Journal of applied mathematics & informatics

The Korean Society for Computational and Applied Mathematics (한국전산응용수학회)
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DEGREE BOUND FOR EVALUATION OF ALGEBRAIC FUNCTIONS

  • Received : 2010.08.20
  • Accepted : 2010.09.08
  • Published : 2011.01.30
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Abstract

We give a constructive proof that a (partial) evaluation of a multivariate algebraic function with algebraic numbers is again an algebraic function. Especially, we obtain a bound on the degree of an evaluation with the degrees of the original algebraic function and the algebraic numbers evaluated. Furthermore, we show that our bound is sharp with an example.

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References

  1. E. Artin, Algebraic Numbers and Algebraic Functions, AMS Chelsea Publishing, 2006.
  2. G. A. Jones and D. Sinqerman, Complex Functions: An Algebraic and Geometric Viewpoint, Cambridge University Press, 1987.
  3. F. Klein, On Riemann's Theory Of Algebraic Functions And Their Integrals, Merchant Books, 2007.
  4. C. K. Yap, Fundamental Problems of Algorithmic Algebra, Oxford University Press, 2000.
  5. C. K. Yap, Theory of Real Computation According to EGC, In P. Hertling, C. M. Hoff- mann, W. Luther, N. Revol, Eds., Reliable Implementation of Real Number Algorithms: Theory and Practice, International Seminar Dagstuhl Castle, Germany, January 8-13, 2006, Revised Papers, Lecture Notes in Computer Science 5045(2008), 193-237.