Computational algebraic geometry

Computational algebraic geometry is a branch of mathematics that uses algorithms and computer calculations to study geometric objects defined by polynomial equations. It helps understand shapes like curves, surfaces, and more complex structures by analyzing their equations, finding points, intersections, or properties. This field combines algebra (manipulating equations) with geometry (studying shapes) to solve problems that are difficult to handle by hand, enabling applications in areas like robotics, computer graphics, coding theory, and physics. Essentially, it transforms intricate geometric problems into algebraic computations that computers can efficiently solve.