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- Theory_of_equations abstract "In mathematics, the theory of equations is a part of algebra. More precisely, "theory of equations" is a shortcut for "theory of algebraic equations", an algebraic equation (also called polynomial equation) being an equation defined by a polynomial. The term "theory of equations" is mainly used in the context of the history of mathematics.Until the end of 19th century, "theory of equations" was almost synonymous with "algebra". For a long time, the main problem was to find the solutions of a single non-linear equation in a single unknown. The fact that a complex solution always exists is the fundamental theorem of algebra, which had been proved only at the beginning of 19th century and does not have a purely algebraic proof. Nevertheless, the main concern of the algebraists was to solve in terms of radicals, that is to express the solutions by a formula which is built with the four operations of arithmetics and nth roots. This has been done up to degree four during 16th century (see Gerolamo Cardano, quadratic formula, cubic equation, quartic equation). The case of higher degrees remained open until 19th century, when Niels Henrik Abel proved that some fifth degree equations cannot be solved in radicals (Abel–Ruffini theorem) and Évariste Galois introduced a theory (presently called Galois theory) to decide which equations are solvable by radicals.Other classical problems of the theory of equations are the following: Linear equations: this problem was solved during antiquity. Simultaneous linear equations: The general theoretical solution was provided by Gabriel Cramer in 1750. However devising efficient methods (algorithms) to solve these systems remains an active subject of research now called linear algebra. Finding the integer solutions of an equation or of a system of equations. These problems are now called Diophantine equations, which is considered as a part of number theory (see also integer programming). Systems of polynomial equations: Because of their difficulty these systems, with few exceptions, have been studied only since the second part of 19th century. They have led to the development of algebraic geometry.".
- Theory_of_equations wikiPageID "583600".
- Theory_of_equations wikiPageRevisionID "591608068".
- Theory_of_equations hasPhotoCollection Theory_of_equations.
- Theory_of_equations subject Category:Equations.
- Theory_of_equations subject Category:History_of_algebra.
- Theory_of_equations subject Category:Polynomials.
- Theory_of_equations type Abstraction100002137.
- Theory_of_equations type Function113783816.
- Theory_of_equations type MathematicalRelation113783581.
- Theory_of_equations type Polynomial105861855.
- Theory_of_equations type Polynomials.
- Theory_of_equations type Relation100031921.
- Theory_of_equations comment "In mathematics, the theory of equations is a part of algebra. More precisely, "theory of equations" is a shortcut for "theory of algebraic equations", an algebraic equation (also called polynomial equation) being an equation defined by a polynomial. The term "theory of equations" is mainly used in the context of the history of mathematics.Until the end of 19th century, "theory of equations" was almost synonymous with "algebra".".
- Theory_of_equations label "Teoria delle equazioni".
- Theory_of_equations label "Teoría de ecuaciones".
- Theory_of_equations label "Theory of equations".
- Theory_of_equations label "Théorie des équations (histoire des sciences)".
- Theory_of_equations label "方程理论".
- Theory_of_equations sameAs Teoría_de_ecuaciones.
- Theory_of_equations sameAs Théorie_des_équations_(histoire_des_sciences).
- Theory_of_equations sameAs Teoria_delle_equazioni.
- Theory_of_equations sameAs m.02sf7t.
- Theory_of_equations sameAs Q2551226.
- Theory_of_equations sameAs Q2551226.
- Theory_of_equations sameAs Theory_of_equations.
- Theory_of_equations wasDerivedFrom Theory_of_equations?oldid=591608068.
- Theory_of_equations isPrimaryTopicOf Theory_of_equations.