On Tue, Sep 1, 2009 at 8:18 AM, Schroeppel, Richard<rschroe@sandia.gov> wrote:
I expected Gosper to step in, since it's his area. Doesn't the obvious generalization to 6x6 matrices work?
Rich
Um. It's not obvious to me--how would that work? In ab + dc, it's a sum of terms with two variables, so it's a product of two matrices. In the example system of fractions, you get a0 b0 b1 b2 + d00 c0 b1 b2 + d01 c1 b0 b2 + d02 c2 b0 b1 as a numerator, so I thought it may be the case that you have to multiply four matrices, and I'm not sure how that would work either.
-----Original Message----- From: math-fun-bounces@mailman.xmission.com [mailto:math-fun-bounces@mailman.xmission.com] On Behalf Of Fred lunnon Sent: Monday, August 31, 2009 4:25 PM To: math-fun Subject: Re: [math-fun] Systems of continued fractions
Looks like we're the only two left, Mike --- did we miss Armageddon? WFL
On 8/31/09, Mike Stay <metaweta@gmail.com> wrote:
Reposting, since I never saw it on the list and got no replies...
On Fri, Aug 28, 2009 at 9:28 AM, Mike Stay<metaweta@gmail.com> wrote: > Given a finite continued fraction, you can start at the last term and > build up the cf by > > | b d c ab + dc > | - -> a + --- = ------- > | c b b > > where 'b/c' is the current fraction, 'a' is the current term, and 'd' > is usually 1. This operation is nicely represented with a 2x2 matrix: > > | [ a d ] [ b ] = [ ab + dc ] > | [ 1 0 ] [ c ] [ b ] > > I'm looking at a situation where I have multiple fractions: > > | b0 b1 b2 > | --, --, -- > | c0 c1 c2 > > and an update rule that takes these to > > | d00 c0 d01 c1 d02 c2 > | a0 + ------ + ------ + ------, > | b0 b1 b2 > | > | d10 c0 d11 c1 d12 c2 > | a1 + ------ + ------ + ------, > | b0 b1 b2 > | > | d20 c0 d21 c1 d22 c2 > | a2 + ------ + ------ + ------, > | b0 b1 b2 > > Is there a way to do this case with matrices? > -- > Mike Stay - metaweta@gmail.com > http://math.ucr.edu/~mike > http://reperiendi.wordpress.com >
-- Mike Stay - metaweta@gmail.com http://math.ucr.edu/~mike http://reperiendi.wordpress.com
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-- Mike Stay - metaweta@gmail.com http://math.ucr.edu/~mike http://reperiendi.wordpress.com