[Jprogramming] Code for multiplying continued fractions?

[Kip Murray]

... and I did omit a right paren, but I think you will see where it goes.  /Kip


Kip Murray wrote:
> Henry,
> 
> I do not have code but can point you to formulas in the Handbook of 
> Mathematical Functions by Abramowitz and Stegun, Chapter 3 Elementary 
> Mathematical Methods, Section 3.10 Theorems on Continued Fractions (page 
> 19 in my edition).  Be sure to read both columns of formulas.
> 
> There is no unique continued fraction product for two continued 
> fractions, but you could try the following to find _a_ product.  First 
> given two infinite continued fractions f and g use the recursive matrix 
> multiplication given in formula (3) of Section 3.10 to find the 
> numerators and denominators of the n^th convergents
> 
> f_n = A_n/B_n
>                 n = 1,2,3,...
> g_n = C_n/D_n
> 
> (conventional notation, _n means subscript n).  The convergents converge 
> to the value of the continued fraction.
> 
> Let
> 
> E_n = A_n * C_n
>                  n = 1,2,3...
> F_n = B_n * D_n
> 
> Then, to find a continued fraction h (this is your product) with 
> convergents
> 
> h_n = E_n/F_n   n = 1,2,3...
> 
> solve the matrix recursion (3) for for the entries e_n and f_n in
> 
> h = f_0 + e_1
>           ---------
>           f_1 + e_2
>                 --------
>                 f_2 + ...
> 
> (I hope that comes out right on your screen.)
> 
> The recursion (3) written for the continued fraction h is
> 
> (E_n , F_n) = ((E_(n-1) , F_(n-1)) ,. (E_(n-2) , F_(n-2)) o (f_n , e_n)
> 
> using a mix of standard notation and J, where o is +/ . *
> 
> Starting values are E_(-1) = 1, E_0 = f_0, F_(-1) = 0, F_0 = 1.  You can 
> use f_0 = 0.
> 
> Please get the correct formulas from Abramowitz and Stegun -- in case I 
> mistyped something.  And of course you have %. for solving for (f_n , e_n).
> 
> Kip Murray
> 
> 
> Henry Rich wrote:
>> Does anyone have J code for multiplying two numbers expressed as 
>> simple continued fractions, producing a continued-fraction result?
>>
>> Henry Rich
> 
> 
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