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

The current quantity features a choice of refereed papers from the MEGA-94 symposium held in Santander, Spain, in April 1994. They conceal contemporary advancements within the concept and perform of computation in algebraic geometry and current new purposes in technological know-how and engineering, fairly desktop imaginative and prescient and conception of robotics. the quantity can be of curiosity to researchers operating within the components of machine algebra and symbolic computation in addition to to mathematicians and computing device scientists drawn to getting access to those subject matters.

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**Example text**

Ie-l (Xl, ... ,x£-I) >, • Q£+l is expressed as a polynomial A£+! (QI, ... , Q£), • Qn is expressed as a polynomial An (QI' ... , Q£). Moreover, by letting fi(XI, ... ,X£,Xi) = Xi - Ai(xl, ... ,Xf) for defining = £ + 1, ... , n, we have more convenient representation of Kr i Q;, Computation of the splitting fields where J is the ideal generated by polynomials II, .... fn· J relations between the roots 01, ... e" 33 IS the ideal of Definition 1 We call f the length of the representation of K f with resperi to For each i, i = 1, ....

28, pp. 97-116 (1981). [PI] P. 88 (1988). [P2] P. PHILIPPON, "Denominateurs dans Ie theoreme des zeros de Hilbert", Acta Arith. 58, pp. 1-25 (1991). [ZS] O. ZARISKI and P. 2, Van Nostrand, Princeton 1960; Springer-Verlag, Berlin-Heidelberg-New York 1986. F. Amoroso (amoroso@dm. unipi. it) Dip. di Matematica, University of Pisa, Via F. Buonarroti, 2. 56100 Pisa (Italy). Progress in Mathematics, Vol. 143, © 1996 Birkhauser Verlag Basel/Switzerland Computation of the splitting fields and the Galois groups of polynomials H.

Q£) = 0, where Ie(XI, ... ,X£-I,X) is a non-linear irreducible factor of f(x) over Ql[XI, ... ,x£-lll < ft (xI), ... ,Ie-l (Xl, ... ,x£-I) >, • Q£+l is expressed as a polynomial A£+! (QI, ... , Q£), • Qn is expressed as a polynomial An (QI' ... , Q£). Moreover, by letting fi(XI, ... ,X£,Xi) = Xi - Ai(xl, ... ,Xf) for defining = £ + 1, ... , n, we have more convenient representation of Kr i Q;, Computation of the splitting fields where J is the ideal generated by polynomials II, .... fn· J relations between the roots 01, ...