On May 16, 2007, at 22:20 , William Stein wrote:
>
> On 5/16/07, Michel <[EMAIL PROTECTED]> wrote:
>>
>> Consider
>>
>> sage: x,y,z=QQ['x','y','z'].gens()
>> sage: u,v,w=W['u','v','w'].gens()
>
> Syntax error -- W is not defined. What is W?
Presumably a number field. Interesting that the loop timing for the
number field case is only mildly affected by the degree of the
extension (at least for low degrees):
Degree 4:
10 loops, best of 3: 28.4 ms per loop
Degree 6:
10 loops, best of 3: 28.4 ms per loop
Degree 27:
10 loops, best of 3: 29.6 ms per loop
Degree 77:
10 loops, best of 3: 31.2 ms per loop
[snip]
> It's not at all clear to me without further discussion and
> benchmarking
> what the right optimization is so that rational functions over
> fields are
> sufficiently fast. I definitely wouldn't make any changes
> to this without some discussion. Basically, are you suggesting
> that one
> not call reduce until, e.g., printing? Or at least until some sort of
> operations that require the thing be reduced? When do you want
> to call reduce?
>
> I definitely don't dispute that rational functions are slow.
> No real attempt has been made to optimize them, and I
> greatly welcome any such attempts and any discussion
> along these lines.
Lest I misunderstand, I think the issue is that there is a
significant difference between the timing for evaluating elements of
QQ(x,y,z) and QQ(\sqrt[77]{a})(x,y,z) (roughly speaking).
Justin
--
Justin C. Walker, Curmudgeon at Large
Director
Institute for the Enhancement of the Director's Income
-----------
Nobody knows the trouble I've been
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