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Deux moments dans l’histoire du théorème d’algèbre de Ch. F. Sturm. (Two moments in the history of Ch. F. Sturm’s theorem of algebra). (French. English summary) Zbl 0645.01009
The importance of Sturm’s theorem of 1829 on the number of real roots between given limits of a polynomial equation was widely recognised at the time; it gave an effective procedure for locatingthe (real) roots of any polynomial (earlier results from Descartes to Fourier had merely given upper bounds to the number of roots). The author of this paper places Sturm’s theorem in the context of Fourier’s ideas of finding effective methods of finding the roots of equations and further notes the frequent neglect of the theorem in algebra texts and by historians of mathematics. The algorithmic aspect of the proof provided the tool which enabled Tarski, in the 1930s, to solve decision problems in model theory via the elimination of quantifiers.
Reviewer: G.Smith

MSC:
01A55 History of mathematics in the 19th century
01A60 History of mathematics in the 20th century
12-03 History of field theory
Biographic References:
Sturm, Ch. F.
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