William Stein wrote:
> On Nov 27, 2007 10:47 AM, Jaap Spies <[EMAIL PROTECTED]> wrote:

>> This is my favorite application of permanents: counting the number of
>> permutations with restricted positions!
> 
> That is indeed very beautiful.    It's not so good from an efficiency
> point of view though:
> 
> sage: time a=derangements(10000,0)
> CPU time: 45.73 s,  Wall time: 47.70 s
> sage: time b=rencontres_number(10000,0)
> CPU time: 1.11 s,  Wall time: 1.21 s
> 
> at least not practically.  This might be because factorial and
> multiprecision arithmetic are both so fast in sage.
> 

Yes, I know/knew, but a thing of beauty is a joy forever :-)!
It is not always speed that counts.

Jaap


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