Download Automated Deduction in Geometry: 10th International by Francisco Botana, Pedro Quaresma PDF

By Francisco Botana, Pedro Quaresma

ISBN-10: 331921361X

ISBN-13: 9783319213613

This e-book constitutes the completely refereed post-workshop complaints of the tenth foreign Workshop on automatic Deduction in Geometry, ADG 2014, held in Coimbra, Portugal, in July 2014. The eleven revised complete papers awarded during this quantity have been conscientiously chosen from 20 submissions. The papers exhibit the craze set of present learn in computerized reasoning in geometry.

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Read or Download Automated Deduction in Geometry: 10th International Workshop, ADG 2014, Coimbra, Portugal, July 9-11, 2014, Revised Selected Papers PDF

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Additional resources for Automated Deduction in Geometry: 10th International Workshop, ADG 2014, Coimbra, Portugal, July 9-11, 2014, Revised Selected Papers

Sample text

Generalizing finite frameworks to a periodic setting [8–10] has led to many advances in understanding bar-and-joint frameworks. In a similar spirit, we have initiated in [7] the study of rigidity theoretic properties of volume frameworks, where the generalization goes from graphs with fixed edge lengths to hypergraphs with fixed hyperedge volumes. Deformation Spaces of Polygons. Deformation spaces of bar-and-joint structures have been characterized only in special cases [23,30]. Particularly studied, and in different geometries, is the polygonal case [5,24–27].

Inf. Process. Lett. 62(5), 245–250 (1997) 8. : On finding shortest paths on convex polyhedra. Technical report 1495, University of Maryland (1985) 9. : On shortest paths in polyhedral spaces. SIAM J. Comput. 15(1), 193–215 (1986) Volume Frameworks and Deformation Varieties Ciprian S. edu Abstract. A volume framework is a (d + 1)-uniform hypergraph with real numbers associated to its hyperedges. A realization is given by placing the vertices as points in Rd in such a way that the volumes of the simplices induced by the hyperdges have the assigned values.

Xn ), where Qi ∈ {∀, ∃} and Φ is a Boolean combination of relations involving polynomials pi (x1 , . . , xn ), find an equivalent Ψ (x1 , . . , xk ), where Ψ is a Boolean combination of relations involving polynomials qi (x1 , . . , xk ). In fact, we cannot solve this in the language of algebraic geometry: we need semi-algebraic geometry, allowing > as well1 as =. The necessity of > follows from the fact of the example ∃y : x = y 2 ⇔ (x > 0) ∨ (x = 0); its sufficiency is the point of Tarski’s work.

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