Henry wrote:
> Does anyone have J code for multiplying two numbers expressed as
> simple continued fractions, producing a continued-fraction result?
Roger responded:
> As a first approximation, convert to two single (rational) numbers;
> mutliply; convert back. *&.conv
Here's one way to do that:
NB. Continued fraction to decimal
cf2d =: (+%)/
NB. Decimal to continued fraction
d2cf =: }:@:<.@:(%@:(-<.)^:(_&>)^:a:&.x:)
NB. continued fraction <-> decimal
cf =: cf2d :. d2cf
NB. Multiply continued fractions
cfM =: *&.cf
I'm sure there are superior algorithms, in particular for d2cf . I'm
thinking along the line of Euler's GCD algorithm. There's a lot of depth
hidden in J's rational numbers and the relevant primitives (e.g. +. |
#: ).
There might also be a direct way (without the intermediate conversion to
decimal), but no ideas occur to me, personally.
-Dan
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