By M.-E. Alonso, E. Becker, M. F. Roy (auth.), Laureano González-Vega, Tomás Recio (eds.)

The current quantity includes a number of refereed papers from the MEGA-94 symposium held in Santander, Spain, in April 1994. They disguise fresh advancements within the idea and perform of computation in algebraic geometry and current new purposes in technology and engineering, fairly computing device imaginative and prescient and conception of robotics. the quantity could be of curiosity to researchers operating within the components of computing device algebra and symbolic computation in addition to to mathematicians and computing device scientists drawn to having access to those issues.

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In the Appendix. we list several bench-mark results of the method implemented on the Risa/ Asir system. 2 Representation of the splitting field Here, we provide some notions on the splitting fields which can be found in text books on Galois theory. Let f(x) be an irreducible and monic polynomial in x over the rational number field Q. We denote the set of all roots of f(x) in the algebraic closure Q of Q by f and thus, f = {al,'" ,an}, where n = deg(f(x)). ThelL the splitting field K f of f (x) is the finite extension field Q( 0, f) by adjoining all roots.

GIuSTI and C. SESSA. "The membership problem for unmixed polynomial ideals is solvable in single exponential time", Discrete Appl. Math. 33, pp. 73-94 (1991). M. ELKADI, "Bornes pour Ie degre et les hauteurs dans Ie probleme de division", to appear in Michigan Math . TournaI. [FG] N. FITCHAS and A. GALLIGO, "Nullstellensatz effectif et conjecture de Serre (Theorcme de Quillen-Suslin) pour Ie Caleul Forme]"" . l\Iath. Nachr, 149, pp. 231 253 (1990). [GPL] L. GRUSON. R. LAZARSFELD and C. PESKINE.

It has been shown to be much faster, and in fact of polynomial complexity in n and the number of points, to use the Ruchberger-MejJJer algorithm for this task (ef. [MMM]). Based on the results of this algorithm, many elementary properties of X and its homogeneous coordinate ring R like its Hilhert function, Cohen-Macaulay type, a minimal system of generators of h:. the separators (ef. [GKR], sect. 2), etc. can be easily computed. What is the canonical module! In this paper we want to deal computationally with deeper geometric properties of X resp.