A constructive proof of the Fundamental Theorem of Algebra without using the rationals

Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

Volumn 2277, Issue , 2002, Pages 96-111

  Geuvers, Herman ^a   Wiedijk, Freek ^a   Zwanenburg, Jan ^a  

^a RADBOUD UNIVERSITY NIJMEGEN   (Netherlands)

Author keywords

[No Author keywords available]

Indexed keywords

ALGEBRA; ARTIFICIAL INTELLIGENCE;

AXIOMATI-SATION; COMPLEX NUMBER; CONSTRUCTIVE PROOF; CONSTRUCTIVE REALS; FORMALISATION; FUNDAMENTAL THEOREMS; ORDERED FIELDS; RATIONAL NUMBERS;

THEOREM PROVING; ALGEBRA;

EID: 26844561948     PISSN: 03029743     EISSN: 16113349     Source Type: Journal    
DOI: 10.1007/3-540-45842-5_7     Document Type: Article

References (18)

1. E. Bishop and D. Bridges, Constructive Analysis, Number 279 in Grundlehren der mathematischen Wissenschaften. Springer, 1985.
2. L.E.J. Brouwer and B. de Loor, Intuitionistischer Beweis des Fundamentalsatzes der Algebra, in Proceedings of the KNAW, 27, pp. 186-188, 1924.
3. L.E.J. Brouwer, Intuitionistische Ergänzung des Fundamentalsatzes der Algebra, in Proceedings of the KNAW, 27, pp. 631-634, 1924.
4. B. Dejon and P. Henrici, Editors, Constructive Aspects of the Fundamental Theorem of Algebra, Proceedings of a symposium at IBM Research Lab, Zürich-Rüschlikon, June 5-7, 1967, Wiley-Interscience, London.
5. H.-D. Ebbinghaus et al. (eds.), Numbers, Springer, 1991, 395 pp.
6. B. Fine and G. Rosenberger, The Fundamental Theorem of Algebra, Undergraduate Texts in Mathematics, Springer, 1997, xii+208 pp.
7. H. Geuvers, F. Wiedijk, J. Zwanenburg, R. Pollack, M. Niqui, H. Barendregt, FTA project, http://www.cs.kun.nl/gi/projects/fta/.
8. H. Geuvers, R. Pollack, F. Wiedijk, and J. Zwanenburg. The algebraic hierarchy of the FTA project, in Calculemus 2001 workshop proceedings, pp. 13-27, Siena, 2001.
9. H. Geuvers, M. Niqui, Constructive Reals in Coq: Axioms and Categoricity, Types 2000 Workshop, Durham, UK, this volume.
10. P. Henrici and I. Gargantini, Uniformly convergent algorithms for the simultaneous approximation of all zeros of a polynomial, in [4], pp. 77-113.
11. H. Kneser, Der Fundamentalsatz der Algebra und der Intuitionismus, Math. Zeitschrift, 46, 1940, pp. 287-302.
12. M. Kneser, Ergänzung zu einer Arbeit von Hellmuth Kneser über den Fundamentalsatz der Algebra, Math. Zeitschrift, 177, 1981, pp. 285-287.
13. J.E. Littlewood, Every polynomial has a root, Journal of the London Math. Soc. 16, 1941, pp. 95-98.
14. B. de Loor, Die Hoofstelling van die Algebra van Intuïtionistiese standpunt, Ph.D. Thesis, Univ. of Amsterdam, Netherlands, Feb. 1925, pp. 63 (South-African).
15. Helmut Schwichtenberg, Ein konstruktiver Beweis des Fundamentalsatzes, Appendix A (pp. 91-96) of Algebra, Lecture notes, Mathematisches Institut der Universit ät München 1998, http://www.mathematik.uni-muenchen.de/ schwicht/lectures/algebra/ws98/skript.ps
16. E. Specker, The Fundamental Theorem of Algebra in Recursive Analysis, in [4], pp. 321-329.
17. A. Troelstra and D. van Dalen, Constructivism in Mathematics, vols. 121 and 123 in Studies in Logic and The Found. of Math., North-Holland, 1988.
18. H. Weyl, Randbemerkungen zu Hauptproblemen der Mathematik, Math. Zeitschrift, 20, 1924, pp. 131-150.