Karim Belabas on Wed, 07 Mar 2018 16:48:47 +0100


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Re: Partitions with numbpart() 

* Paul Underwood [2018-03-07 15:06]:
> What makes the latest PARI/GP much quicker when calculating partition
> numbers? Compare versions 2.7.2 and 2.9.1.

A direct formula due to Selberg replaced the naive sum involving
Dedekind sums, see Algorithm 1 in

  http://dx.doi.org/10.1112/S1461157012001088

(suggested by Fredrik Johansson). Done in

  commit dd11540e961686b625fd9638f2adc29030008c5c
  Author: Bill Allombert <Bill.Allombert@math.u-bordeaux1.fr>
  Date:   Wed Sep 24 19:02:21 2014 +0200

> To what extent has the latest version been tested?

To my knowledge, not extensively. (Checked explicitly for all integers
up to 400.000 and for isolated values up to 10^9.) Feel free to extend
that range !

Cheers,

    K.B.
--
Karim Belabas, IMB (UMR 5251)  Tel: (+33) (0)5 40 00 26 17
Universite de Bordeaux         Fax: (+33) (0)5 40 00 21 23
351, cours de la Liberation    http://www.math.u-bordeaux.fr/~kbelabas/
F-33405 Talence (France)       http://pari.math.u-bordeaux.fr/  [PARI/GP]
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