Rational points near curves and small nonzero |x^3-y^2| via lattice reduction · HackerPapers discussions

Rational points near curves and small nonzero |x^3-y^2| via lattice reduction — mentioned by tmyklebu

Fri, 27 Aug 2021 02:22:31 GMT

If you're just looking for hard-to-round inputs, you can also enumerate the double precision space completely with some cleverness and modest patience. Elkies [0] computes a piecewise linear approximation to his (number-theoretic) function of interest and does a lattice reduction on each piece to filter out the vast majority of the space. The same approach, works almost everywhere on all of the transcendental functions I've tried, and I believe the CRlibm group uses it. [0] https://arxiv.org/pdf/math/0005139.pdf

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Rational points near curves and small nonzero |x^3-y^2| via lattice reduction — mentioned by sillysaurus3

Mon, 03 Nov 2014 03:18:44 GMT

It seems that advancements in technology have made mathematical trolling much more difficult. :) In case anyone is curious, the above "solutions" are called near-misses, since they're almost correct. A clever person came up with an algorithm to generate interesting near-misses for low exponents. See the table on page 15: http://arxiv.org/pdf/math/0005139v1.pdf Related: http://math.stackexchange.com/questions/526330/fermats-last-... Have fun!

Paper and discussion history. A mention is not an endorsement.