#15196: Use mpmath for numerical evaluation of the beta function
-------------------------------------------------+-------------------------
Reporter: eviatarbach | Owner:
Type: defect | Status:
| needs_work
Priority: major | Milestone: sage-7.3
Component: numerical | Resolution:
Keywords: | Merged in:
Authors: | Reviewers:
Report Upstream: Fixed upstream, in a later | Work issues:
stable release. |
Branch: | Commit:
Dependencies: | Stopgaps:
| incorrectAnswer
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Changes (by rws):
* status: needs_info => needs_work
Old description:
> Currently,
>
> {{{
> sage: beta(-1.3,-0.4)
> NaN
> sage: (gamma(-1.3) * gamma(-0.4)) / gamma(-1.3 - 0.4) # expected
> functionality
> -4.92909641669610
> }}}
>
> This is because GiNaC uses
> `exp(log_gamma(-1.3)+log_gamma(-0.4)-log_gamma(-1.3-0.4))` to evaluate,
> and `log_gamma` is broken for some input (see #12521). Using mpmath is
> faster and avoids roundoff errors as well.
New description:
Currently,
{{{
sage: beta(-1.3,-0.4)
NaN
sage: (gamma(-1.3) * gamma(-0.4)) / gamma(-1.3 - 0.4) # expected
functionality
-4.92909641669610
}}}
This is because GiNaC uses
`exp(log_gamma(-1.3)+log_gamma(-0.4)-log_gamma(-1.3-0.4))` to evaluate,
and `log_gamma` is broken for some input (see #12521). Using mpmath is
faster and avoids roundoff errors as well.
The ticket is fixed in Pynac and should doctest the issue.
--
Comment:
Replying to [comment:10 paulmasson]:
> Waiting for pynac 0.6.8
Yes Yes 8-)) I was at it all the time but had to rewrite things.
--
Ticket URL: <https://trac.sagemath.org/ticket/15196#comment:11>
Sage <http://www.sagemath.org>
Sage: Creating a Viable Open Source Alternative to Magma, Maple, Mathematica,
and MATLAB
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