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- Sturms_theorem abstract "In mathematics, the Sturm's sequence of a univariate polynomial p is a sequence of polynomials associated with p and its derivative by a variant of Euclid's algorithm for polynomials. Sturm's theorem expresses the number of distinct real roots of p located in an interval in terms of the number of changes of signs of the values of the Sturm's sequence at the bounds of the interval. Applied to the interval of all the real numbers, it gives the total number of real roots of p. Whereas the fundamental theorem of algebra readily yields the overall number of complex roots, counted with multiplicity, it does not provide a procedure for calculating them. Sturm's theorem counts the number of distinct real roots and locates them in intervals. By subdividing the intervals containing some roots, it can isolate the roots into arbitrary small intervals, each containing exactly one root. This yields an arbitrary-precision numeric root finding algorithm for univariate polynomials.Sturm's sequence and Sturm's theorems are named after Jacques Charles François Sturm.".
- Sturms_theorem wikiPageExternalLink berlin.
- Sturms_theorem wikiPageExternalLink Sturm.
- Sturms_theorem wikiPageID "1221919".
- Sturms_theorem wikiPageLength "21571".
- Sturms_theorem wikiPageOutDegree "44".
- Sturms_theorem wikiPageRevisionID "673882723".
- Sturms_theorem wikiPageWikiLink Augustin-Louis_Cauchy.
- Sturms_theorem wikiPageWikiLink Augustin_Louis_Cauchy.
- Sturms_theorem wikiPageWikiLink Budans_theorem.
- Sturms_theorem wikiPageWikiLink Category:Articles_containing_proofs.
- Sturms_theorem wikiPageWikiLink Category:Computer_algebra.
- Sturms_theorem wikiPageWikiLink Category:Polynomials.
- Sturms_theorem wikiPageWikiLink Category:Theorems_in_real_analysis.
- Sturms_theorem wikiPageWikiLink Complex_number.
- Sturms_theorem wikiPageWikiLink Continuous_function.
- Sturms_theorem wikiPageWikiLink Degree_of_a_polynomial.
- Sturms_theorem wikiPageWikiLink Derivative.
- Sturms_theorem wikiPageWikiLink Descartes_rule_of_signs.
- Sturms_theorem wikiPageWikiLink Euclidean_algorithm.
- Sturms_theorem wikiPageWikiLink Euclids_algorithm.
- Sturms_theorem wikiPageWikiLink Euclids_algorithm_for_polynomials.
- Sturms_theorem wikiPageWikiLink Fundamental_theorem_of_algebra.
- Sturms_theorem wikiPageWikiLink Gauss–Lucas_theorem.
- Sturms_theorem wikiPageWikiLink Hurwitzs_theorem_(complex_analysis).
- Sturms_theorem wikiPageWikiLink Interval_(mathematics).
- Sturms_theorem wikiPageWikiLink Jacques_Charles_François_Sturm.
- Sturms_theorem wikiPageWikiLink Mathematics.
- Sturms_theorem wikiPageWikiLink Multiplicity_(mathematics).
- Sturms_theorem wikiPageWikiLink Oxford_University_Press.
- Sturms_theorem wikiPageWikiLink Polynomial.
- Sturms_theorem wikiPageWikiLink Polynomial_greatest_common_divisor.
- Sturms_theorem wikiPageWikiLink Polynomial_long_division.
- Sturms_theorem wikiPageWikiLink Properties_of_polynomial_roots.
- Sturms_theorem wikiPageWikiLink Real_number.
- Sturms_theorem wikiPageWikiLink Root-finding_algorithm.
- Sturms_theorem wikiPageWikiLink Root_finding_algorithm.
- Sturms_theorem wikiPageWikiLink Root_of_a_function.
- Sturms_theorem wikiPageWikiLink Rouchxc3xa9s_theorem.
- Sturms_theorem wikiPageWikiLink Routh–Hurwitz_theorem.
- Sturms_theorem wikiPageWikiLink Square-free_factorization.
- Sturms_theorem wikiPageWikiLink Square-free_polynomial.
- Sturms_theorem wikiPageWikiLink Turxc3xa1ns_inequalities.
- Sturms_theorem wikiPageWikiLink Vincents_theorem.
- Sturms_theorem wikiPageWikiLink Zero_of_a_function.
- Sturms_theorem wikiPageWikiLinkText "Sturm chain".
- Sturms_theorem wikiPageWikiLinkText "Sturm functions".
- Sturms_theorem wikiPageWikiLinkText "Sturm".
- Sturms_theorem wikiPageWikiLinkText "Sturm%27s_theorem".
- Sturms_theorem wikiPageWikiLinkText "Sturm's theorem".
- Sturms_theorem wikiPageWikiLinkText "generalized Sturm chain".
- Sturms_theorem wikiPageWikiLinkText "method".
- Sturms_theorem wikiPageWikiLinkText "theorem".
- Sturms_theorem hasPhotoCollection Sturms_theorem.
- Sturms_theorem wikiPageUsesTemplate Template:Citation.
- Sturms_theorem wikiPageUsesTemplate Template:Cite_book.
- Sturms_theorem wikiPageUsesTemplate Template:Cite_journal.
- Sturms_theorem wikiPageUsesTemplate Template:Math.
- Sturms_theorem wikiPageUsesTemplate Template:Mvar.
- Sturms_theorem wikiPageUsesTemplate Template:Reflist.
- Sturms_theorem subject Category:Articles_containing_proofs.
- Sturms_theorem subject Category:Computer_algebra.
- Sturms_theorem subject Category:Polynomials.
- Sturms_theorem subject Category:Theorems_in_real_analysis.
- Sturms_theorem hypernym Sequence.
- Sturms_theorem comment "In mathematics, the Sturm's sequence of a univariate polynomial p is a sequence of polynomials associated with p and its derivative by a variant of Euclid's algorithm for polynomials. Sturm's theorem expresses the number of distinct real roots of p located in an interval in terms of the number of changes of signs of the values of the Sturm's sequence at the bounds of the interval. Applied to the interval of all the real numbers, it gives the total number of real roots of p.".
- Sturms_theorem label "Sturm's theorem".
- Sturms_theorem sameAs مبرهنة_ستورم.
- Sturms_theorem sameAs Teorema_de_Sturm.
- Sturms_theorem sameAs Sturmsche_Kette.
- Sturms_theorem sameAs Teorema_de_Sturm.
- Sturms_theorem sameAs Théorème_de_Sturm.
- Sturms_theorem sameAs Algoritmo_di_Sturm.
- Sturms_theorem sameAs スツルムの定理.
- Sturms_theorem sameAs Twierdzenie_Sturma.
- Sturms_theorem sameAs m.04jq6v.
- Sturms_theorem sameAs Ряд_Штурма.
- Sturms_theorem sameAs Метод_Штурма.
- Sturms_theorem sameAs Q1632301.
- Sturms_theorem sameAs Q1632301.
- Sturms_theorem sameAs 施图姆定理.
- Sturms_theorem wasDerivedFrom Sturms_theoremoldid=673882723.
- Sturms_theorem isPrimaryTopicOf Sturms_theorem.