> (Implement's Euler's formula using memo-ization.) Yikes! Senility! Should be:
(Implements Euler's formula using memo-ization.) ----- Original Message ----- From: Roger Hui <[email protected]> Date: Saturday, January 22, 2011 11:50 Subject: Re: [Jchat] partition numbers - was Fwd: [k4] major number theory breakthrough! To: Chat forum <[email protected]>, Michael Rosenberg <[email protected]> > 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 > ---------------------------------------------------------------------- For information about J forums see http://www.jsoftware.com/forums.htm
