Changes between Initial Version and Version 13 of Ticket #20127


Ignore:
Timestamp:
03/09/16 09:14:35 (5 years ago)
Author:
behackl
Comment:

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  • Ticket #20127

    • Property Commit changed from to 4ddf10c1c65acabc21bae40d80b51735cf26be24
    • Property Component changed from symbolics to numerical
    • Property Branch changed from to u/behackl/symbolic/test_relation/noconvergence
    • Property Summary changed from test_relation: uncaught NoConvergence to zetaderiv: numerically unstable
  • Ticket #20127 – Description

    initial v13  
    1 Testing the following expression for zero randomly results in a `NoConvergence` error being thrown from `mpmath`:
     1The implementation of the derivative of the zeta function `zetaderiv` is numerically unstable and very slow (for large negative values):
    22
    33{{{
    4 sage: var('k')
    5 k
    6 sage: bool(gamma(k*pi) * zetaderiv(1, k*pi*I)/log(2)^2 == 0)
    7 False
     4sage: zetaderiv(1, CIF(-600))
     5Traceback (most recent call last):
     6...
     7NoConvergence: zeta: too much cancellation
    88}}}
    99
    10 or
     10{{{
     11sage: timeit('zetaderiv(1, CIF(-500))')
     125 loops, best of 3: 3.08 s per loop
     13}}}
    1114
     15Could either the current implementation be improved or an alternative numerical implementation be used?
     16
     17---
     18
     19This also causes errors when testing relations like
    1220{{{
    1321sage: bool(gamma(k*pi) * zetaderiv(1, k*pi*I)/log(2)^2 == 0)
     
    1624NoConvergence: zeta: too much cancellation
    1725}}}
    18 
    19 This ticket adds this error to the list of caught errors in `test_relation`.