Ignacio F. Rúa

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A finite semifield D is a finite nonassociative ring with identity such that the set D * = D \ {0} is closed under the product. From any finite semifield a projective plane can be constructed. In this paper we obtain new semifield planes of order 81 by means of computational methods. These computer-assisted results yield to a complete classification (up to(More)
This paper is devoted to introducing a new approach for computing the topology of a real algebraic plane curve presented either parametrically or defined by its implicit equation when the corresponding polynomials which describe the curve are known only " by values ". This approach is based on the replacement of the usual algebraic manipulation of the(More)
We present a collection of methods and tools for computing the topology of real algebraic plane curves de .ned by bivariate polynomial equations that are known at certain values or easy to evaluate, but whose explicit description is not available.The principal techniques used are the reduction of the computation of the real roots of the discriminant to a(More)
Finite semifields (finite non necessarily associative division rings) have traditionally been considered in the context of finite geometries (they coordinatize projective semifield planes). New applications to coding theory, combinatorics and graph theory have broaden the potential interest in these rings. We show recent progress in the study of these(More)