#5739: Have zeta of 1 return value be consistent in different rings
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Reporter: was | Owner: fredrik
Type: defect | Status: needs_work
Priority: major | Milestone: sage-4.3.2
Component: number theory | Keywords:
Author: Mike Hansen | Upstream: N/A
Reviewer: Karl-Dieter Crisman, Robert Bradshaw | Merged:
Work_issues: |
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Comment(by fredrik.johansson):
kcrisman:
Starting with the next version, mpmath uses the Riemann-Siegel formula, so
it should be much faster than Pari for large imaginary parts near the
critical strip. Right now I even get a segmentation fault if I try to
compute zeta(CDF(1/2+10000000*I)) in Sage.
For CDF, zeta could also use mpmath.fp.zeta that will be available in the
next version of mpmath. This function is currently typically 10-50 times
faster than mpmath.mp.zeta. However, fp.zeta loses accuracy proportional
to the magnitude of the imaginary part near the critical strip, so the
question is whether this loss would be acceptable. For small imaginary
parts, it's quite accurate.
Both functions could be accelerated in Sage by overriding the base case of
an internal function (mpmath/functions/zeta.py/_zetasum in the svn trunk,
if anyone wants a go). This should require just few lines of Cython.
Other than that, I would recommend keeping Pari where it's faster.
--
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/5739#comment:8>
Sage <http://www.sagemath.org>
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