👉 Remainder computing is a mathematical discipline that focuses on the properties and algorithms of polynomials over finite fields, particularly when these fields have a large number of elements. It extends classical polynomial arithmetic to these settings, enabling efficient computation and analysis of polynomials with coefficients in finite fields. This is crucial for various applications, including cryptography, coding theory, and computational number theory, where large finite fields are commonly used. In remainder computing, the goal is to perform operations like polynomial division, evaluation, and interpolation in a way that minimizes computational complexity and memory usage, often leveraging properties such as the Chinese Remainder Theorem and fast polynomial multiplication techniques like the Fast Fourier Transform (FFT) over finite fields.
