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2011•Journal of applied mathematics & informaticsRequires access

DEGREE BOUND FOR EVALUATION OF ALGEBRAIC FUNCTIONS

Sung-Woo Choi

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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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What this paper is about

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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Available 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.

Key concepts: Mathematics, Algebraic function, Algebraic number, Degree (music), Function field of an algebraic variety, Real algebraic geometry, Algebraic surface, Dimension of an algebraic variety

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