semialgebraic geometry

Semialgebraic geometry is a branch of mathematics that studies shapes and spaces defined by polynomial equations and inequalities, involving real numbers. It focuses on understanding the structure of sets formed by solutions to these algebraic expressions, such as regions bounded by curves or surfaces determined by polynomial conditions. This field combines algebraic and geometric ideas to analyze properties like connectivity, dimension, and the nature of these sets, which are often used in optimization, robotics, and computer science to model and solve real-world problems involving complex constraints.