Nick Hobson on Sat, 02 Dec 2006 00:07:15 +0100


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Re: Two factor questions 

Thanks Bill.

Nick
On Sat, 25 Nov 2006 21:54:08 -0000, Bill Allombert <Bill.Allombert@math.u-bordeaux1.fr> wrote: 


On Sat, Nov 25, 2006 at 09:20:20PM -0000, Nick Hobson wrote:

Hi,

I have a couple of questions about the factor function, as applied to
integers.

1) Does it sort the results by prime (i.e., first column)?  All the
results I've seen have been sorted, but I notice the manual doesn't
specify this behavior.  (Unless I'm missing something.)


Yes. (beware that for negative numbers the first line is [-1,1]).
2) Is it possible to request only the smallest prime factor, rather than a 
complete factorization?
Not really. The only algorithm available in PARI that can _prove_ a factor is the smallest is trial division, and there are no toggle in place to stop 
trial division at the first hit. However you can easily implement that
yourself using the prime number table.

On the other hand, if you want a small prime factor without a proof it is
the smallest, then it is possible at least in library mode.

Cheers,
Bill.