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A system of polynomial equations (sometimes simply a polynomial system) is a set of simultaneous equations f1 = 0, ..., fh = 0 where the fi are polynomials in several variables, say x1, ..., xn, over some field k. A solution of a polynomial system is a set of values for the xis which belong to some algebraically closed field extension K of k, and make all equations true. When k is the field of rational numbers, K is generally assumed to be the field of complex numbers, because each solution belongs to a field extension of k, which is isomorphic to a subfield of the complex numbers.

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rdf:type	yago:Abstraction100002137 yago:Communication100033020 yago:Equation106669864 yago:Function113783816 yago:MathematicalRelation113783581 yago:MathematicalStatement106732169 yago:Message106598915 yago:Polynomial105861855 yago:Relation100031921 yago:Statement106722453 yago:WikicatEquations yago:WikicatPolynomials
rdfs:label	Sistema de ecuaciones algebraicas (es) Système d'équations algébriques (fr) Sistem persamaan polinomial (in) System of polynomial equations (en)
rdfs:comment	En matemáticas, un sistema de ecuaciones algebraicas es un conjunto de ecuaciones con más de una incógnita que conforman un problema matemático que consiste en encontrar los valores de las incógnitas que satisfacen dichas operaciones. Las incógnitas se suelen representar utilizando las últimas letras del alfabeto latino, o si son demasiadas, con subíndices. (es) Sistem persamaan polinomial (terkadang hanya sistem polinomial) adalah himpunan persamaan simultan f1 = 0, ..., fh = 0 dimana fi adalah polinomial dalam beberapa variabel, misalnya x1, ..., xn, atas beberapa bidang k. Solusi dari sistem polinomial adalah sekumpulan nilai untuk xi yang termasuk dalam beberapa ekstensi bidang K dari k , dan membuat semua persamaan menjadi benar. Jika k adalah bidang bilangan rasional, K umumnya diasumsikan sebagai bidang bilangan kompleks, karena setiap solusi milik ekstensi bidang dari k , yang isomorfik ke subkolom dari bilangan kompleks. (in) A system of polynomial equations (sometimes simply a polynomial system) is a set of simultaneous equations f1 = 0, ..., fh = 0 where the fi are polynomials in several variables, say x1, ..., xn, over some field k. A solution of a polynomial system is a set of values for the xis which belong to some algebraically closed field extension K of k, and make all equations true. When k is the field of rational numbers, K is generally assumed to be the field of complex numbers, because each solution belongs to a field extension of k, which is isomorphic to a subfield of the complex numbers. (en) En mathématiques, un système d'équations algébriques est un ensemble d'équations polynomiales f1 = 0, ..., fh = 0 où les fi sont des polynômes de plusieurs variables (ou indéterminées), x1, ..., xn, à coefficients pris dans un corps ou un anneau k. Une « solution » est un ensemble de valeurs à substituer aux indéterminées annulant toutes les équations du système. Généralement les solutions peuvent être cherchées dans une extension du corps k comme la clôture algébrique de ce corps (ou la clôture algébrique du corps des fractions de k celui-ci est un anneau). (fr)
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dcterms:subject	Equations Algebra Polynomials Algebraic geometry Computer algebra
Wikipage page ID	27420015 (xsd:integer)
Wikipage revision ID	1120311132 (xsd:integer)
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sameAs	System of polynomial equations System of polynomial equations System of polynomial equations System of polynomial equations System of polynomial equations

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