algorithmic framework for symbolic-numeric sign analysis of mathematical expressions

This paper presents a comprehensive algorithmic framework for analyzing the sign behavior of mathematical expressions over the real domain. the maple implementation combines symbolic computation, numerical analysis, and interval arithmetic to determine whether an expression is always positive, always negative, or changes sign, while precisely identifying the intervals of positivity and negativity. the algorithm offers a robust solution that handles a wide range of mathematical expressions, including polynomials, radicals, trigonometric functions, and rational expressions.