About: Factorization of polynomials over finite fields

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In mathematics and computer algebra the factorization of a polynomial consists of decomposing it into a product of irreducible factors. This decomposition is theoretically possible and is unique for polynomials with coefficients in any field, but rather strong restrictions on the field of the coefficients are needed to allow the computation of the factorization by means of an algorithm. In practice, algorithms have been designed only for polynomials with coefficients in a finite field, in the field of rationals or in a finitely generated field extension of one of them.

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rdf:type	yago:Abstraction100002137 yago:Function113783816 yago:MathematicalRelation113783581 yago:Polynomial105861855 yago:Relation100031921 yago:WikicatPolynomials
rdfs:label	Factorización de polinomios sobre cuerpos finitos (es) Factorization of polynomials over finite fields (en)
rdfs:comment	In mathematics and computer algebra the factorization of a polynomial consists of decomposing it into a product of irreducible factors. This decomposition is theoretically possible and is unique for polynomials with coefficients in any field, but rather strong restrictions on the field of the coefficients are needed to allow the computation of the factorization by means of an algorithm. In practice, algorithms have been designed only for polynomials with coefficients in a finite field, in the field of rationals or in a finitely generated field extension of one of them. (en) En matemáticas y cálculo simbólico la factorización de un polinomio consiste en descomponerlo en un producto de factores irreducibles. Esta descomposición es teóricamente posible y es única para polinomios con coeficientes en cualquier cuerpo, pero se necesitan restricciones bastante fuertes en el cuerpo de los coeficientes para permitir el cálculo de la factorización mediante un algoritmo. En la práctica, los algoritmos se han diseñado solo para polinomios con coeficientes en un cuerpo finito, en los números racionales o en una extensión de cuerpos de uno de ellos. (es)
dcterms:subject	Cryptography Polynomials factorization algorithms Algebra Coding theory Computational number theory Polynomials Computer algebra
Wikipage page ID	30059275 (xsd:integer)
Wikipage revision ID	1088727562 (xsd:integer)
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Link from a Wikipage to an external page	http://designtheory.org/library/encyc/topics/gf.pdf http://www.science.unitn.it/~degraaf/compalg/polfact.pdf https://www.shoup.net/papers/smooth.ps http://www.jmilne.org/math/CourseNotes/FT.pdf http://www.math.umn.edu/~garrett/m/algebra/notes/07.pdf https://dx.doi.org/10.1006/jsco.1999.1002 https://dx.doi.org/10.1007/b102438 https://www.ams.org/journals/mcom/1990-54-189/S0025-5718-1990-0993933-0/S0025-5718-1990-0993933-0.pdf https://www.sciencedirect.com/science/article/pii/0022314X69900304/pdf%3Fmd5=c31af090ceec6b08d71eedf57d709ab0&isDTMRedir=Y&pid=1-s2.0-0022314X69900304-main.pdf&_valck=1
sameAs	Factorization of polynomials over finite fields Factorization of polynomials over finite fields Factorization of polynomials over finite fields Factorization of polynomials over finite fields Factorization of polynomials over finite fields

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