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- Sturm's_theorem abstract "In mathematics, the Sturm's sequence of a polynomial p is a sequence of polynomials associated to 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, Sturm's theorem yields the number of distinct real roots and locates them in intervals. By subdividing the intervals containing some roots, it allows eventually to isolate the roots in arbitrary small intervals each containing exactly one root. This yields a symbolic root finding algorithm, that is available in most computer algebra systems, although some more efficient methods are now usually preferred (see below).Sturm's sequence and Sturm's theorems are named after Jacques Charles François Sturm.".
- Sturm's_theorem wikiPageExternalLink Sturm.
- Sturm's_theorem wikiPageExternalLink berlin.
- Sturm's_theorem wikiPageID "1221919".
- Sturm's_theorem wikiPageRevisionID "604193488".
- Sturm's_theorem hasPhotoCollection Sturm's_theorem.
- Sturm's_theorem subject Category:Articles_containing_proofs.
- Sturm's_theorem subject Category:Computer_algebra.
- Sturm's_theorem subject Category:Polynomials.
- Sturm's_theorem subject Category:Theorems_in_real_analysis.
- Sturm's_theorem type Abstraction100002137.
- Sturm's_theorem type Communication100033020.
- Sturm's_theorem type Function113783816.
- Sturm's_theorem type MathematicalRelation113783581.
- Sturm's_theorem type Message106598915.
- Sturm's_theorem type Polynomial105861855.
- Sturm's_theorem type Polynomials.
- Sturm's_theorem type Proposition106750804.
- Sturm's_theorem type Relation100031921.
- Sturm's_theorem type Statement106722453.
- Sturm's_theorem type Theorem106752293.
- Sturm's_theorem type TheoremsInRealAnalysis.
- Sturm's_theorem comment "In mathematics, the Sturm's sequence of a polynomial p is a sequence of polynomials associated to 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.".
- Sturm's_theorem label "Algoritmo di Sturm".
- Sturm's_theorem label "Sturm's theorem".
- Sturm's_theorem label "Sturmsche Kette".
- Sturm's_theorem label "Teorema de Sturm".
- Sturm's_theorem label "Théorème de Sturm".
- Sturm's_theorem label "Twierdzenie Sturma".
- Sturm's_theorem label "Ряд Штурма".
- Sturm's_theorem label "مبرهنة ستورم".
- Sturm's_theorem label "スツルムの定理".
- Sturm's_theorem label "施图姆定理".
- Sturm's_theorem sameAs Sturmsche_Kette.
- Sturm's_theorem sameAs Teorema_de_Sturm.
- Sturm's_theorem sameAs Théorème_de_Sturm.
- Sturm's_theorem sameAs Algoritmo_di_Sturm.
- Sturm's_theorem sameAs スツルムの定理.
- Sturm's_theorem sameAs Twierdzenie_Sturma.
- Sturm's_theorem sameAs m.04jq6v.
- Sturm's_theorem sameAs Q1632301.
- Sturm's_theorem sameAs Q1632301.
- Sturm's_theorem sameAs Sturm's_theorem.
- Sturm's_theorem wasDerivedFrom Sturm's_theorem?oldid=604193488.
- Sturm's_theorem isPrimaryTopicOf Sturm's_theorem.