Abstract
It is proved that the projection needed by the CAD algorithm needs only to compute the resultants, the discriminants, the leading coefficients and the constant coefficients of the input polynomials, provided they have be made square—free and relatively prime by GCD computations. This improves [7] first improvement by removing any dimension condition and dropping out from the projection set all coefficients of the input polynomials, other than the leading and the constant ones.
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References
Arnon, D. S., (1988), A Bibliography for Quantifier Elimination for Real Closed Fields, J. Symbolic Computation 5, pp. 267–274.
Arnon, D. S. and McCallum, S., (1982), Cylindrical Algebraic Decomposition by Quantifier Elimination, Proceedings of the European Computer Algebra Conference (EUROCAM ’82),Springer Lect. Notes Comp. Sci. 144, pp. 215–222.
Benedetti, R. and Risler J.-J., (1990), Real Algebraic and Semi-Algebraic Sets, Hermann (Paris).
Collins, G. E., (1975), Quantifier Elimination for the Elementary Theory of Real Closed Fields by Cylindrical Algebraic Decomposition, Lect Notes Comput. Sci., 33, pp. 134–183.
Collins, G. E. and Loos, R., (1982), Reals Zeros of Polynomials, Symbolic and Algebraic Computations (Computing Supplementum 4), (ed. Buchberger, B., Collins, G. E. and Loos R.), Springer Verlag (Wien, New York), pp. 83–94.
Davenport, J. H. and Heintz, J., (1988)., Real Quantifier Elimination is Doubly Exponential, J. Symbolic Computation, 5, pp. 29–35.
McCallum, S., (1984)., An Improved Projection Operator for Cylindrical Algebraic Decomposition, PhD Thesis, Univ. Wisconsin, Madison.
McCallum, S., (1988)., An Improved Projection Operator for Cylindrical Algebraic Decomposition of Three Dimensional Space, J. Symbolic Computation, 5, pp. 141–161.
Schwartz, J. T. and Sharir, M., (1983)., On the “Piano Movers” Problem, II, General Techniques for Computing Topological Properties of Real Algebraic Manifolds,Adv. Applied Math. 4, pp. 298–351.
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© 1994 Springer-Verlag New York, Inc.
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Lazard, D. (1994). An Improved Projection for Cylindrical Algebraic Decomposition. In: Bajaj, C.L. (eds) Algebraic Geometry and its Applications. Springer, New York, NY. https://doi.org/10.1007/978-1-4612-2628-4_29
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DOI: https://doi.org/10.1007/978-1-4612-2628-4_29
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