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Download e-book for iPad: Algorithms in Algebraic Geometry and Applications by M.-E. Alonso, E. Becker, M. F. Roy (auth.), Laureano

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 hide contemporary advancements within the conception and perform of computation in algebraic geometry and current new purposes in technology and engineering, really machine imaginative and prescient and thought of robotics. the quantity may be of curiosity to researchers operating within the parts of desktop algebra and symbolic computation in addition to to mathematicians and laptop scientists attracted to getting access to those subject matters.

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Example text

Since the splitting field K j is expressed by the residue class ring, we can check zero-relations among elements in Kf as the membership of the polynomials derived from zero-relations to the ideal. Corollary 6 We use the same notation as in theorem 5. Then: (1) There is an element gin Gj having (Cl, ... ,Ct) as its first t-part, if and only if fk (X Cl , ••• ,XCk ) belongs to the ideal J for k = 1, ... , t. (2) In the case (2) in theorem 5, for i = £ + 1, ... , n, i g is determined as an integer k such that Xk - Ai(x Cl , ...

G; + j) ----+ () (3) gives (since any associated prime of J i contains neither Xo nor I. we have H,,(nIAIJd = O:A/J, L i + l = 0). Therefore. Ii - dim AI L i + 1 > 1 and our definition of type. the last line implies x~iyPi AI = O. From this and (2) we obtaill our 0 ~m. Lemma 6. Let us assume that J; has type (Ei' Pi)' Then J i + 1 has type (3E;+h/~ 1. 3Pi +i+ 1). Proof. I; - dim AI(o). From (~~l we get (4) On the other hand, the exact sequence gives rise to E +bif- l -I P ,+i+l k'll (' I From Iemma 5 we k now tlat :r' o IS.

Symbolic. Compo 8, pp. 429-448 (1989). , Takeshima, T, Risa/AsiT - a computer algebra sys/,ern, ill ·"Froc. " ACM Press, pp. 387-396 (1992). I. Algebra. pp. 127-137 (1982). 50 H. Anai, M. Noro, K Yokoyama [15] Smedley, T. , A new modular algorithm for computation of algebraic number polynomial gcds, in Proc. ISSAC '89," ACM Press, pp. 91-94 (1989). [16] Soicher, L. , An algorithm for computing Galois groups, in "Computational Group Theory," Academic Press, pp. 291-296 (1984). [17] Stauduhar, R.

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