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Definitions

Definitions. group , ring and field polynomial over a field F degree of a polynomial over F F[x] degree of a polynomial in F[x] gcd of two polynomials from F[x] irreducible polynomial over F function induced by a polynomial root of a polynomial

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Definitions

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  1. Definitions • group, ring and field • polynomial over a field F • degree of a polynomial over F • F[x] • degree of a polynomial in F[x] • gcdof two polynomials from F[x] • irreducible polynomial over F • function induced by a polynomial • root of a polynomial • minimal polynomial f(x) in GFp[x] for an element of u of

  2. Definitions • extension field K of field F • splitting field of polynomial f(x)  F[x] • prime subfield of a finite field F • F*, where F is a field • primitive element of field F • primitive polynomial over GFp

  3. Tasks • Work with elements of the group of permutations on n symbols (Sn) • Carry out arithmetic operations (+, *, /, raise to a power) on polynomials over a field F • Construct using an irreducible polynomial g(x)  GFp • Decide whether a polynomial f(x)  GFp of degree at most 3 is irreducible • …

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