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...

François Sturm (29 September 1803 – 15 December 1855) was a French mathematician, who made a significant addition to equation theory with his work, Sturm's theorem...

the values of a sequence of polynomials, called Sturm's sequence, at the ends of the interval. Sturm's sequence is the sequence of remainders that occur...

systems design, the Routh–Hurwitz theorem and Routh array emerge by using the Euclidean algorithm and Sturm's theorem in evaluating Cauchy indices. Given...

w(−∞) can be viewed as the complex counterpart of Sturm's theorem. Note the differences: in Sturm's theorem, the left member is p + q and the w from the right...

the successive derivatives at a point. For Sturm's theorem it is the sequence of values at a point of the Sturm sequence. All results described in this article...

field of ordinary differential equations, Sturm separation theorem, named after Jacques Charles François Sturm, describes the location of roots of solutions...

differential equations Sturm, Ruger & Co., a firearms manufacturer Sturm series, associated with polynomials Sturm's theorem, a method for counting the...

isolation algorithm was given by Jacques Charles François Sturm in 1829, known as the Sturm's theorem. In 1836, a mathematician named Mr. Vincent proposed...

existence of a root in an interval (Descartes' rule of signs, Sturm's theorem, Budan's theorem). They allow extending the bisection method into efficient...

(algebra) Strassmann's theorem (field theory) Sturm's theorem (theory of equations) Vieta's formulas (quadratics) Artin approximation theorem (commutative algebra)...

short descriptions of redirect targets Riemann mapping theorem – Mathematical theorem Sturm's theorem – Counting polynomial roots in an interval Estermann...

N {\displaystyle N} the polynomials can be determined exactly and Sturm's theorem can be used to determine the number of real roots, while the roots...

and Sturm's theorem in evaluating Cauchy indices. Hurwitz derived his conditions differently. The criterion is related to Routh–Hurwitz theorem. From...

a point a. Sturm's theorem asserts that V(a) − V(b) is the number of real roots of the polynomial in the interval [a, b]. Thus the Sturm sequence allows...

Elimination theory Gröbner basis Regular chain Triangular decomposition Sturm's theorem Descartes' rule of signs Carlitz–Wan conjecture Polynomial decomposition...

polynomials, it was almost totally forgotten, having been overshadowed by Sturm's theorem; consequently, it does not appear in any of the classical books on...

differential equations, the Sturm–Picone comparison theorem, named after Jacques Charles François Sturm and Mauro Picone, is a classical theorem which provides criteria...

same values of the variables. Tarski's proof uses a generalization of Sturm's theorem. Since the truth of quantifier-free formulas without free variables...

Motzkin in 1936. 1835 Sturm's theorem on real root counting 1856 Hermite's theorem on real root counting. 1876 Harnack's curve theorem. (This bound on the...

solutions of a regular Sturm–Liouville equation cannot vanish simultaneously as a consequence of the Sturm separation theorem. This trick gives a solution...

are other methods such as Descartes' rule of signs, Budan's theorem and Sturm's theorem for bounding or determining the number of roots in an interval...

to determine the number of distinct real roots of a polynomial by Sturm's theorem This disambiguation page lists mathematics articles associated with...

students. His best ever proposal type claim is commonly known as "Sturm's Theorem" based on finding the complex imaginary roots of an infinite arbitrary-integer...

isosceles. The theorem was first mentioned in 1840 in a letter by C. L. Lehmus to C. Sturm, in which he asked for a purely geometric proof. Sturm passed the...

at the end of the project. The IRR satisfies a polynomial equation. Sturm's theorem can be used to determine if that equation has a unique real solution...

the so-called Pfaffian functions. Sturm's theorem – Counting polynomial roots in an interval Rational root theorem – Relationship between the rational...

due to modern computers it is not as important), an application of Sturm's theorem to evaluate Cauchy indices through the use of the Euclidean algorithm...

The fundamental theorem of algebra, also called d'Alembert's theorem or the d'Alembert–Gauss theorem, states that every non-constant single-variable polynomial...

comparison theorem Sturm comparison theorem Hille-Wintner comparison theorem In Riemannian geometry, it is a traditional name for a number of theorems that...