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Bezout theorem

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  • Bézout's theorem — is a statement in algebraic geometry concerning the number of common points, or intersection points, of two plane algebraic curves. The theorem claims that the number of common points of two such curves X and Y is equal to the product of their… …   Wikipedia

  • Bézout's identity — In number theory, Bézout s identity for two integers a, b is an expression where x and y are integers (called Bézout coefficients for (a,b)), such that d is a common divisor of a and b. Bézout s lemma states that such coefficients exist for every …   Wikipedia

  • Bézout domain — In mathematics, a Bézout domain is an integral domain which is, in a certain sense, a non Noetherian analogue of a principal ideal domain. More precisely, a Bézout domain is a domain in which every finitely generated ideal is principal. A… …   Wikipedia

  • Bézout matrix — In mathematics, a Bézout matrix (or Bézoutian) is a special square matrix associated to two polynomials. Such matrices are sometimes used to test the stability of a given polynomial.DefinitionLet f ( z ) and g ( z ) be two complex polynomials of… …   Wikipedia

  • Anneau de Bézout — En algèbre commutative un anneau de Bézout est un anneau où la propriété de Bézout va se trouver vérifiée. Plus formellement, c est un anneau dans lequel tout idéal de type fini est principal. Si, en toute théorie, la définition d un anneau de… …   Wikipédia en Français

  • Étienne Bézout — (March 31, 1730 September 27, 1783) was a French mathematician who was born in Nemours, Seine et Marne, France, and died in Basses Loges (near Fontainebleau), France.WorkIn 1758 Bézout was elected an adjoint in mechanics of the French Academy of… …   Wikipedia

  • De Franchis theorem — In mathematics, the de Franchis theorem is one of a number of closely related statements applying to compact Riemann surfaces, or, more generally, algebraic curves, X and Y, in the case of genus g > 1. The simplest is that the automorphism… …   Wikipedia

  • Proofs of Fermat's little theorem — This article collects together a variety of proofs of Fermat s little theorem, which states that:a^p equiv a pmod p ,!for every prime number p and every integer a (see modular arithmetic). Simplifications Some of the proofs of Fermat s little… …   Wikipedia

  • Cayley-Bacharach theorem — In mathematics, the Cayley Bacharach theorem is a statement in projective geometry which contains as a special case Pascal s theorem. The Cayley Bacharach theorem pertains to the family of cubic curves (plane curves of degree three) passing… …   Wikipedia

  • AF+BG theorem — In algebraic geometry, a field of mathematics, the AF+BG theorem is a result of Max Noether which describes when the equation of an algebraic curve in the complex projective plane can be written in terms of the equations of two other algebraic… …   Wikipedia

  • Enumerative geometry — In mathematics, enumerative geometry is the branch of algebraic geometry concerned with counting numbers of solutions to geometric questions, mainly by means of intersection theory.HistoryThe problem of Apollonius is one of the earliest examples… …   Wikipedia

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