Playground

Finite field calculator

Arithmetic on a clock with v hours is a field exactly when v is prime. Every other finite field has pᵉ elements for a prime p, and is built from polynomials with coefficients mod p, divided by an irreducible polynomial f of degree e. Pick a mode, then explore. The address bar keeps your settings, so you can share a view.

Background: Lesson 5 (which clocks are fields), Lesson 7 (polynomial fields), and Lesson 8 (powers and logs).