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5 votes

Nonnegative coefficients of a product of polynomials

If however, as I suspect, there is no algorithm (to decide strict positivity on an orthant), then there is a problem. …
David Handelman's user avatar
8 votes
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One of Poincaré's theorems about positive rational functions

For the more general problem, given $P$ with nonnegative coefficients, and $f$, iff conditions for there to be $n$ such that $P^n f$ has no negative coefficients are given in Deciding eventual positivityPositivity at the zero-dimensional faces comes for free from $f > 0$ on the positive orthant. …
David Handelman's user avatar
17 votes
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When can a function be made positive by averaging?

A fine variation is given in Deciding eventual positivity of polynomials, Ergodic theory and dynamical systems (1986) 6, 57-79, which determines, given $P$ with no negative coefficients, when there exists …
David Handelman's user avatar