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

ISBN-10: 3034899084

ISBN-13: 9783034899086

The current quantity encompasses a number of refereed papers from the MEGA-94 symposium held in Santander, Spain, in April 1994. They disguise fresh advancements within the concept and perform of computation in algebraic geometry and current new functions in technological know-how and engineering, relatively desktop imaginative and prescient and thought of robotics. the quantity may be of curiosity to researchers operating within the components of computing device algebra and symbolic computation in addition to to mathematicians and desktop scientists drawn to having access to those issues.

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**Sample text**

Iii) The modified Trager algorithm for algebraic factorization proposed by Noro and Takeshima [13] has been extended and applied effectively to computation of splitting fields of polynomials. By this extension, we can compute the splitting field of a given polynomial very efficiently. (iv) From a practical point of view, we think, there are cases where the direct approach works well such as a case where no table is known for the degree of an input polynomial but its splitting field is considerably small.

We want to give explicitly two integers, 'Yi+1 and 'T]i+1, such that 1 Xo,i+1 -1'7i+ JH 1 ~ (Ji, G H 1 ) . To this end, let DH1 = deg AIKi+1' which is easily estimated by Bezout's theorem. From (1), we find that c5i+1-1H1J J Xo i+1 ~ H1 n I H1 n K H1· (2) Thus, we must only control the embedded components with a suitable modification of Kollar's method in Patrice Philippon's algebraic version (see [PI] and [P2]). Definition. Let J ~ A be a homogeneous ideal. We say that J has type (E, p) if for any and for any a < dim AIJ - dim AI(a) we have x6 .

By Gl.. i or simply G(il' we denote the poinlwise stab'ilize'r oj 1, .... i in G. lhal is, G(il = {g E Glj9 = j for j = 1, ... , i}. Moreover set G(O) = G. Then. /liP have a chain of stabilizers: Let k be the smallest integer such that G(kl = 1. We call a sequence [1,2 .... ,k] 36 H. Anai, M. Noro, K. Yokoyama a basis for C. For each i in the basis [1, ... , kJ, we denote by Si a set of all (right) coset representatives of G(i) in G(i-l)' Therefore, by setting Si = (i) (i) {8 1 , ... , Sti }, Then, the union S = U~=1 Si generates G.