@article{CSHM_1991_2_1__41_0, author = {Becker, Eberhard}, title = {Sums of squares and quadratric forms in real algebraic geometry}, journal = {Cahiers du s\'eminaire d'histoire des math\'ematiques}, volume = {12}, year = {1991}, pages = {41-57}, mrnumber = {1122204}, zbl = {0746.14021}, language = {en}, url = {http://dml.mathdoc.fr/item/CSHM_1991_2_1__41_0} }
Becker, Eberhard. Sums of squares and quadratric forms in real algebraic geometry. Cahiers du séminaire d'histoire des mathématiques, Tome 12 (1991) pp. 41-57. http://gdmltest.u-ga.fr/item/CSHM_1991_2_1__41_0/
[A] Uber die Zerlegung definiter Funktionen in Quadrate. Hamb. Abh. 5,100-115 ( 1927). | JFM 52.0122.01
:[A-B] Real stability index of rings and its application to semialgebraic geometry. In : Séminaire sur les structures algébriques ordonnées ( 1984-1987), Publications mathématiques de l'Université de Paris VII33, 61-86 ( 1990). | MR 1071791 | Zbl 0742.14043
and :[Ba] Quadratic forms over semi-local rings. LN in Math. 655 ( 1978). | Zbl 0382.10014
:[Bel] Valuations and real places in the theory of formally real fields. In : Géométrie algébrique réelle et formes quadratiques, LN in Mathematics 959,1-40 ( 1982). | MR 683127 | Zbl 0508.14013
:[Be2] The real holomorphy ring and sum of 2n-th power. In : Géométrie algébrique réelle et formes quadratiques, LN in Mathematics 959, 139-181 ( 1982). | MR 683132 | Zbl 0508.12020
:[Be3] On the real spectrum of a ring and its application to semialgebraic geometry, Bull. AMS 15,1 ( 1986), 19-60. | MR 838786 | Zbl 0634.14016
:[B-B-D-G] Hilbert's 17th problem for sums 2n-th powers. Preprint ( 1990).
, , , :[B-R] Real algebraic and semi algebraic sets. Hermann Editeurs, Paris ( 1990). | MR 1070358 | Zbl 0694.14006
, :[B-C-R] Géométrie algébrique réelle, Ergebn. der Math. 3 Folge Bd. 12, Springer-Verlag, Berlin-Heidelberg ( 1987). | MR 949442 | Zbl 0633.14016
, , :[B1] Développements sur l'équation à l'aide de laquelle on détermine les inégalités séculaires du mouvement des planètes. J. Math. Pures Appl. 12, 50-67 (5) ( 1847),
:[B2] Remarque relative à la note précédente. J. Reine Angew. Math. 53, 367-368 ( 1857). | Zbl 053.1410cj
:[Br1] Witt rings and K-theory. Rocky Mtn. J. Math. 14, 733-765 ( 1984). | MR 773113 | Zbl 0576.14024
:[Br2] The real spectrum of an ideal and KO-theory exact sequences. K-theory 1 211-235 ( 1987). | MR 908991 | Zbl 0631.14018
:[Brö] Minimale Erzeugung von Positivbereichen. Geom. Dedicata 16,335-350 ( 1984). | MR 765338 | Zbl 0546.14016
:[Bu] Gröbner bases : an algorithrnic method in polynomial ideal theory. In : Multidimensional Systems Theory (N.K. Bose ed.), D. Reidel Publishing Company, Dordrecht-Boston-Lancaster, 184-232 ( 1985). | MR 835951 | Zbl 0587.13009
:[CaGaHe] Some new effectivity bounds in computational geometry. In : LN in Computer Science 357 ( 1988). | MR 1008498 | Zbl 0685.68044
, , :[G] Applications of the theory of matrices. Interscience Publischers, New-York - London - Sidney ( 1959). | MR 107648 | Zbl 0085.01001
:[GiTrZ] Gröbner bases and primary decomposition of polynomial ideals. In : Computational aspects of commutative algebra (L. Robbiano ed.), Acad. Press London, 15-33 ( 1989). | MR 988410
, , :[GLRR] Spécialisation de la suite de Sturm et sous-résultants. Revue d'informatique théorique, to appear. | Numdam | Zbl 0732.68059
, , , :[H1] Sur l'extension du théorème de M. Sturm à un système d'équation simultanées. C.R. Acad. Sci. Paris 35, 52-54 (6,11,12,12) ( 1852).
:[H2] Remarques sur le théorème de M. Sturm, C.R. Acad. Sci. Paris 36 294-297 (6,8,10) ( 1853).
:[H3] Extrait d'une lettre de Mr. Ch. Hermite de Paris à Mr. Borchardt de Berlin, sur le nombre des racines d'une équation algébrique comprises entre les limites données, J. Reine Angew. Math. 52, 39-51 (6,7,17,20,24,27,27,32) ( 1856). | Zbl 052.1365cj
:[H-M] Séparations des composantes connexes réelles dans le cas des variétés projectives. In : LN in Math. 959, 358-370 ( 1982). | MR 683142 | Zbl 0521.14008
, :[K] Hankel and Toeplitz matrices and forms. Birkhäuser-Verlag, Boston-Basel-Stuttgart ( 1982). | MR 677503 | Zbl 0493.15018
:[Kn] An invitation to real spectra. In : 1983 Conference on quadratic forms and hermitian K-theory (C.R. Riehm, J, Hambleton ed.) Can. Math. Soc. Conf. Proc. 4 ( 1984). | MR 776447 | Zbl 0586.14015
:[Kn-S] Einfürhrung in die reelle Algebra. Vieweg-Verlag, Braunschweig/Wiesbaden ( 1989). | MR 1029278 | Zbl 0732.12001
, :[Kr-N] The method of symmetric and hermitian forms in the theory of the separation of the roots of algebraic equations. Linear and Multilinear Algebra 10, 265-308 ( 1981). | MR 638124 | Zbl 0584.12018
, :[L] An introduction to real algebra. Rocky Mtn. J. Math. 14, 767-814 ( 1984). | MR 773114 | Zbl 0577.14016
:[Ma1] Signatures et composantes connexes. Math. Ann. 260, 191-210 ( 1982). | MR 664376 | Zbl 0507.14019
:[Ma2] Théorème de Pfister pour les variétés et anneaux de Witt réduits. Invent. Math. 85, 53-72 ( 1986). | MR 842048 | Zbl 0601.14019
:[M-H] Symmetric bilinear forms. Ergebn. der Math. 73, Springer-Verlag, Berlin-Heidelberg ( 1973). | MR 506372 | Zbl 0292.10016
, :[Ob] Verteilung und Berechnung der Nulsstellen reeller Polynom., VEB Deutscher Verlagder Wissenschaften, Berlin ( 1963). | MR 164003 | Zbl 0156.28202
:[P] Hilbert's seventeenth problem and related problem on definite forms. In : Mathematical developments arising from Hilbert Problems, Proc. Symp. Pure Math. 28, part 2, 483-489 ( 1976). | MR 424679 | Zbl 0337.12101
:[Sch] Stability index of real varieties. Invent. Math. 97, 467-483 ( 1989). | MR 1005003 | Zbl 0715.14049
:[Se] Constructions in Algebra. Trans AMS 197, 273-313 ( 1974). | MR 349648 | Zbl 0356.13007
:[S] 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. Philos. Trans. Roy. Soc. London 143,407-548 (7,8,10,13,17,19) ( 1853).
:[Schw] Der Raum der Zusammenhangskomponenten einer reellen Varietät, Geom. Dedicata 13 ( 1983), 361-397. | MR 699882 | Zbl 0508.14015
: