A solution to Kahan's problem (SIGSAM problem no. 9)

ABSTRACT

The problem was ([Kah75]) :Let the variables a,b,c,d (which are supposed to take real values) be interpreted as the center (c,d) and the principal semiaxes a,b of an ellipse. Find necessary and sufficient conditions for a,b,c,d such that[EQUATION]holds. Furthermore the conditions should be given as polynomial inequalities.

REFERENCES

• 1: W. Kahan, Problem #9: an ellipse problem, ACM SIGSAM Bulletin, v.9 n.3, p.11-12, August 1975 [doi>10.1145/1088309.1088312]
• 2: George E. Collins, The SAC-1 system: An introduction and survey, Proceedings of the second ACM symposium on Symbolic and algebraic manipulation, p.144-152, March 23-25, 1971, Los Angeles, California, United States [doi>10.1145/800204.806279]
• 3: George E. Collins, The Calculation of Multivariate Polynomial Resultants, Journal of the ACM (JACM), v.18 n.4, p.515-532, Oct. 1971 [doi>10.1145/321662.321666]
• 4: {Web} H. Weber, "Lehrbuch der Algebra", Vol. 1, 3rd edition, Chelsea Publishing Company, New York, N. Y., § 84.