Finite fields | Computer algebra

Conway polynomial (finite fields)

In mathematics, the Conway polynomial Cp,n for the finite field Fpn is a particular irreducible polynomial of degree n over Fp that can be used to define a standard representation of Fpn as a splitting field of Cp,n. Conway polynomials were named after John H. Conway by Richard A. Parker, who was the first to define them and compute examples. Conway polynomials satisfy a certain compatibility condition that had been proposed by Conway between the representation of a field and the representations of its subfields. They are important in computer algebra where they provide portability among different mathematical databases and computer algebra systems. Since Conway polynomials are expensive to compute, they must be stored to be used in practice. Databases of Conway polynomials are available in the computer algebra systems GAP, Macaulay2, Magma, SageMath, and at the web site of Frank Lübeck. (Wikipedia).

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From playlist Is it a polynomial or not?

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From playlist Math talks

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From playlist Vertex Operator Algebras

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From playlist Math talks

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From playlist Abstract Algebra

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From playlist Linear Algebra Done Right

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From playlist Knots Through Web (Online)

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From playlist Conversations with Special Guests

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From playlist Field Theory

Related pages

Splitting field | SageMath | Primitive polynomial (field theory) | Irreducible polynomial | Monic polynomial | Computer algebra | Finite field | Macaulay2 | Cyclic group | Primitive element (finite field) | Minimal polynomial (field theory) | Isomorphism