bpv (was problems with Maxima in Ubuntu 9.04)

Agreed. 

There is a Maxima-level variable 'ifactor_verbose' in ifactor.lisp 
which controls the output of information about the factoring steps. 
Unfortunately the output of the bpv is not wrapped in 
(when $ifactor_verbose. Seems that this was overseen. I'll fix it. 

Volker van Nek

Stavros Macrakis schrieb:
> Thanks for the explanation.
>
> I agree with you that factor should not be printing bpv.
>
>             -s
>
> On 5/6/09, reyssat <eric.reyssat at math.unicaen.fr> wrote:
>   
>> Stavros Macrakis a ?crit :
>>     
>>> (%i5) factor(50!+1);
>>> bpv: 74195127103       <<<<<<<<<< hmm, I don't know what this means
>>> Evaluation took 5.3100 seconds (5.3100 elapsed)
>>> (%o5)
>>> 149*3989*74195127103*6854870037011*100612041036938568804690996722352077
>>>       
>> bpv stands for big prime variation (see implementation of p-1
>> factorisation method in ifactor.lisp).
>>
>> The usual p-1 factoring method due to Pollard can find a prime factor p
>> of n if p-1 has only small prime factors (smaller than some
>> computationaly reasonable bound B). A variation of this method extends
>> it to the case where p-1 is the product of primes <B and ONE prime <B^2
>> (much larger).
>>
>> The number 74195127103 found above has a prime factor p (in fact itself)
>> having this form since p-1=2*3*83*283*526453 has only one "big prime"
>> factor 526453.
>>
>> Conversely, using this big prime 526453, you can construct an n giving
>> lots of bpv outputs. Try this :
>> n:1$
>> for i:1 thru 25 do (p:1+i!*526453, if primep(p) then n:n*p)$
>> n;  factor(n);
>>
>> The same algorithm, written in Pascal (?) can be found here with same
>> notations as in ifactor.lisp :
>> ftp://ftp.mathematik.uni-muenchen.de/pub/forster/aribas/v/alnth/p1factor.ari
>> The book
>> http://www.mathematik.uni-muenchen.de/~forster/books/azth/algzth.html
>> might contain a desciption of the algorithm, I couldn't and didn't check.
>>
>> In both implementations (pascal and lisp), a message is displayed when a
>> factor using "big prime variation" has been found.
>> I am not convinced of the usefulness of outputting the message in the
>> algorithm, except for debugging or teaching purposes (which is probably
>> the case for the algorithm by Forster mentioned above).
>>
>> Eric Reyssat
>>
>>     
>
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