43 citations · 137 across the 39 of their papers we have counts for
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Trinomials and Deterministic Complexity Limits for Real Solving
Emma Boniface, Weixun Deng, J. Maurice Rojas
We detail an algorithm that -- for all but a fraction of with exactly monomial terms, degree , and all coefficients in $\{-H,\ldo…
Smoothed Analysis for the Condition Number of Structured Real Polynomial Systems
Alperen A. Ergür, Grigoris Paouris, J. Maurice Rojas
We consider the sensitivity of real zeros of structured polynomial systems to perturbations of their coefficients. In particular, we provide explicit estimates for condition number…
New Subexponential Fewnomial Hypersurface Bounds
Jens Forsgård, Mounir Nisse, J. Maurice Rojas
Suppose are real numbers, is a set of points not all lying in the same affine hyperplane, $y\!\in\!\mathbb{R}^n…
A-Discriminants for Complex Exponents, and Counting Real Isotopy Types
J. Maurice Rojas, Korben Rusek
We extend the definition of -discriminant varieties, and Kapranov's parametrization of -discriminant varieties, to complex exponents. As an application, w…
Randomization, Sums of Squares, and Faster Real Root Counting for Tetranomials and Beyond
Osbert Bastani, Christopher J. Hillar, Dimitar Popov +1
Suppose f is a real univariate polynomial of degree D with exactly 4 monomial terms. We present an algorithm, with complexity polynomial in log D on average (relative to the stable…
Fewnomial Systems with Many Roots, and an Adelic Tau Conjecture
Kaitlyn Phillipson, J. Maurice Rojas
Consider a system F of n polynomials in n variables, with a total of n+k distinct exponent vectors, over any local field L. We discuss conjecturally tight bounds on the maximal num…