Quantifier Elimination for Trigonometric Polynomials by Cylindrical Trigonometric Decomposition

Pau, Petru; Schicho, Josef

doi:10.1006/jsco.1999.0352

Cited by 7 publications

(2 citation statements)

References 36 publications

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“…Their work is also related to the one by Armengol et al [Armengol et al 1998] and Gardeñes et al [Gardeñes and Trepat 1980;Gardeñes and Mielgo 1986] on modal interval arithmetic. Yet, these approaches require algebraizing trigonometric constraints, an operation known to slow down computation [Pau and Schicho 2000].…”

Section: Discussionmentioning

confidence: 99%

Interval constraint solving for camera control and motion planning

Benhamou

Goualard

Languénou

et al. 2004

ACM Trans. Comput. Logic

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Many problems in robust control and motion planning can be reduced to either finding a sound approximation of the solution space determined by a set of nonlinear inequalities, or to the "guaranteed tuning problem" as defined by Jaulin and Walter, which amounts to finding a value for some tuning parameter such that a set of inequalities be verified for all the possible values of some perturbation vector. A classical approach to solving these problems, which satisfies the strong soundness requirement, involves some quantifier elimination procedure such as Collins' Cylindrical Algebraic Decomposition symbolic method. Sound numerical methods using interval arithmetic and local consistency enforcement to prune the search space are presented in this article as much faster alternatives for both soundly solving systems of nonlinear inequalities, and addressing the guaranteed tuning problem whenever the perturbation vector has dimension 1. The use of these methods in camera control is investigated, and experiments with the prototype of a declarative modeler to express camera motion using a cinematic language are reported and commented upon.

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Section: Discussionmentioning

confidence: 99%

Interval constraint solving for camera control and motion planning

Benhamou

Goualard

Languénou

et al. 2004

ACM Trans. Comput. Logic

View full text Add to dashboard Cite

show abstract

“…These approaches might suffice for resolving constraints that arise during a computation, but proving nontrivial inequalities goes well beyond their capabilities. Some steps towards algorithms for proving inequalities involving elementary functions have been made [39,2], but these seem rather of theoretical interest and have not yet led to algorithmic proofs of inequalities that are interesting in their own right. It has also been pointed out that some difficult inequalities can be proven by reducing them to a special function identity which can then be shown by computer algebra [21,40,41,43], but this approach requires significant human interaction and is restricted to a very limited number of examples.…”

Section: Introductionmentioning

confidence: 99%