Symbolic computation

Symbolic computation, also known as symbolic processing, is a form of computing that uses symbols to represent data. It contrasts with numerical computation, which typically uses numbers to represent data. Symbolic computation is used in a variety of fields, including computer science, mathematics, and engineering.

Symbolic computation can be used to solve problems that would be impossible or too time-consuming to solve with traditional numerical methods. For example, it can be used to find solutions to equations that can’t be handled with numerical methods. It is also used to solve problems that require more than just numerical calculation.

Symbolic computation works by transforming symbols into more basic elements of the problem. For example, the term “x + y” can be broken down into two symbols “x” and “y,” which themselves can be broken down further into individual operations. This process of breaking down problems into smaller pieces is known as symbolic manipulation.

Symbolic computation systems use algorithms to find solutions to problems. These algorithms are based on the principles of logic, such as the distributive law and De Morgan’s laws.

Symbolic computation has been used in fields such as artificial intelligence, robotics, and language processing. Symbolic computation is also used to solve problems related to optimization, search, and planning. It has been applied in fields such as operations research, economics, and game theory.

Symbolic computation also plays a role in mathematical software, such as computer algebra systems and theorem provers. Computer algebra systems use symbolic computation to solve algebraic equations and simplifications. Theorem provers can be used to verify mathematical proofs.

Symbolic computation has grown in popularity since its introduction in the 1960s. With its increased use, there is a greater need for efficient techniques to solve problems. For this reason, research in symbolic computation has been ongoing for many years and continues to be an important field in computer science.