### Some articles on *sturm, sequence, sturm sequence*:

Sturm's Theorem

... In mathematics, the

... 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**... the overall number of complex roots, counted with multiplicity,**Sturm**'s theorem yields the number of distinct real roots and locates them in intervals ...Greatest Common Divisor Of Two Polynomials - Univariate Polynomials With Coefficients in A Field - GCD and Root Finding -

... The

**Sturm Sequence**... The

**Sturm sequence**of a polynomial with real coefficients is the**sequence**of the remainders provided by a variant of Euclid's algorithm applied to the polynomial and ... For getting the**Sturm sequence**, one simply replaces the instruction of Euclid's algorithm by Let V(a) be the number of changes of signs in the**sequence**, when evaluated at a point a ...**Sturm**'s theorem asserts that V(a)-V(b) is the number of real roots of the polynomial in the interval ...### Famous quotes containing the word sequence:

“We have defined a story as a narrative of events arranged in their time-*sequence*. A plot is also a narrative of events, the emphasis falling on causality. “The king died and then the queen died” is a story. “The king died, and then the queen died of grief” is a plot. The time *sequence* is preserved, but the sense of causality overshadows it.”

—E.M. (Edward Morgan)

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