#18386: fix polylog evalf
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Reporter: rws | Owner:
Type: defect | Status:
| needs_work
Priority: major | Milestone: sage-7.4
Component: symbolics | Resolution:
Keywords: pynac special | Merged in:
Authors: Ralf Stephan | Reviewers: Paul
Report Upstream: Fixed upstream, in a later | Masson
stable release. | Work issues:
Branch: | Commit:
Dependencies: #21034 | Stopgaps:
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Comment (by rws):
Polylog has a branch point/discontinuity at arguments (2,1). Anyway, we're
just taking what arb is giving us:
{{{
sage: RBF=ComplexBallField(53)
sage: RBF(1.5).polylog(RBF(2.5))
[2.27833425640 +/- 2.25e-12] + [-0.61016023975 +/- 3.09e-12]*I
sage: RBF(.99999999).polylog(RBF(2.))
[1.6449338726414 +/- 9.23e-14] + [+/- 2.46e-13]*I
sage: RBF(1.).polylog(RBF(2.))
nan + nan*I
sage: RBF(1.00000001).polylog(RBF(2.))
[1.644934261055 +/- 1.08e-13] + [-3.1416e-8 +/- 3.19e-13]*I
sage: polylog(2,1)
1/6*pi^2
}}}
This is very sensible because if you need the exact value say so, and if
you need an inexact value to 53 (or any) digits the result cannot be give
in that precision so it's NaN. I'll concede that, similar to #19439 it may
be desired to return the symbolic NaN.
--
Ticket URL: <https://trac.sagemath.org/ticket/18386#comment:7>
Sage <http://www.sagemath.org>
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