A recipe for symbolic geometric computing: Long geometric product, BREEFS and Clifford factorization

Proceedings of the International Symposium on Symbolic and Algebraic Computation, ISSAC

Volumn , Issue , 2007, Pages 261-268

  Li, Hongbo ^a  

^a INSTITUTE OF GEOLOGY AND GEOPHYSICS   (China)

Author keywords

Conformal geometric algebra; Geometric invariance; Geometric theorem proving; Null bracket algebra; Symbolic geometric computing

Indexed keywords

COMPUTATIONAL GEOMETRY; POLYNOMIALS; THEOREM PROVING;

BRACKET ALGEBRA; CLIFFORD FACTORIZATION; CONFORMAL GEOMETRIC ALGEBRA; GEOMETRIC INVARIANCE; GEOMETRIC THEOREM PROVING; NULL BRACKET ALGEBRA (NBA); SYMBOLIC GEOMETRIC COMPUTING;

FACTORIZATION;

EID: 36349024704     PISSN: None     EISSN: None     Source Type: Conference Proceeding    
DOI: 10.1145/1277548.1277584     Document Type: Conference Paper

References (14)

1. S. C. Chou. Mechanical Geometry Theorem Proving. D. Reidel, Dordrecht, 1988.
2. S. C. Chou, X. S. Gao, J. Z. Zhang. Machine Proofs in Geometry. World Scientific, Singapore, 1994.
3. H. Crapo, J. Richter-Gebert. Automatic Proving of Geometric Theorems. In: Invariant Methods in Discrete and Computational Geometry, N. White (ed.), pp. 107-139, Kluwer, Dordrecht, 1994.
4. T. Havel. Some Examples of the Use of Distances as Coordinates for Euclidean Geometry. J. of Symbolic Computation 11: 579-593, 1991.
5. D. Hestenes, G. Sobczyk. Clifford Algebra to Geometric Calculus, Kluwer, Dordrecht, 1984.
6. H. Li, D. Hestenes, A. Rockwood. Generalized Homogeneous Coordinates for Computational Geometry. In: Geometric Computing with Clifford Algebras, G. Sommer (ed.), pp. 27-60, Springer, Heidelberg, 2001.
7. H. Li. Automated Theorem Proving in the Homogeneous Model with Clifford Bracket Algebra. In: Applications of Geometric Algebra in Computer Science and Engineering, L. Dorst et al. (eds.), pp. 69-78, Birkhauser, Boston, 2002.
8. H. Li. Symbolic Computation in the Homogeneous Geometric Model with Clifford Algebra. In: Proc. ISSA C 2004, J. Gutierrez (ed.), ACM Press, New York, pp. 221-228, 2004.
9. H. Li. On Miquel's Five-Circle Theorem. Computer Algebra and Geometric Algebra with Applications, H. Li et al. (eds), LNCS 3519, pp. 217-228, Springer Berlin Heidelberg, 2005.
10. H. Li. Conformal Geometric Algebra and Algebraic Manipulations of Geometric Invariants. Journal of Computer-Aided Design and Computer Graphics 18(7): 902-911, 2006. (in Chinese)
11. H. Li, Y. Wu. Automated Short Proof Generation in Projective Geometry with Cayley and Bracket Algebras I. Incidence Geometry. J. of Symbolic Computation 36(5): 717-762, 2003.
12. B. Mourrain and N. Stolfi, Computational Symbolic Geometry, in Invariant Methods in Discrete and Computational Geometry, N. L. White (ed), pp. 107-139, D. Reidel, Dordrecht, 1995.
13. D. Wang. Geometric Reasoning with Geometric Algebra. In: Geometric Algebra with Applications in Science and Engineering, E. Bayro-Corrochano et al. (eds.), pp. 89-109, Birkhauser, Boston, 2001.
14. N. White. Multilinear Cayley Factorization. J. of Symbolic Computation 11: 421-438, 1991.