I expected Gosper to step in, since it's his area. Doesn't the obvious generalization to 6x6 matrices work? Rich -----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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