[seqfan] Re: Worry about old sequence, A030077, paths in K_n

[Pierre Abbat]

On Saturday, April 2, 2022 9:03:43 AM EDT David Applegate wrote:
> I worry about using floating point (extended or not) to check if
> different sums of square roots are equal or not.  Using finite precision
> for this is extremely tricky This is a notoriously hard problem in
> general.  For example, to see that
> sqrt(7)+sqrt(14)+sqrt(39)+sqrt(70)+sqrt(72)+sqrt(76)+sqrt(85) !=
> sqrt(13)+sqrt(16)+sqrt(55)+sqrt(67)+sqrt(73)+sqrt(79) you already need
> more than double-precision floating point (their difference is 10^-19,
> see
> http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.156.3838&rep=rep1&t
> ype=pdf). There is a randomized polynomial time algorithm for testing
> equality, but it isn't just compute the result to enough precision.

The sum is missing sqrt(46). I've thought of solving a similar problem in my 
program Quadlods, since such nearly equal sums of quadratic irrationals would 
result in planes of points when generating n-dimensional Richtmyer sequences.

Pierre

-- 
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