Of course. I agree that there should be an algorithm parameter, but I
bet most people/functions will end up using the default which should
be something reasonable.
On Mar 3, 2007, at 8:25 AM, William Stein wrote:
> I want to add that however random's are changed, e.g., for the
> integers,
> the current behavior MUST still be available. The reason is because
> most
> benchmarks I know about for other systems use uniformly chosen random
> numbers in an interval. Loosing this behavior would make it much
> much
> more painful to do comparative benchmarks.
>
> On 3/2/07, David Roe <[EMAIL PROTECTED]> wrote:
>> I've been thinking about random elements a bit for p-adics. There
>> are lots
>> of good and reasonable ways to generate random elements of
>> things. For
>> example, in addition to Robert's suggestion, we could have a Gaussian
>> distribution with a specified mean, or a Poisson distribution...
>> It seems
>> like a reasonable way to do it would be to have an algorithm =
>> {uniform,
>> gaussian,...} argument to the random element function and thus
>> have lots
>> available (ie however many we decide to write). Then if someone
>> wants to
>> know what kind of random distributions they can generate, they can
>> just
>> check the docstring for the function. Of course, this still
>> leaves the
>> question of which is the default...
>>
>> Anyway, I'm planning on doing this for p-adics. Thought I might
>> throw the
>> idea in for integers too.
>> David
>>
>>
>>> 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
>>
>>
>>>
>>
>
>
> --
> William Stein
> Associate Professor of Mathematics
> University of Washington
>
>
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