This research was partially supported by National Science Foundation grants GJ-30125X and DCR74-13278.
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References
Brown, W.S., On Euclid's Algorithm and the Computation of Polynomial Greatest Common Divisors, J. ACM, vol. 18, no. 4 (Oct. 1971) pp. 478–504.
Brown, W.S., and Traub, J.F., On Euclid's Algorithm and the Theory of Subresultants, J. ACM, vol. 18, no. 4 (Oct. 1971), pp. 505–514.
Cohen, P.J., Decision Procedures for Real and p-adic Fields, Comm. Pure and Applied Math., vol. XXII, no. 2 (March 1969), pp. 131–151.
Collins, G.E., Subresultants and Reduced Polynomial Remainder Sequences, J. ACM, vol. 14, no. 1, (Jan. 1967), pp. 128–142.
Collins, G.E., The Calculation of Multivariate Polynomial Resultants, J. ACM, vol. 18, no. 4 (Oct. 1971), pp. 515–532.
Collins, G.E., Computer Algebra of Polynomials and Rational Functions, Am. Math. Monthly, vol. 80, no. 7 (Aug.-Sept. 1973), pp. 725–755.
Collins, G.E., Efficient Quantifier Elimination for Elementary Algebra (abstract), Symposium on Complexity of Sequential and Parallel Numerical Algorithms, Carnegie-Mellon University, May 1973.
Collins, G.E., Quantifier Elimination for Real Closed Fields by Cylindrical Algebraic Decomposition — Preliminary Report, Proceedings of EUROSAM 74, STGSAM Bulletin, Vol. 8, no. 3 (August 1974), pp. 80–90.
Fischer, M.J., and Rabin, M.O., Super-Exponential Complexity of Presburger Arithmetic, M.I.T. MAC Tech. Memo. 43, Feb. 1974.
Goldhaber, J.K., and Ehrlich, G., Algebra, MacMillan Co., 1970.
Heindel, L.E., Integer Arithmetic Algorithms for Polynomial Real Zero Determination, J. ACM, vo. 18, no. 4 (Oct. 1971), pp. 533–548.
Loos, R., G.K., A Constructive Approach to Algebraic Numbers, SIAM Journal on Computing, to appear.
Marden, M., The Geometry of the Zeros of a Polynomial in a Complex Variable, Am. Math. Soc., Providence, 1949.
Musser, D.R., Algorithms for Polynomial Factorization (Ph.D. Thesis), Univ. of Wisconsin Computer Sciences Dept. Tech. Report No. 134, Sept. 1971.
Musser, D.R., Multivariate Polynomial Factorization, J.ACM., Vol. 22, No. 2 (April 1975), pp. 291–308.
Rubald, C.M., Algorithms for Polynomials over a Real Algebraic Number Field (Ph.D. Thesis), Computer Sciences Dept. Tech. Report No. 206, Jan. 1974.
Seidenberg, A., A New Decision Method for Elementary Algebra, Annals of Math., vol. 60, no. 2 (Sept. 1954), pp. 365–374.
Tarski, A., A Decision Method for Elementary Algebra and Geometry, second ed., rev., Univ. of California Press, Berkeley, 1951.
van der Waerden, B.L., Modern Algebra, vol. I, F. Ungar Co., New York, 1953.
Böge, W., private communication, June 1973
Holthusen, C., Vereinfachungen für Tarski's Entscheidungsverfahren der Elementaren Reelen Algebra (Diplomarbeit, University of Heidelberg), January 1974.
Collins, G.E., and E. Horowitz, The Minimum Root Separation of a Polynomial, Math. of Comp., Vol. 28, No. 126, (April 1974), pp. 589–597.
Mignotte, M., An Inequality About Factors of Polynomials, Math. of Comp., Vol. 28, No. 128 (October 1974), pp. 1153–1157.
Knuth, D.E., The Art of Computer Programming, Vol. 2: Seminumerical Algorithms, Addison-Wesley, Reading, 1969.
Schönhage, A., and V. Strassen, Schnelle Multiplikation großer Zahlen, Computing, Vol. 7, pp. 281–292.
Ferrante, J., and C. Rackoff, A Decision Procedure for the First Order Theory of Real Addition with Order, SIAM Journal on Computing, Vol. 4, No. 1 (March 1975), pp. 69–76.
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Collins, G.E. (1975). Quantifier elimination for real closed fields by cylindrical algebraic decompostion. In: Brakhage, H. (eds) Automata Theory and Formal Languages. Lecture Notes in Computer Science, vol 33. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-07407-4_17
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