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

collaborators

39 papers

cs.SC2022

Sturm's Theorem with Endpoints

Philippe Pébay, J. Maurice Rojas, David C. Thompson

Sturm's Theorem is a fundamental 19th century result relating the number of real roots of a polynomial $f$ in an interval to the number of sign alternations in a sequence of polyno…

math.AG2022

Trinomials and Deterministic Complexity Limits for Real Solving

Emma Boniface, Weixun Deng, J. Maurice Rojas

We detail an algorithm that -- for all but a $\frac{1}{Ω ( l o g ( d H ))}$ fraction of $f \in Z [x]$ with exactly $3$ monomial terms, degree $d$ , and all coefficients in $\{-H,\ldo…

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