Gröbner bases in type theory

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

Volumn 1657, Issue , 1999, Pages 33-46

  Coquand, Thierry ^a   Persson, Henrik ^a  

^a CHALMERS UNIVERSITY OF TECHNOLOGY   (Sweden)

Author keywords

[No Author keywords available]

Indexed keywords

ALGEBRA; FORMAL LANGUAGES;

COMPUTATIONAL ALGEBRA; CONSTRUCTIVE PROOF; FORMALISATION; INDUCTIVE DEFINITIONS; INTEGRATED DEVELOPMENT; OPEN INDUCTIONS; S-ALGORITHMS; STANDARD THEORIES;

COMPUTATION THEORY;

EID: 70349930710     PISSN: 03029743     EISSN: 16113349     Source Type: Book Series    
DOI: 10.1007/3-540-48167-2_3     Document Type: Conference Paper

References (26)

1. P. Aczel. An Introduction to Inductive Definitions. In J. Barwise, editor, Handbook of Mathematical Logic, pages 739-782. North-Holland Publishing Company, 1977. 34, 37, 38.
2. L. Augustsson. Cayenne - a language with dependent types. Technical report, Department of Computing Science, Chalmers University of Technology, 1998. Homepage: http://www.cs.chalmers.se/˜augustss/cayenne/. 42.
3. U. Berger and H. Schwichtenberg. The greatest common divisor: a case study for program extraction from classical proofs. In Proceedings of the Workshop TYPES ’95, Torino, Italy, June 1995, number 1158 in Lecture Notes in Computer Science. Springer-Verlag, 1996. 34.
4. B. Buchberger. An Algorithm for Finding a Basis for the Residue Class Ring of a Zero-Dimensional Polynomial Ideal (German). PhD thesis, University of Innsbruck, 1965. 33.
5. B. Buchberger. Gröbner bases: An algorithmic method in polynomial ideal theory. In N. K. Bose, editor, Multidimensional systems theory, pages 184-232. Reidel Publ. Co., 1985. 33, 34.
6. B. Buchberger. Introduction to Gröbner bases. In B. Buchberger and F.Winkler, editors, Gröbner bases and applications, pages 3-31. Cambridge University Press, 1998. 34.
7. T. Becker and V. Weispfenning. Gröbner bases, volume 141 of Graduate Texts in Mathematics. Springer-Verlag, New York, 1993. In cooperation with H. Kredel. 34, 35, 39, 42.
8. D. Cox, J. Little, and D. O’Shea. Ideals, varieties, and algorithms. Undergraduate Texts in Mathematics. Springer-Verlag, New York, second edition, 1997. 34.
9. R. L. Constable et al. Implementing Mathematics with the NuPRL Proof Development System. Prentice-Hall, Englewood Cliffs, NJ, 1986. 35.
10. Th. Coquand. Constructive topology and combinatorics. In proceeding of the conference Constructivity in Computer Science, San Antonio, LNCS 613, pages 28-32, 1992. 33, 34, 37, 38, 39.
11. C. Coquand. The homepage of the Agda type checker. Homepage: http://www.cs.chalmers.se/˜catarina/Agda/, 1998. 42.
12. L. E. Dickson. Finiteness of the odd perfect and primitive abundant numbers with n distinct prime factors. Am. J. Math., 35:413-422, 1913. 34.
13. P. Dybjer. Comparing integrated and external logics of functional programs. Science of Computer Programming, 14:59-79, 1990. 33.
14. Frö97. R. Fröberg. An introduction to Gröbner bases. John Wiley & Sons, 1997. 34.
15. J-Y Girard. Linear logic and parallelism. In M. Venturini Zilli, editor, Mathematical Models for the Semantics of Parallelism, number LNCS 280, pages 166-182. Springer-Verlag, September 1986. 33.
16. G. Huet, G. Kahn, and C. Paulin-Mohring. The Coq proof assistant: A tutorial. Technical report, Rapport Technique 204, INRIA, 1997. 34.
17. P. B. Jackson. Enhancing the Nuprl proof development system and applying it to computational abstract algebra. PhD thesis, Cornell University, 1995. 35, 41.
18. C. Jacobsson and C. Löfwall. Standard bases for general coefficient rings and a new constructive proof of Hilbert’s basis theorem. J. Symbolic Comput., 12(3):337-371, 1991. 34, 39.
19. P. Martin-Löf. Notes on Constructive Mathematics. Almqvist & Wiksell, 1968. 37.
20. R.Mines, F. Richman, and W. Ruitenburg. A course in constructive algebra. Universitext. Springer-Verlag, New York, 1988. 39.
21. B. Nordström, K. Petersson, and J. M. Smith. Programming in Martin-Löf ’s Type Theory. An Introduction. Oxford University Press, 1990. 33.
22. C. Nash-Williams. On well-quasi-ordering finite trees. Proceedings of the Cambridge Philosophical Society, 59:833-835, 1963. 41.
23. Loïc Pottier. Dixon’s lemma. URL: ftp://www.inria.fr/safir/pottier/MON, 1996. 34.
24. J-C. Raoult. Proving open properties by induction. Information processing letters, 29:19-23, 1988. 33, 34, 37, 39.
25. F. Richman. Constructive aspects of noetherian rings. In Proc. AMS 44, pages 436-441, 1974. 39.
26. L. Théry. Proving and computing: A certified version of the Buchberger’s algorithm. In proceeding of the 15th International Conference on Automated Deduction, Lindau, Germany, LNAI 1421, 1998. 34, 41.