J. Rojas

activity

19972022

most citedHigh Probability Analysis of the Condition Number of Sparse Polynomial Systems

43 citations · 137 across the 39 of their papers we have counts for

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14 papers · 1 filter

math.NT2021

Root Repulsion and Faster Solving for Very Sparse Polynomials Over $p$ -adic Fields

J. Maurice Rojas, Yuyu Zhu

For any fixed field $K \in {Q_{2}, Q_{3}, Q_{5}, \dots}$ , we prove that all polynomials $f \in Z [x]$ with exactly $3$ (resp. $2$ ) monomial terms,…

math.NT2021

Sub-Linear Point Counting for Variable Separated Curves over Prime Power Rings

Caleb Robelle, J. Maurice Rojas, Yuyu Zhu

Let $k, p \in N$ with $p$ prime and let $f \in Z [x_{1}, x_{2}]$ be a bivariate polynomial with degree $d$ and all coefficients of absolute value at most $p^{k}$ . Suppose als…

math.NT2020

Computing zeta functions of large polynomial systems over finite fields

Qi Cheng, J. Maurice Rojas, Daqing Wan

In this paper, we improve the algorithms of Lauder-Wan \cite{LW} and Harvey \cite{Ha} to compute the zeta function of a system of $m$ polynomial equations in $n$ variables over the…

math.NT2020★ 1 cited

A complexity chasm for solving univariate sparse polynomial equations over $p$ -adic fields

J. Maurice Rojas, Yuyu Zhu

We reveal a complexity chasm, separating the trinomial and tetranomial cases, for solving univariate sparse polynomial equations over certain local fields. First, for any fixed fie…

math.NT2017★ 9 cited

Counting Roots of Polynomials Over Prime Power Rings

Qi Cheng, Shuhong Gao, J. Maurice Rojas +1

Suppose $p$ is a prime, $t$ is a positive integer, and $f \in Z [x]$ is a univariate polynomial of degree $d$ with coefficients of absolute value $< p^{t}$ . We show that f…

math.NT2014★ 2 cited

Sparse Univariate Polynomials with Many Roots Over Finite Fields