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- Q1632301 subject Q6425293.
- Q1632301 subject Q7138882.
- Q1632301 subject Q7139549.
- Q1632301 subject Q8266681.
- Q1632301 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.".
- Q1632301 wikiPageExternalLink Sturm.
- Q1632301 wikiPageExternalLink berlin.
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- Q1632301 wikiPageWikiLink Q6425293.
- Q1632301 wikiPageWikiLink Q7138882.
- Q1632301 wikiPageWikiLink Q7139549.
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- Q1632301 wikiPageWikiLink Q8266681.
- Q1632301 wikiPageWikiLink Q8814.
- Q1632301 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.".
- Q1632301 label "Sturm's theorem".