#17066: always simplify hypergeometric() when it's a polynomial
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Reporter: rws | Owner:
Type: defect | Status: needs_review
Priority: major | Milestone: sage-6.4
Component: symbolics | Resolution:
Keywords: special, | Merged in:
functions, pFq, evaluation | Reviewers:
Authors: Ralf Stephan | Work issues:
Report Upstream: N/A | Commit:
Branch: | 0e0fef65a021a9b0a9db30a2bc6d300ede68bf14
u/rws/work_around_mpmath_problem_with_hypergeometric___zeroes| Stopgaps:
Dependencies: |
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Comment (by kcrisman):
> Expanding hypergeometric functions in polynomial closed form before
evaluating them can lead to numerical cancellation. Compare for example
> {{{
> sage: hypergeometric([1,-100],[3], 0.7)
> 0.0278923450568346
> sage: hypergeometric([1,-100],[3], Reals(1000)(0.7)).n()
> 0.0278923450568346
> sage:
sage.functions.hypergeometric.closed_form(hypergeometric([1,-100],[3],x)).subs(x=0.7)
> -376.859920391941
> }}}
> Won't that be a problem with this ticket? (I didn't read beyond the
ticket's description, so please ignore my comment if it is beside the
point.)
Just so I follow, what you are saying is that the polynomial (rational
function, I guess) given will be ''correct'', but that substituting
floating point numbers are likely to be inaccurate unless carried out to a
very high degree of precision? I'm torn here because on the one hand,
presumably that could happen with ''any'' rational function, there are
standard examples given in a lot of calculus books, but on the other hand
we "expect" hg to return a hg function and not a polynomial.
> The real fix for this cannot be provided by hypergeometric though but
must be done in subs, if at all.
Well, it could provide a good reason ''not'' to "always simplify
hypergeometric when it's a polynomial"... I didn't realize that people
meant rational function when they said polynomial. Is it possible to
really only simplify when it's a true polynomial, or is that a very
unlikely event?
--
Ticket URL: <http://trac.sagemath.org/ticket/17066#comment:23>
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