Real algebraic expressions are expressions whose leaves are integers and whose internal nodes are additions, subtractions, multiplications, divisions, k-th root operations for integral k, and taking roots of polynomials whose coefficients are given by the values of sub expressions. We consider the sign computation of real algebraic expressions, a task vital for the implementation of geometric algorithms. We prove a new separation bound for real algebraic expressions and compare it analytically and experimentally with previous bounds. The bound is used in the sign test of the number type leda_real.
CITATION STYLE
Burnikel, C., Funke, S., Mehlhorn, K., Schirra, S., & Schmitt, S. (2001). A separation bound for real algebraic expressions. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 2161, pp. 254–265). Springer Verlag. https://doi.org/10.1007/3-540-44676-1_21
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