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
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