[sage-devel] Re: random number generation
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)
0.000
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.
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3251.patch
Description: Binary data
[sage-devel] Re: random number generation
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)
0.000
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
--~--~-~--~~~---~--~~
To post to this group, send email to sage-devel@googlegroups.com
To unsubscribe from this group, send email to [EMAIL PROTECTED]
For more options, visit this group at http://groups.google.com/group/sage-devel
URLs: http://sage.scipy.org/sage/ and http://modular.math.washington.edu/sage/
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[sage-devel] Re: random number generation
Sure, go for it!
On 3/2/07, Robert Bradshaw [EMAIL PROTECTED] wrote:
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)
0.000
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
--
William Stein
Associate Professor of Mathematics
University of Washington
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To post to this group, send email to sage-devel@googlegroups.com
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URLs: http://sage.scipy.org/sage/ and http://modular.math.washington.edu/sage/
-~--~~~~--~~--~--~---
[sage-devel] Re: random number generation
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)
0.000
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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URLs: http://sage.scipy.org/sage/ and http://modular.math.washington.edu/sage/
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