#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: Jeroen Demeyer
Report Upstream: N/A | Work issues:
Branch: | Commit:
u/vdelecroix/17852 | faf206825e26344ae20fbe41363b00ba4e301c07
Dependencies: #16878 | Stopgaps:
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Comment (by vdelecroix):
Replying to [comment:78 vdelecroix]:
> Replying to [comment:72 jdemeyer]:
> > Sorry but I still don't like the `binomial` code.
> >
> > In particular, do we really need the coercion there? The arguments `x`
and `m` play a very different role, note that `m` is immediately converted
to an integer anyway.
>
> I am not sure I understand. You don't want the case 2 that tries to
convert `x` to an integer? It is much faster that way for real or rational
input that are actually integers.
>
> > Also, the check that `factorial(m)` is invertible has no mathematical
meaning and should just be removed.
>
> I am not sure that what I did in the branch is the best, but there is
definitely something that needs to be specified (see #12179). Would you be
satisfied with
> {{{
> sage: factorial(Zmod(12)(10), 4)
> 3
> }}}
Actually, it does matter. When an operation on a given quotient ring is
implemented from the initial ring, you expect it to not depend on the
representative you used... but
{{{
sage: R = Integers(6)
sage: R(binomial(5,2))
4
sage: R(binomial(5+6,2))
1
}}}
Note that it would have been fine on quotients in which `2!` is
invertible.
--
Ticket URL: <http://trac.sagemath.org/ticket/17852#comment:79>
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