Proving geometric theorems using clifford algebra and rewrite rules

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

Volumn 1421, Issue , 1998, Pages 17-32

  Fèvre, Stéphane ^a   Wang, Dongming ^a  

^a Leibniz IMAG Laboratory   (France)

Author keywords

[No Author keywords available]

Indexed keywords

AUTOMATION; THEOREM PROVING;

CLIFFORD; CLIFFORD ALGEBRA; COORDINATE-FREE; REWRITE RULES; TERM REWRITING SYSTEMS;

ALGEBRA;

EID: 84957050186     PISSN: 03029743     EISSN: 16113349     Source Type: Book Series    
DOI: 10.1007/bfb0054242     Document Type: Conference Paper

References (22)

1. Ablamowicz, R., Lounesto, P., Parra J.M.: Clifford algebras with numeric and symbolic computations. Birkhäuser, Boston (1996).
2. Balbiani, P., Fariñas del Cerro, L.: Affine geometry of collinearity and conditional term rewriting. In: Proc. French Spring School Theor. Comput. Sci. (Font-romeu, May 17-21, 1993), LNCS 909, pp. 196-213 (1995).
3. Chou, S.-C.: Mechanical geometry theorem proving. Reidel, Dordrecht (1988).
4. Chou, S.-C., Schelter, W.F.: Proving geometry theorems with rewrite rules. J. Automat. Reason. 2: 253-273 (1986).
5. Chou, S.-C., Gao, X.-S., Zhang, J.-Z.: Automated geometry theorem proving by vector calculation. In: Proc. ISSAC '93 (Kiev, July 6-8, 1993), pp. 284-291.
6. Chou, S.-C., Gao, X.-S., Zhang, J.-Z.: Machine proofs in geometry. World Scientific, Singapore (1994).
7. Contejean, E., Marché, C., Rabehasaina, L.: Rewrite systems for natural, integral and rational arithmetic. Technical report, L.R.I., Université de Paris-Sud, France (1997).
8. Fèvre, S.: Integration of reasoning and algebraic calculus in geometry. In: Automated deduction in geometry (D. Wang et al., eds.), LNAI 1360, pp. 218-234 (1998).
9. Havel, T.F.: Some examples of the use of distances as coordinates for Euclidean geometry. J. Symb. Comput. 11: 579-593 (1991).
10. Hestenes, D., Sobczyk, G.: Clifford algebra to geometric calculus. Reidel, Dordrecht (1984).
11. Kapur, D.: Using Gröbner bases to reason about geometry problems. J. Symb. Comput. 2: 399-408 (1986).
12. Kapur, D., Saxena, T., Yang, L.: Algebraic and geometric reasoning using Dixon resultants. In: Proc. ISSAC '94 (Oxford, July 20-22, 1994), pp. 99-107.
13. Kutzler, B., Stifter, S.: On the application of Buchberger's algorithm to automated geometry theorem proving. J. Symb. Comput. 2: 389-397 (1986).
14. Li, H.: New explorations on mechanical theorem proving of geometries. Ph. D thesis, Beijing University, China (1994).
15. Li, H., Cheng, M.-T.: Proving theorems in elementary geometry with Clifford algebraic method. Chinese Math. Progress 26: 357-371 (1997).
16. Marche, C.: Normalized rewriting: An alternative to rewriting modulo a set of equations. J. Symb. Comput. 3: 253-288 (1996).
17. Richter-Gebert, J.: Mechanical theorem proving in projective geometry. Ann. Math. Artif. Intell. 13: 139-172 (1995).
18. Stifter, S.: Geometry theorem proving in vector spaces by means of Gröbner bases. In: Proc. ISSAC '93 (Kiev, July 6-8, 1993), pp. 301-310.
19. Wang, D.: Elimination procedures for mechanical theorem proving in geometry. Ann. Math. Artif. Intell. 13: 1-24 (1995).
20. Wang, D.: Clifford algebraic calculus for geometric reasoning with application to computer vision. In: Automated deduction in geometry (D. Wang et al., eds.), LNAI 1360, pp. 115-140 (1998).
21. Wu, W.-T.: Basic principles of mechanical theorem proving in elementary geometries. J. Syst. Sci. Math. Sci. 4: 207-235 (1984).
22. Wu, W.-T.: Mechanical theorem proving in geometries: Basic principles. Springer, Wien (1994).