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Computing in the Field of Complex Algebraic Numbers

Adam Strzebonski
Organization: Wolfram Research, Inc.
Department: Kernel Technology
Journal / Anthology

Journal of Symbolic Computation
Year: 1997
Volume: 24
Issue: 6
Page range: 647-656

In this paper we present two methods of computing with complex algebraic numbers. The first uses isolating rectangles to distinguish between the roots of the minimal polynomial, the second method uses validated numeric approximations. We present algorithms for arithmetic and for solving polynomial equations, and compare implementations of both methods in Mathematica.

*Mathematics > Algebra > Polynomials
*Mathematics > Calculus and Analysis > Complex Analysis