Doctests for: fix polylog evalf

[rwst]

The polylog function (from Pynac) treats 1.0 like 1 and does not immediately evalf with some numeric arguments.

sage: polylog(2,1)
1/6*pi^2
sage: polylog(2.,1)
1.64493406684823
sage: polylog(2,1.0)
1/6*pi^2
sage: polylog(2,0.9)
polylog(2, 0.900000000000000)
sage: _.n()
TypeError: cannot evaluate symbolic expression numerically

What makes polylog different is that the Sage polylog has no special value logic and calls Pynac's Li_eval for everything. This handles special values (incorrectly if an arg is FP) and sends everything else back with .hold(). So you need N() to get FP results that are not special. With FP Pynac is called which then calls Sage/mpmath. But this then bombs with FP args.

Depends on #22969
Depends on #23077
Depends on #23134

CC: @kiwifb

Component: symbolics

Keywords: pynac special

Author: Ralf Stephan

Branch/Commit: 59d4b29

Reviewer: Paul Masson, Dima Pasechnik

Issue created by migration from https://trac.sagemath.org/ticket/18386

[rwst]

Description changed:

--- 
+++ 
@@ -11,3 +11,4 @@
 polylog(2, 0.900000000000000)
 
 ```
+https://github.com/pynac/pynac/issues/48

[rwst]

Upstream: Reported upstream. Developers acknowledge bug.

[rwst]

Description changed:

--- 
+++ 
@@ -9,6 +9,11 @@
 1/6*pi^2
 sage: polylog(2,0.9)
 polylog(2, 0.900000000000000)
+sage: _.n()
+TypeError: cannot evaluate symbolic expression numerically
+```
+What makes `polylog` different is that the Sage `polylog` has no special value logic and calls Pynac's `Li_eval` for everything. This handles special values (incorrectly if an arg is FP) and sends everything else back with `.hold()`. So you need `N()` to get FP results that are not special. With FP  Pynac is called which then calls Sage/mpmath. But this then bombs with FP args.
 
-```
-https://github.com/pynac/pynac/issues/48
+It seems better to simply implement everything in Sage because only the special value logic is still in Pynac, and buggy too.
+
+Consequently, `polylog` should be removed from the Pynac function registry.

[rwst]

Description changed:

--- 
+++ 
@@ -14,6 +14,3 @@
 ```
 What makes `polylog` different is that the Sage `polylog` has no special value logic and calls Pynac's `Li_eval` for everything. This handles special values (incorrectly if an arg is FP) and sends everything else back with `.hold()`. So you need `N()` to get FP results that are not special. With FP  Pynac is called which then calls Sage/mpmath. But this then bombs with FP args.
 
-It seems better to simply implement everything in Sage because only the special value logic is still in Pynac, and buggy too.
-
-Consequently, `polylog` should be removed from the Pynac function registry.

[rwst]

Changed upstream from Reported upstream. Developers acknowledge bug. to Fixed upstream, in a later stable release.