Karim Belabas on Sun, 25 Aug 2013 11:29:09 +0200 |
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Re: Two questions about products |
* Charles Greathouse [2013-08-21 15:43]: > A quick second question: I notice that prodeuler() works like prod(X=a,b, > 1.) rather than prod(X=a,b). Is this intentional? Yes, though seemingly a little inconsistent since prod/sum allow this extra argument. The idea behind the design was that prodeuler() should be a decent, albeit naive, way of estimating "full" Euler products, over all primes. So it's implemented as a "transcendental" function, taking a 'prec' argument, etc. Whereas sum/prod are basic iterators. Nowadays, the function prodeulerrat() in http://pari.math.u-bordeaux1.fr/Scripts/cohen.gp should be used instead, whenever f(p) = 1 + O(p^(-2)). > Would it be possible to > give it a third argument so that prodeuler(p=a, b, 1) could be used if an > integer result was desired? It's possible, but what's wrong with C = 1; forprime(p = a,b, C *= f(p)) ? K.B. P.S. Plans to clean up http://pari.math.u-bordeaux1.fr/Scripts/ and make it more useful / accessible were discussed during the last Atelier. See http://pari.math.u-bordeaux1.fr/Events/PARI2013/talks/scripts.pdf and the sample script http://pari.math.u-bordeaux1.fr/Events/PARI2013/talks/bifactor.gp But I had no time for it last semester :-(. Anybody interested in helping out for that project ? -- Karim Belabas, IMB (UMR 5251) Tel: (+33) (0)5 40 00 26 17 Universite Bordeaux 1 Fax: (+33) (0)5 40 00 69 50 351, cours de la Liberation http://www.math.u-bordeaux1.fr/~kbelabas/ F-33405 Talence (France) http://pari.math.u-bordeaux1.fr/ [PARI/GP] `