Irreducibility of Polynomials with Low Absolute Values
نویسنده
چکیده
منابع مشابه
Deterministic Irreducibility Testing of Polynomials over Large Finite Fields
We present a sequential deterministic polynomial-time algorithm for testing dense multivariate polynomials over a large finite field for irreducibility. All previously known algorithms were of a probabilistic nature. Our deterministic solution is based on our algorithm for absolute irreducibility testing combined with Berlekamp’s algorithm.
متن کاملIndecomposability of Polynomials via Jacobian Matrix
Indecomposable polynomials are a special class of absolutely irreducible polynomials. Some improvements of important effective results on absolute irreducibility have recently appeared using Ruppert’s matrix. In a similar way, we show in this paper that the use of a Jacobian matrix gives sharp bounds for the indecomposability problem.
متن کاملFast Parallel Absolute Irreducibility Testing
We present a fast parallel deterministic algorithm for testing multivariate integral polynomials for absolute irreducibility, that is irreducibility over the complex numbers. More precisely, we establish that the set of absolutely irreducible integral polynomials belongs to the complexity class NC of Boolean circuits of polynomial size and logarithmic depth. Therefore it also belongs to the cla...
متن کاملA Construction for Absolute Values in Polynomial Rings
‖b+ c‖ ≤ max (‖b‖, ‖c‖) then the value ‖b‖ is called non-archimedean. The thus delimited nonarchimedean values are of considerable arithmetic interest. They are useful in questions of divisibility and irreducibility and in fact often correspond exactly to the prime ideals of the given ring. This paper is devoted to the explicit construction of non-archimedean values. More specifically, given al...
متن کاملPolynomial irreducibility testing through Minkowski summand computation
In this paper, we address the problem of deciding absolute irreducibility of multivariate polynomials. Our work has been motivated by a recent work due to Gao et. al. [1, 2, 3] where they have considered the problem for bivariate polynomials by studying the integral decomposability of polygons in the sense of Minkowski sum. We have generalized their result to polynomials containing arbitrary nu...
متن کامل