By Mohamed Elkadi (Editor), Bernard Mourrain (Editor), Ragni Piene (Editor)
This ebook spans the space among algebraic descriptions of geometric gadgets and the rendering of electronic geometric shapes in response to algebraic types. those contrasting issues of view motivate a radical research of the main demanding situations and the way they're met. The articles specialize in vital sessions of difficulties: implicitization, type, and intersection. Combining illustrative images, computations and evaluation articles this booklet is helping the reader achieve a company sensible take hold of of those topics.
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Extra info for Algebraic Geometry and Geometric Modeling (Mathematics and Visualization)
Laurent, P. Sablonniere, and L. ), pp. 163-172, Vanderbilt University Press, Nashville. 37. Khetan, A. (2003), The resultant of an unmixed bivariate system, Journal of Symbolic Computation, Vol. 36, pp. 425-442. 38. , and Goldman, R. (2004), Sylvester A-resultants for bivariate polynomials with planar Newton polygons, Proceedings of the 2004 International Symposium on Symbolic and Algebraic Computation (ISSAC), Santander, Spain. Algebraic geometry and geometric modeling: insight and computation 21 39.
Goldman and R. Krasauskas, AMS Contemporary Mathematics, Vol. 334, pp. 151-168. fr Summary. This paper describes a method, exploiting approximation complexes, for computing the implicit equation of a parameterized hypersurface. The fundamental ingredients and properties used in this approach are recalled and illustrated on simple examples. 1 Introduction We present in this short account a method for computing the image of a rational map from Pn−1 to Pn , under suitable hypotheses on the base locus and on the image.
As RI is the bigraded domain deﬁning Γ , the projection π(Γ ) is deﬁned by the graded domain RI ∩ k[T0 , . . , Tn ]. We have assumed that π(Γ ) is the hypersurface H = 0, so that this may be rewritten: (H) = P ∩ k[T0 , . . , Tn ]. In our example, with SE := RE [x, y, z, t] = Q[a, b, c, x, y, z, t]: P = ay−bz, at−cz, bt−cy, act−b(a+c)x)+(bx(z +t)−at2 )+(xy(z +t)−zt2 where we have separated the (minimal) generators of degrees 1, 2 and 3 for simplicity. Of course it follows that H = xy(z + t) − zt2 .