50G fraction question Q-> function max denominator

[DavidM]

(11-08-2019 09:01 PM)Joe Horn Wrote:  Albert's method automatically does that, if you use a power of 2 for D, no?

(11-08-2019 10:05 PM)Albert Chan Wrote:  x' = round(x D) / D will gives you the same answer (for this case D = 2^n)

Perhaps it is easier to visualize if you consider denominator as the maximum D
In other words, fraction is not (yet) allowed to be simplified

x = (x D) / D = y / D

x' = y' / D, y' an integer

Now, what integer value of y' will minimize error ? y' = round(y)

error = |x - x'| = |y - y'| / D ≤ 0.5 / D

OIC (Oh, I see!)

So changes are in order for my last program:
1) The maximum denominator (D in your explanation) will need to be "pinned" to the greatest power-of-2 ≤ the given value
2) After determining a,b,c in 'a+b/c', the GCD for b and c will be used to simplify the rational

I'm building the rational manually instead of using the CAS so that the program is flag-agnostic (I want it to behave the same way regardless of flag settings). I also prefer -(1+1/2) to -1+-1/2 when displaying negative symbolics, which is easily done by placing the negation as its final component. I find the former easier to read than the latter when on the stack.

Thanks to both of you for the education!