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

ISBN-10: 3034891040

ISBN-13: 9783034891042

ISBN-10: 3034899084

ISBN-13: 9783034899086

The current quantity incorporates a choice of refereed papers from the MEGA-94 symposium held in Santander, Spain, in April 1994. They conceal contemporary advancements within the idea and perform of computation in algebraic geometry and current new purposes in technology and engineering, rather computing device imaginative and prescient and thought of robotics. the amount 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 attracted to having access to those subject matters.

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**Extra resources for Algorithms in Algebraic Geometry and Applications**

**Sample text**

From this, we think that both approaches are important for further study of the subject. Especially, usage of a certain knowledge of the Galois group will make direct methods more efficient. Anyway, since both approaches llse factorization as their parts, progress of factorization will make them more efficient. Appendix Risa/ Asir [13] is a computer algebra system, which provides a programming system Asir with several subroutine libraries which can also be used as the parts of other programs. It runs on major UNIX workstatiolls.

N} \ C do 9 <- CHECK([l, ... ,j, kJ, DP) Computation of the splitting fields 37 if g # 0 then L i-~ L U {g} else g i-- CHECK([i] , DP) L i-- L U {g} for each gEL do hi-- COMPLETE(g,DP) 5i--5U{h} return 5 end \Ve will give a bound on the number of normal form computations with respect to the ideal J. Since the total complexity of the procedure is the product of the number of polynomials for which we compute the normal forms and the cost of one normal form computation. the following bound shows the efficiency of the procedure.

Fz. f. f;) is ir-reducible if mi = 1 for a factor fi' Proof. By the definition of the norm, f is a factor of NurmK(n)/K(J) over K(a). Since f is square-free, we have f = GCIJ(J . f;). By lemma 12, each fi contains some irreducible factors of f. Therefore. f. f;) is not a constant. If mi = I, fi must be the norm of an irreducible factor h of f. This implies that GCD(f, fi) is irreducible. D. r1:=l AFACTOJLTRAGER is a recursive procedure. At the hottom of the recursion, factorizer for integral polynomials is called.

### Algorithms in Algebraic Geometry and Applications by M.-E. Alonso, E. Becker, M. F. Roy (auth.), Laureano González-Vega, Tomás Recio (eds.)

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