By Mohamed Elkadi (Editor), Bernard Mourrain (Editor), Ragni Piene (Editor)

This booklet spans the gap among algebraic descriptions of geometric items and the rendering of electronic geometric shapes in response to algebraic types. those contrasting issues of view encourage an intensive research of the major demanding situations and the way they're met. The articles specialise in very important periods of difficulties: implicitization, category, and intersection. Combining illustrative photos, computations and evaluate articles this publication is helping the reader achieve an organization useful clutch of those matters.

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**Example text**

2001), Resultant over the residual of a complete intersection, Jour. of Pure and Applied Algebra, Vol. 164, pp. 35-57. 6. Bus´e, L. P. (2003), On the closed image of a rational map and the implicitization problem, Journal of Algebra, Vol. 265, pp. 312-357 7. Chen, F. and Wang, W. (2004), Computing the singular points of a planar rational curve using the µ-basis, preprint. 8. Chtcherba, A. and Kapur, D. (2000), Conditions for exact resultants using the Dixon formulation, International Symposium on Symbolic and Algebraic Computation (ISSAC 2000), St.

Thomassen2,3 , Elmar M. Wurm1 , uttler1 Tor Dokken2 and Bert J¨ 1 2 3 Institute of Applied Geometry, Johannes Kepler University, Altenberger Str. O. O. no Summary. We compare several methods for approximate implicitization by piecewise polynomials which have been developed by the authors, and a linear-algebrabased numerical method for implicitization which is provided as a part of MAPLE. We investigate both quantitative criteria (such as computing time, memory use, and the error of the approximation) and qualitative criteria.

Bus´e, L. (2001), Residual resultant over the projective plane and the implicitization problem, Proceedings of ISSAC 2001, pp. 48-55. 3. Bus´e, L. and Chardin, M. (2004), Implicitizing rational hypersurfaces using approximation complexes, submitted to Journal of Symbolic Computation. 4. , and D’Andrea, C. (2003), Implicitization of surfaces in P3 in the presence of base points, Journal of Algebra and its Applications, Vol. 2, pp. 189-214. 5. , and Mourrain, B. (2001), Resultant over the residual of a complete intersection, Jour.