Well, it's not like you can't calculate them before. From http://www.jsoftware.com/help/dictionary/dmcapdot.htm http://www.jsoftware.com/jwiki/Essays/Partitions#TheNumberofPartitions (Implement's Euler's formula using memo-ization.)
pn =: -/@(+/)@:($:"0)@rec ` (x:@(0&=)) @. (0>:]) M. rec=: - (-: (*"1) _1 1 +/ 3 * ]) @ (>:@i.@>.@%:@((2%3)&*)) timer 'p=: pn 1000' 0.0808349 p 24061467864032622473692149727991 When timing the thing be careful that the M. can give misleadingly fast times on subsequent executions. ----- Original Message ----- From: Mike Day <[email protected]> Date: Saturday, January 22, 2011 10:39 Subject: [Jchat] partition numbers - was Fwd: [k4] major number theory breakthrough! To: Chat forum <[email protected]> Cc: Michael Rosenberg <[email protected]> > Good News? Over to Roger! > Mike > > -------- Original Message -------- > Subject: [k4] major number theory breakthrough! > Date: Sat, 22 Jan 2011 12:54:35 -0500 > From: Michael Rosenberg <[email protected]> > Reply-To: [email protected] > To: k4 <[email protected]> > > > > you don't see a lot of new discoveries in math, but apparently > we've got > a huge one in partition theory that may have repercussions everywhere! > > check it out > <http://esciencecommons.blogspot.com/2011/01/new-theories- > reveal-nature-of-numbers.html>! > > as a bonus, embedded in the article is a 10 minute youtube video > that is > the best "zoom" into the mandelbrot set i've ever seen. > > as a teaser, here's the punch line: > > “We found a function, that we call P, that is like a magical > oracle,” > Ono says. “I can take any number, plug it into P, and instantly > calculate the partitions of that number. P does not return > gruesome > numbers with infinitely many decimal places. It’s the finite, > algebraic > formula that we have all been looking for.” ---------------------------------------------------------------------- For information about J forums see http://www.jsoftware.com/forums.htm
