new functions

[Karim BELABAS <Karim.Belabas@math.u-psud.fr>]

Hi,

1)  I have just enabled the possibility to type nfroots(, P), omitting the nf
parameter, in order to get rational roots of a rational polynomial.
[ nfroot(nfinit(y), P) is still possible, but slower ].

2)  I have edited the p(n) function that was contributed by Ralf Stefan
[ p(n) := number of unrestricted partitions of n, using Rademacher's
formula], and I will add it to the PARI core.

It could be useful to also have an actual function generating a list of
partitions [ already there, static to galois.c ], and a forpart() iterator.

We already have numdiv [ numbdiv in library mode! ] / divisors / fordiv

So what about numbpart / partitions / forpart ?  [ I don't really like
numpart, and I would change numdiv --> numbdiv were it not for compatibility
problems ]

Cheers,

    Karim.

P.S: in Maple, partition(n)  [ 'partitions' seems more natural... ] returns
the actual partitions of n and not their number, and p(n) is denoted by
numbpart(n). In Mathematica, it's Partitions / PartitionsP (or
NumberOfPartitions...).
-- 
Karim Belabas                    Tel: (+33) (0)1 69 15 57 48
Dép. de Mathématiques, Bât. 425  Fax: (+33) (0)1 69 15 60 19
Université Paris-Sud             Email: Karim.Belabas@math.u-psud.fr
F-91405 Orsay (France)           http://www.math.u-psud.fr/~belabas/
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