Search Results - "Rojas, J. Maurice"

Counting Real Roots in Polynomial-Time via Diophantine Approximation by Rojas, J. Maurice

“…Suppose A = { a 1 , … , a n + 2 } ⊂ Z n has cardinality n + 2 , with all the coordinates of the a j having absolute value at most d , and the a j do not all…”
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Practical conversion from torsion space to Cartesian space for in silico protein synthesis by Parsons, Jerod, Holmes, J. Bradley, Rojas, J. Maurice, Tsai, Jerry, Strauss, Charlie E. M.

“…Many applications require a method for translating a large list of bond angles and bond lengths to precise atomic Cartesian coordinates. This simple but…”
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Computing zeta functions of large polynomial systems over finite fields by Cheng, Qi, Maurice Rojas, J., Wan, Daqing

“…We improve the algorithms of Lauder-Wan [11] and Harvey [8] to compute the zeta function of a system of m polynomial equations in n variables, over the q…”
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Optimizing n-variate (n+k)-nomials for small k by Pébay, Philippe, Maurice Rojas, J., Thompson, David C.

“…We give a high precision polynomial-time approximation scheme for the supremum of any honest n-variate (n+2)-nomial with a constant term, allowing real…”
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Correction to: Tropical varieties for exponential sums by Ergür, Alperen A., Paouris, Grigoris, Rojas, J. Maurice

“…A correction to this paper has been published: https ://doi.org/10.1007/s00208-019-01808-5 A subsidiary result (Theorem 1.1, on the undecidability of…”
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Probabilistic Condition Number Estimates for Real Polynomial Systems I: A Broader Family of Distributions by Ergür, Alperen A., Paouris, Grigoris, Rojas, J. Maurice

“…We consider the sensitivity of real roots of polynomial systems with respect to perturbations of the coefficients. In particular—for a version of the condition…”
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Tropical varieties for exponential sums by Ergür, Alperen A., Paouris, Grigoris, Rojas, J. Maurice

“…We study the complexity of approximating complex zero sets of certain n -variate exponential sums. We show that the real part, R , of such a zero set can be…”
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Sparse univariate polynomials with many roots over finite fields by Cheng, Qi, Gao, Shuhong, Maurice Rojas, J., Wan, Daqing

“…Suppose q is a prime power and f∈Fq[x] is a univariate polynomial with exactly t monomial terms and degree <q−1. To establish a finite field analogue of…”
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Counting Real Connected Components of Trinomial Curve Intersections and m -nomial Hypersurfaces by Li, Tien-Yien, Rojas, J. Maurice, Wang, Xiaoshen

“…We prove that any pair of bivariate trinomials has at most five isolated roots in the positive quadrant. The best previous upper bounds independent of the…”
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Root repulsion and faster solving for very sparse polynomials over p-adic fields by Rojas, J. Maurice, Zhu, Yuyu

“…For any fixed field K∈{Q2,Q3,Q5,…}, we prove that all univariate polynomials f with exactly 3 (resp. 2) monomial terms, degree d, and all coefficients in…”
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Tropical Varieties for Exponential Sums by Ergür, Alperen, Paouris, Grigoris, Rojas, J. Maurice

“…Mathematische Annalen, Vol. 377, pp. 863-882 (2020) We study the complexity of approximating complex zero sets of certain $n$-variate exponential sums. We show…”
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Arithmetic Multivariate Descartes' Rule by Rojas, J. Maurice

“…Let L be any number field or p-adic field and consider F:=(f1,...,fk) where f1,...,fk ΕL[x1, . . . ,xn] and no more than µ, distinct exponent vectors occur in…”
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Counting Roots of Polynomials Over Prime Power Rings by Cheng, Qi, Gao, Shuhong, Rojas, J. Maurice, Wan, Daqing

“…Open Book Series 2 (2019) 191-205 Suppose $p$ is a prime, $t$ is a positive integer, and $f\!\in\!\mathbb{Z}[x]$ is a univariate polynomial of degree $d$ with…”
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Probabilistic Condition Number Estimates For Real Polynomial Systems I: A Broader Family Of Distributions by Ergür, Alperen A, Rojas, J. Maurice, Paouris, Grigoris

“…FOCM 2018 We consider the sensitivity of real roots of polynomial systems with respect to perturbations of the coefficients. In particular - for a version of…”
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On the BCSS Proof of the Fundamental Theorem of Algebra by Rojas, J. Maurice

“…Section 10.4 of the 1998 Springer-Verlag book {\em Complexity and Real Computation}, by Blum, Cucker, Shub, and Smale, contains a particularly elegant proof of…”
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On the complexity of diophantine geometry in low dimensions by Rojas, J.M.

“…We consider the average-case complexity of some otherwise undecidable or open Diophantine problems. More precisely, we show that the following two problems can…”
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Counting Real Roots in Polynomial-Time for Systems Supported on Circuits by Rojas, J. Maurice

“…Suppose $A=\{a_1,\ldots,a_{n+2}\}\subset\mathbb{Z}^n$ has cardinality $n+2$, with all the coordinates of the $a_j$ having absolute value at most $d$, and the…”
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Optimizing n-variate (n + k)-nomials for small k: Symbolic and Numerical Algorithms by PEBAY, Philippe, ROJAS, J. Maurice, THOMPSON, David C

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Faster p-adic feasibility for certain multivariate sparse polynomials by Avendaño, Martín, Ibrahim, Ashraf, Rojas, J. Maurice, Rusek, Korben

“…We present algorithms revealing new families of polynomials admitting sub-exponential detection of p-adic rational roots, relative to the sparse encoding. For…”
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Root Repulsion and Faster Solving for Very Sparse Polynomials Over $p$-adic Fields by Rojas, J. Maurice, Zhu, Yuyu

“…For any fixed field $K\!\in\!\{\mathbb{Q}_2,\mathbb{Q}_3,\mathbb{Q}_5, \ldots\}$, we prove that all polynomials $f\!\in\!\mathbb{Z}[x]$ with exactly $3$ (resp…”
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