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
}}}
didier
>
> 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
> 0: it assumes that this is the default argument to pass to get a choice that
> is as spread across the ring as possible. Now, the problem is that
> ZZ.random_element(0) calls GMP's mpz_urandomm() function, which throws a
> division by zero exception when you call it with 0; it only knows how to
> generate a random element between two bounds (at least, according to the
> comments in the source). So I'm not sure which of the following things is
> the "right" fix for this:
>
> 1) Fix ZZ.random_element so that it calls off to mpz_urandomm with a large
> bound; if so, I'm not sure what bound to use.
>
> 2) Change R.random_element so that it doesn't try to pass off a 0 to
> ZZ.random_element , which seems like the wrong solution -- this code is in
> PolynomialRing.random_element, which really shouldn't know in general how to
> ask for a random element in its base_ring. However, this means that we
> should document somewhere that in any ring, random_element(0) is the request
> for "as general a random element as possible."
>
> 3) Decide to think about it later, and throw an exception. This was
> apparently GMP's solution. ;)
>
> I think (1) is the right solution, but I'm not sure what bound to use. But
> maybe one of the other choices is better? What does everyone else think?
>
> -cc
>
> >
>
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