A Separation Bound for Real Algebraic Expressions
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 subexpressions. 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.