It's always bugged me that the default distribution for integers (and
rationals) is just a uniform distribution over some small range. What
if instead we chose the distribution ZZ.random_element() = floor(1/r)
where r is uniformly distributed in (-1,1). Then P(n) = 1 / (2 |n| (|
n| + 1)) for all n in Z-{0}. This gives mostly small numbers with the
occasional large ones thrown in at ever decreasing probabilities.
A random rational could then be the ratio of two such integers.
- Robert
On Mar 2, 2007, at 9:57 AM, William Stein wrote:
> On 3/1/07, didier deshommes <[EMAIL PROTECTED]> wrote:
>> On 2/25/07, Craig Citro <[EMAIL PROTECTED]> wrote:
>>> Hey all,
>>>
>>> So I tried to generate a random polynomial today, and ran into
>>> some trouble.
>>> Here's what I did:
>>>
>>> sage: R.<x> = ZZ['x']
>>> sage: R.random_element(3)
>>> <sage crashes>
>>
>> That is a nice edge case. I would say that or you just return 0
>> everytime. Other rings seem to do that:
>> {{{
>> sage: RR.random_element(0)
>> 0.000000000000000
>> sage: QQ.random_element(0)
>> 0
>> sage: RDF.random_element(0)
>> 0.143951483848
>> }}}
>
>>> I traced back the problem, and it's not clear what the right fix
>>> is. So
>>> R.random_element makes a list of the appropriate length and calls
>>> ZZ.random_element(0) to fill it up. In the comments, it clearly
>>> explains why
>
> I've fixed this for sage > 2.2. The patch is attached in case you're
> interested.
>
> >
> <3251.patch>
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