Conway polynomial (finite fields) (original) (raw)
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 i
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| dbo:abstract | 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. (en) En mathématiques, le polynôme de Conway Cp,n sur le corps fini Fp,n est un polynôme irréductible particulier de degré n sur Fp qui peut être utilisé pour définir une représentation standard de Fp,n en tant que corps de décomposition de Cp,n. Les polynômes de Conway ont été baptisés d'après John Horton Conway par (en), qui a été le premier à les définir et à calculer des exemples. Les polynômes de Conway satisfont une certaine condition de compatibilité, proposée par Conway, entre la représentation d'un corps et celles de ses sous-corps. Ils sont utiles pour le calcul formel pour lequel ils fournissent une portabilité parmi différentes bases de données mathématiques et des systèmes de calcul formel. Étant donné le coût important du calcul des polynômes de Conway, ils doivent être enregistrés pour être utilisés en pratique. Des bases de données de polynômes de Conway sont disponibles dans les systèmes de calcul formel GAP, (en), Magma, SageMath, et le site internet de Frank Lübeck. (fr) |
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| rdfs:comment | 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 i (en) En mathématiques, le polynôme de Conway Cp,n sur le corps fini Fp,n est un polynôme irréductible particulier de degré n sur Fp qui peut être utilisé pour définir une représentation standard de Fp,n en tant que corps de décomposition de Cp,n. Les polynômes de Conway ont été baptisés d'après John Horton Conway par (en), qui a été le premier à les définir et à calculer des exemples. Les polynômes de Conway satisfont une certaine condition de compatibilité, proposée par Conway, entre la représentation d'un corps et celles de ses sous-corps. Ils sont utiles pour le calcul formel pour lequel ils fournissent une portabilité parmi différentes bases de données mathématiques et des systèmes de calcul formel. Étant donné le coût important du calcul des polynômes de Conway, ils doivent être enregistr (fr) |
| rdfs:label | Conway polynomial (finite fields) (en) Polynôme de Conway (corps finis) (fr) |
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