of the Nielsen Generalized Polylogarithm which is not in mpmath. I have changed the description accordingly.