Editing Sturm's theorem (section)

==References==

{{reflist}}

* {{cite book
|first1=Saugata
|last1=Basu
|first2=Richard
|last2=Pollack
|authorlink2=Richard M. Pollack
|first3=Marie-Françoise
|last3=Roy
|authorlink3=Marie-Françoise Roy
|title=Algorithms in real algebraic geometry
|year=2006
|publisher=[[Springer Science+Business Media|Springer]]
|pages=52–57
|section=Section 2.2.2
|isbn=978-3-540-33098-1
|edition=2nd
}}
* {{cite journal
|first1=Jacques Charles François
|last1=Sturm
|year=1829
|title=Mémoire sur la résolution des équations numériques
|journal=Bulletin des Sciences de Férussac
|volume=11
|pages=419–425
}}
* {{cite journal
|first1=J. J.
|last1=Sylvester
|year=1853
|title=On a theory of the syzygetic relations of two rational integral functions, comprising an application to the theory of Sturm's functions, and that of the greatest algebraical common measure
|journal=Phil. Trans. R. Soc. Lond.
|volume=143
|pages=407–548
|jstor=108572
|doi=10.1098/rstl.1853.0018
|url=https://zenodo.org/record/1432412
|doi-access=free
}}
* {{cite journal
|first1=Joseph Miller
|last1=Thomas
|title=Sturm's theorem for multiple roots
|year=1941
|journal=National Mathematics Magazine
|volume=15
|number=8
|pages=391–394
|jstor=3028551
|mr=0005945
|doi=10.2307/3028551
}}
* {{cite conference
|first1=Lee E.
|last1=Heindel
|title=Integer arithmetic algorithms for polynomial real zero determination
|journal=Proc. SYMSAC '71
|year=1971
|page=415
|mr=0300434
|doi=10.1145/800204.806312
|s2cid=9971778
}}
* {{cite book
|first1=Leonardo
|last1=de Moura
|first2=Grant Olney
|last2=Passmore
|title=Automated Deduction – CADE-24
|chapter=Computation in Real Closed Infinitesimal and Transcendental Extensions of the Rationals
|series=Lecture Notes in Computer Science
|year=2013
|volume=7898
|page=178-192
|doi=10.1007/978-3-642-38574-2_12
|isbn=978-3-642-38573-5
|s2cid=9308312
|chapter-url=https://www.research.ed.ac.uk/en/publications/6875c2b6-d53a-4ec7-b353-550d902756d0
}}
* {{cite journal
|first1=Don B.
|last1=Panton
|first2=William A.
|last2=Verdini
|title=A fortran program for applying Sturm's theorem in counting internal rates of return
|journal=J. Financ. Quant. Anal.
|year=1981
|volume=16
|number=3
|pages=381–388
|jstor=2330245
|doi=10.2307/2330245
|s2cid=154334522
}}
* {{cite journal
|title=Reflections on a pair of theorems by Budan and Fourier
|journal=Math. Mag.
|first1=Alkiviadis G.
|last1=Akritas
|mr=0678195
|year=1982
|volume=55
|number=5
|pages=292–298
|jstor=2690097
|doi=10.2307/2690097
}}
*{{cite conference
 | last = Pedersen | first = Paul
 | editor1-last = Mattson | editor1-first = Harold F.
 | editor2-last = Mora | editor2-first = Teo
 | editor3-last = Rao | editor3-first = T. R. N.
 | contribution = Multivariate Sturm theory
 | doi = 10.1007/3-540-54522-0_120
 | isbn = 978-3-540-54522-4
 | location = Berlin
 | mr = 1229329
 | pages = 318–332
 | publisher = Springer
 | series = Lecture Notes in Computer Science
 | title = Applied Algebra, Algebraic Algorithms and Error-Correcting Codes, 9th International Symposium, AAECC-9, New Orleans, LA, USA, October 7–11, 1991, Proceedings
 | volume = 539
 | year = 1991}}
* {{cite book|first1=Chee
|last1=Yap
|url=http://www.cs.nyu.edu/yap/book/berlin/
|title=Fundamental Problems in Algorithmic Algebra
|publisher=[[Oxford University Press]]
|year=2000
|isbn=0-19-512516-9
}}
* {{cite book | last1=Rahman | first1=Q. I. | last2=Schmeisser | first2=G. | title=Analytic theory of polynomials | series=London Mathematical Society Monographs. New Series | volume=26 | location=Oxford | publisher=[[Oxford University Press]] | year=2002 | isbn=0-19-853493-0 | zbl=1072.30006 }}
*Baumol, William. ''Economic Dynamics'', chapter 12, Section 3, "Qualitative information on real roots"
* D.G. Hook and P. R. McAree, "Using Sturm Sequences To Bracket Real Roots of Polynomial Equations" in Graphic Gems I (A. Glassner ed.), Academic Press, pp.&nbsp;416&ndash;422, 1990.


{{DEFAULTSORT:Sturm's Theorem}}
[[Category:Theorems in real analysis]]
[[Category:Articles containing proofs]]
[[Category:Theorems about polynomials]]
[[Category:Computer algebra]]
[[Category:Real algebraic geometry]]