We present an algorithm that finds polynomials with many roots modulo many primes by rotating candidate Number Field Sieve polynomials using the Chinese Remainder Theorem. We also...
We describe an algorithm to count the number of distinct real zeros of a polynomial (square) system f. The algorithm performs O(log(nD(f))) iterations (grid refinements) where n is...
Felipe Cucker, Teresa Krick, Gregorio Malajovich, ...
We say that a polynomial f(x1, . . . , xn) is indecomposable if it cannot be written as a product of two polynomials that are defined over disjoint sets of variables. The polynom...
The maximization of a positive (semi)definite complex quadratic form over a finite alphabet is NP-hard and achieved through exhaustive search when the form has full rank. Howeve...
Abstract. The goal of this paper is to further study the index calculus method that was first introduced by Semaev for solving the ECDLP and later developed by Gaudry and Diem. In...