Polynomial Factorization Over Henselian Fields
Copyright policy )Polynomial Factorization Over Henselian Fields
Given a valued field $(K,v)$ and an irreducible polynomial $g\in K[x]$, we survey the ideas of Ore, Maclane, Okutsu, Montes, Vaquié and Herrera-Olalla-Mahboub-Spivakovsky, leading (under certain conditions) to an algorithm to find the factorization of $g$ over a henselization of $(K,v)$.
[INFO.INFO-SC]Computer Science [cs]/Symbolic Computation [cs.SC], Àrees temàtiques de la UPC::Matemàtiques i estadística, Classificació AMS::14 Algebraic geometry::14Q Computational aspects in algebraic geometry, [INFO.INFO-SC] Computer Science [cs]/Symbolic Computation [cs.SC], Newton polygon, Classificació AMS::12 Field theory and polynomials::12Y05 Computational aspects of field theory and polynomials, Mathematics - Commutative Algebra, Commutative Algebra (math.AC), Classificació AMS::13 Commutative rings and algebras::13P Computational aspects of commutative algebra, OM-algorithm, Valuation, Henselian field, Key polynomial, FOS: Mathematics, Classificació AMS::13 Commutative rings and algebras::13A General commutative ring theory
[INFO.INFO-SC]Computer Science [cs]/Symbolic Computation [cs.SC], Àrees temàtiques de la UPC::Matemàtiques i estadística, Classificació AMS::14 Algebraic geometry::14Q Computational aspects in algebraic geometry, [INFO.INFO-SC] Computer Science [cs]/Symbolic Computation [cs.SC], Newton polygon, Classificació AMS::12 Field theory and polynomials::12Y05 Computational aspects of field theory and polynomials, Mathematics - Commutative Algebra, Commutative Algebra (math.AC), Classificació AMS::13 Commutative rings and algebras::13P Computational aspects of commutative algebra, OM-algorithm, Valuation, Henselian field, Key polynomial, FOS: Mathematics, Classificació AMS::13 Commutative rings and algebras::13A General commutative ring theory
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