Generalizing The Davenport-Mahler-Mignotte Bound -- The Weighted Case — mentioned by JadeNB

Mon, 24 Jan 2022 17:01:57 GMT

A request: please always link to abstract pages of articles, not directly to PDFs. https://arxiv.org/abs/2005.07843

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

Generalizing The Davenport-Mahler-Mignotte Bound -- The Weighted Case — mentioned by abetusk

Mon, 24 Jan 2022 15:59:31 GMT

So, to state explicitly, given a list of positive integers, a_i, and coefficients, d_i \in {-1,1}, test whether \sum_i d_i sqrt(a_i) <=? 0. Now, construct a polynomial, P(z) = \prod_i (z^2 - a_i), and this gives a (univariate) polynomial so that a Mahler-Mignotte like bound can be used. I guess there's different levels of bounds you can use (Mahler, Mahler-Mignotte, Davenporte-Mahler-Mignotte [0]) but they all involve the discriminant, the deg to the deg power (n^n) and maybe some other factors which put it neatly in a polynomial time bit representation. One bound puts it in the 2^{-2s^2}…

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

Generalizing The Davenport-Mahler-Mignotte Bound -- The Weighted Case · HackerPapers discussions

Generalizing The Davenport-Mahler-Mignotte Bound -- The Weighted Case — mentioned by JadeNB

Generalizing The Davenport-Mahler-Mignotte Bound -- The Weighted Case — mentioned by abetusk