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A field is a set of elements ... with the four operations of arithmetic satisfying the following properties. associativity: ... , ... , commutativity: ... , distributivity: ... , zero and identity: ... , inverses ... if ... . One example of a field is the set of numbers {0,1,2,3,4} modulo 5, and similarly any prime number ... gives a field, GF( ... ). A Galois field is a finite field with order a prime power ... ; these ... are the only finite fields, and can be represented by polynomials with coefficients in GF( ... ) reduced modulo some polynomial. In this Demonstration, pick a prime and polynomial, and the corresponding addition and multiplication tables within that finite field will be shown. Squares colored by grayscale represent the fiield elements.

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      EUN,LOM,LRE4,work-cmr-id:396883,http://demonstrations.wolfram.com:http://demonstrations.wolfram.com/FiniteFieldTables/,ilox,learning resource exchange,LRE metadata application profile,LRE

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