#10075: Make log gamma symbolic
---------------------------+------------------------------------------------
Reporter: kcrisman | Owner: burcin
Type: enhancement | Status: needs_review
Priority: major | Milestone: sage-5.0
Component: symbolics | Keywords: sd35.5
Work_issues: | Upstream: N/A
Reviewer: | Author: Karen T. Kohl
Merged: | Dependencies:
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Comment(by kcrisman):
> Apparently this is how MPFR deals with this function. So maybe all is
well?
I mean, for this ticket. Though we should not claim that it is evaluated
by Ginac, because it isn't (all the above is in Sage with or without this
patch).
Believe it [http://gcc.gnu.org/bugzilla/show_bug.cgi?id=29335 or not]:
{{{
Not any negative value, but in lngamma.c:
/* if x < 0 and -2k-1 <= x <= -2k, then lngamma(x) = NaN */
probably because the gamma value is negative. This is because MPFR defines
lngamma as log(gamma(x)) while the C standard defines it as log|gamma(x)|.
I
wonder if this should be regarded as a bug or if a new function (say,
mpfr_lgamma) should be defined in MPFR (in which case, not before 2.3.0).
Do
other standards (other languages) define such a function, either as
log(gamma(x)) or as log|gamma(x)|?
}}}
I'm cc:ing Paul Z. just to confirm that this is intended MPFR behavior.
We should then open another ticket to make sure to use mpmath or ginac or
something to get complex answers. We currently somehow use PARI to get
the complex versions.
{{{
sage: log_gamma(CC(-2.1))
1.53171380819509 + 3.14159265358979*I
sage: from sage.misc.citation import get_systems
sage: get_systems('log_gamma(CC(-2.1))')
['PARI', 'MPFR']
}}}
--
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/10075#comment:10>
Sage <http://www.sagemath.org>
Sage: Creating a Viable Open Source Alternative to Magma, Maple, Mathematica,
and MATLAB
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