Changes between Initial Version and Version 13 of Ticket #20127
 Timestamp:
 03/09/16 09:14:35 (5 years ago)
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Ticket #20127

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4ddf10c1c65acabc21bae40d80b51735cf26be24

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symbolics
tonumerical

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u/behackl/symbolic/test_relation/noconvergence

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test_relation: uncaught NoConvergence
tozetaderiv: numerically unstable

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Ticket #20127 – Description
initial v13 1 T esting the following expression for zero randomly results in a `NoConvergence` error being thrown from `mpmath`:1 The implementation of the derivative of the zeta function `zetaderiv` is numerically unstable and very slow (for large negative values): 2 2 3 3 {{{ 4 sage: var('k')5 k 6 sage: bool(gamma(k*pi) * zetaderiv(1, k*pi*I)/log(2)^2 == 0) 7 False 4 sage: zetaderiv(1, CIF(600)) 5 Traceback (most recent call last): 6 ... 7 NoConvergence: zeta: too much cancellation 8 8 }}} 9 9 10 or 10 {{{ 11 sage: timeit('zetaderiv(1, CIF(500))') 12 5 loops, best of 3: 3.08 s per loop 13 }}} 11 14 15 Could either the current implementation be improved or an alternative numerical implementation be used? 16 17  18 19 This also causes errors when testing relations like 12 20 {{{ 13 21 sage: bool(gamma(k*pi) * zetaderiv(1, k*pi*I)/log(2)^2 == 0) … … 16 24 NoConvergence: zeta: too much cancellation 17 25 }}} 18 19 This ticket adds this error to the list of caught errors in `test_relation`.