Ono-Bruinier partition formula

[kcrisman]

Just curious if anyone was working on implementing
http://aimath.org/news/partition/brunier-ono for number_of_partitions,
or if this is something useful to do (seems to involve both heavy
modular form work and numeric approximation to ensure algebraic
numbers are sufficiently approximated.

I'm not suggesting there's anything wrong with "Jonathan Bober's
highly optimized implementation (this is the fastest code in the world
for this problem)." as in the docs, just curious, as these papers
attracted a fair amount of attention. Maybe it's not realistically
even implementable at this time?

- kcrisman

[William Stein]

It isn't and even if it were I would be (pleasantly) surprised if it
could be any any faster than the code in Sage already. Unfortunately,
I think their result may be mainly of theoretical (and marketing?)
interest....

William

> - kcrisman
>
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--
William Stein
Professor of Mathematics
University of Washington
http://wstein.org

[kcrisman]

On Apr 15, 7:16 pm, William Stein <wst...@gmail.com> wrote:

> On Friday, April 15, 2011, kcrisman <kcris...@gmail.com> wrote:
> > Just curious if anyone was working on implementing

> >http://aimath.org/news/partition/brunier-onofor number_of_partitions,

> > or if this is something useful to do (seems to involve both heavy
> > modular form work and numeric approximation to ensure algebraic
> > numbers are sufficiently approximated.
>
> > I'm not suggesting there's anything wrong with "Jonathan Bober's
> > highly optimized implementation (this is the fastest code in the world
> > for this problem)." as in the docs, just curious, as these papers
> > attracted a fair amount of attention.  Maybe it's not realistically
> > even implementable at this time?
>
> It isn't and even if it were I would be (pleasantly) surprised if it
> could be any any faster than the code in Sage already.  Unfortunately,
> I think their result may be mainly of theoretical (and marketing?)
> interest....
>

Sort of like the formulas for the nth prime :) One of my first Sage
experiences was trying to get one of those monstrosities to work right
in a class.

- kcrisman

[AndrewVSutherland]

I am currently working with Jan Brunier and Ken Ono on a practical
algorithm to compute the "partition class polynomials" H_n(X) they
define in their paper http://arxiv.org/pdf/1104.1182v1, which have
trace (24n-1)*p(n). By using using a purely algebraic approach that
allows us to work modulo primes that split completely in the ring
class
field (the so-called CRT method), we hope to avoid the need for any
floating point approximations.

It remains to be seen how fast this will be, but I note that this
technique has worked well with many other types of class
polynomials.

Drew

Andrew V. Sutherland
Research Scientist
Department of Mathematics
Massachusetts Institute of Technology

On Apr 15, 8:55 am, kcrisman <kcris...@gmail.com> wrote:
> Just curious if anyone was working on implementinghttp://aimath.org/news/partition/brunier-onofor number_of_partitions,