Fermat (computer algebra system)

Fermat is a computer algebra system (CAS) designed primarily for computations in number theory, abstract algebra, and especially polynomial algebra over finite fields and the integers. Developed by Robert H. Lewis of Fordham University, Fermat is known for its speed and efficiency, particularly in handling large polynomial systems and calculations involving modular arithmetic.

Unlike some general-purpose CAS programs, Fermat is highly specialized. Its strength lies in performing arithmetic with very large integers and polynomials, making it well-suited for tasks such as determining the irreducibility of polynomials over finite fields, computing Gröbner bases, and performing symbolic manipulation of algebraic expressions.

Fermat is a command-line driven program, requiring users to enter commands directly to perform calculations. It lacks a graphical user interface, which contributes to its efficiency but can present a steeper learning curve for new users accustomed to more visual CAS environments. The system is distributed as executable binaries for various operating systems, allowing users to install and run it directly without requiring compilation.

While not as widely used as some other CAS, Fermat remains a valuable tool for researchers and students working in areas of mathematics that demand high-performance computations in number theory and algebraic manipulation. Its dedicated focus allows it to outperform general-purpose systems in specific, computationally intensive tasks within its domain.