#17852: Small cleanup in rings.arith and rings.integer
-------------------------------------+-------------------------------------
       Reporter:  vdelecroix         |        Owner:
           Type:  enhancement        |       Status:  needs_work
       Priority:  major              |    Milestone:  sage-6.6
      Component:  basic arithmetic   |   Resolution:
       Keywords:                     |    Merged in:
        Authors:  Vincent Delecroix  |    Reviewers:
Report Upstream:  N/A                |  Work issues:
         Branch:                     |       Commit:
  u/vdelecroix/17852                 |  cbbb06fa27b0b9178ad3f9d0de3dc3235c5ec1c3
   Dependencies:  #16878             |     Stopgaps:
-------------------------------------+-------------------------------------

Comment (by vdelecroix):

 Replying to [comment:53 jdemeyer]:
 > {{{
 >             sage: hash(-920390823904823094890238490238484)
 >             -873977844            # 32-bit
 >             6874330978542788722   # 64-bit
 > }}}

 Thanks!

 I also noticed that on large input `pari` is faster than `mpir`:
 {{{
 sage: %timeit a = (2**50).binomial(2**10, algorithm='mpir')
 1000 loops, best of 3: 462 µs per loop
 sage: %timeit a = (2**50).binomial(2**10, algorithm='pari')
 1000 loops, best of 3: 221 µs per loop
 }}}
 and the difference is even more significant with larger numbers... I will
 had a note related to that.

 Finally, I have troubles with the modification of the output type in
 `arith.binomial` ([comment:48 comment:48], [comment:51 comment:51] and
 [comment:52 comment:52]). It is responsible for some doctest failure in
 `rings/polynomial/multi_polynomial_ideal.py` (the random generation
 stuff). I was not able to track down the issue.

--
Ticket URL: <http://trac.sagemath.org/ticket/17852#comment:54>
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