Topic
Generic polynomial
About: Generic polynomial is a research topic. Over the lifetime, 608 publications have been published within this topic receiving 6784 citations.
Papers published on a yearly basis
Papers
More filters
TL;DR: In this paper, the authors provide an explicit description of the twisted Lie algebras of PGL3-equivariant derivations on the coordinate rings of F -irreducible PGL 3-torsors in terms of nine-dimensional central simple algesbras over F.
4 citations
Patent•
08 Feb 2002
TL;DR: In this paper, a finite field multiplication of first and second Galois elements having n bit places and belonging to a Galois field GF 2 n described by an irreducible polynomial is performed by forming an intermediate result Z of intermediate sums of partial products of bit width 2n−2 in an addition part of the Galois multiplier, whereby after all XOR's are traversed a result E with n bits is computed.
Abstract: Finite field multiplication of first and second Galois elements having n bit places and belonging to a Galois field GF 2 n described by an irreducible polynomial is performed by forming an intermediate result Z of intermediate sums of partial products of bit width 2n−2 in an addition part of a Galois multiplier. The intermediate result Z is processed in a reduction part of a Galois multiplier by modulo dividing by the irreducible polynomial, whereby after all XOR's are traversed a result E with n bits is computed.
4 citations
Journal Article•
TL;DR: A new approach is given based on the idea of using resultant in order to know the common factors between an empirical polynomial and a generic polynomials in its neighborhood.
Abstract: In this paper the concept of neighborhood of a polynomial is analyzed. This concept is spreading into Scientific Computation where data are often uncertain, thus they have a limited accuracy. In this context we give a new approach based on the idea of using resultant in order to know the common factors between an empirical polynomial and a generic polynomial in its neighborhood. Moreover given a polynomial, the Square Free property for the polynomials in its neighborhood is investigated.
4 citations
TL;DR: In this paper, the authors consider the problem of embedding problems over number fields with the knowledge of the ramification set of the solutions of the embeddings, and show that the problem is solvable with the additional condition that the solutions are unramified outside the ring of integers.
Abstract: An interesting point concerning embedding problems over number fields is the knowledge of the ramification set of its solutions. In the present work, we examine the following problem: Let K be a number field, G K its absolute Galois group, ~b an epimorphism from G K onto a finite group G and L[ K the Galois extension associated to qS. We consider the embedding problem: G~ 1 ~A >E ~G ~1 where E is a central extension of G, i.e. A is a trivial G-module, and assume ~b*e = 0 in H2(GK, A), for e the element in H2(G, A) corresponding to E. For the solvable embedding problem (L J K, e), we want to get a solution field M such that the extension M [ K has a reduced ramification set. To study this problem, we take a finite set S of prime ideals of the ring of integers (9 K of the field K containing the prime ideals ramifying in L[ K. We state the embedding problem (L I K, 0 with the additional condition that the solutions are unramified outside S. We denote this new problem by (L I K, e, S). If G s is the Galois group of the maximal extension of K, unramified outside S, we have a commutative diagram:
4 citations
TL;DR: In this article, the Galois groups over the rationals associated with generalized Laguerre polynomials whose discriminants are rational squares are computed, where n and α are integers.
4 citations