Geometry machines: From AI to SMC

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

Volumn 1138, Issue , 1996, Pages 213-239

  Wang, Dongming ^a  

^a Institut IMAG   (France)

Author keywords

[No Author keywords available]

Indexed keywords

ARTIFICIAL INTELLIGENCE;

AUTOMATED GEOMETRY THEOREM PROVING; SELECTED EXAMPLES; TECHNOLOGICAL APPLICATIONS;

COMPUTATION THEORY;

EID: 84947930542     PISSN: 03029743     EISSN: 16113349     Source Type: Book Series    
DOI: 10.1007/3-540-61732-9_60     Document Type: Conference Paper

References (171)

1. Anderson, J. R.: Tuning of search of the problem space for geometry proofs. In: Proc. IJCAI ‘81 (Vancouver, August 24-28, 1981), pp. 165-170.
2. Anderson, J. R., Boyle, C. F., Yost, G.: The geometry tutor. In: Proc. IJCAI ‘85 (Los Angeles, August 18-23, 1985), pp. 1-7.
3. Arnon, D. S.: Geometric reasoning with logic and algebra. Artif. Intell. 37: 37-60 (1988).
4. Balbiani, P.: Equation solving in projective planes and planar ternary rings. In: LNCS 850, pp. 95-113 (1994).
5. Balbiani, P.: Equation solving in geometrical theories. In: LNCS 968, pp. 31-55 (1995).
6. Balbiani, P., Dugat, V., Fariñas del Cerro, L., Lopez, A.: Eléments de géométrie mécanique. Hermés, Paris (1994).
7. Balbiani, P., Fariñas del Cerro, L.: Affine geometry of collinearity and conditional term rewriting. In: LNCS 909, pp. 196-213 (1995).
8. Balbiani, P., Lopez, A.: Simplification des figures de la geometrie affine plane d’incidence. In: 9e congrés reconnaissance des formes et intell. artif. (Paris, January 11-14, 1994), pp. 341-351.
9. Bledsoe, W. W., Loveland, D. W. (eds.): Automated theorem proving: After 25 years. Comptemp. Math. 29, Amer. Math. Soc., Providence (1984).
10. Boissonnat, J.-D., Laumond, J.-P. (eds.): Geometry and robotics. Springer, Berlin-Heidelberg (1988).
11. Brüderlin, B.: Automatizing geometric proofs and constructions. In: LNCS 333, pp. 232-252 (1988).
12. Buchberger, B.: Gröbner bases: An algorithmic method in polynomial ideal theory. In: Multidimensional systems theory (Bose, N. K., ed.), Reidel, Dordrecht-Boston, pp. 184-232 (1985).
13. Buchberger, B.: Applications of Gröbner bases in non-linear computational geometry. In: Mathematical aspects of scientific software (Rice, J. R., ed.), Springer, New York, pp. 59-87 (1987).
14. Buchberger, B., Collins, G. E., Kutzler, B.: Algebraic methods for geometric reasoning. Ann. Rev. Comput. Sci. 3: 85-119 (1988).
15. Caferra, R., Herment, M.: A generic graphic framework for combining inference tools and editing proofs and formulae. JSC 19: 217-243 (1995).
16. Carrà Ferro, G., Gallo, G.: A procedure to prove statements in differential geometry. JAR 6: 203-209 (1990).
17. Carrà Ferro, G.: An extension of a procedure to prove statements in differential geometry. JAR 12: 351-358 (1994).
18. Cerutti, E., Davis, P. J.: Formac meets Pappus: Some observations on elementary analytic geometry by computer. Amer. Math. Monthly 76: 895-905 (1969).
19. Chou, S.-C.: Proving elementary geometry theorems using Wu’s algorithm. In [9], pp. 243-286 (1984).
20. Chou, S.-C.: GEO-prover - A geometry theorem prover developed at UT. In: LNCS 230, pp. 679-680 (1986).
21. Chou, S.-C.: A method for the mechanical derivation of formulas in elementary geometry. JAR 3: 291-299 (1987).
22. Chou, S.-C.: Mechanical geometry theorem proving. Reidel, Dordrecht-Boston (1988).
23. Chou, S.-C.: Automated reasoning in geometries using the characteristic set method and Gröbner basis method. In: Proc. ISSAC ‘90 (Tokyo, August 20-24, 1990), pp. 255-260.
24. Chou, S.-C.: A geometry theorem prover for Macintoshes. In: LNCS 607, pp. 687-690 (1992).
25. Chou, S.-C., Gao, X.-S.: Mechanical formula derivation in elementary geometries. In: Proc. ISSAC ‘90 (Tokyo, August 20-24, 1990), pp. 265-270.
26. Chou, S.-C., Gao, X.-S.: Ritt-Wu’s decomposition algorithm and geometry theorem proving. In: LNCS 449, pp. 207-220 (1990).
27. Chou, S.-C., Gao, X.-S.: Proving geometry statements of constructive type. In: LNCS 607, pp. 20-34 (1992).
28. Chou, S.-C., Gao, X.-S.: Automated reasoning in differential geometry and mechanics using characteristic method III. In: Automated reasoning (Shi, Z., ed.), Elsevier, North-Holland, pp. 1-12 (1992).
29. Chou, S.-C., Gao, X.-S.: Automated reasoning in differential geometry and mechanics using the characteristic set method - Parts I, II. JAR 10: 161-189 (1993).
30. Chou, S.-C., Gao, X.-S.: Automated reasoning in differential geometry and mechanics using the characteristic method IV. SSMS 6: 186-192 (1993).
31. Chou, S.-C., Gao, X.-S., Amon, D. S.: On the mechanical proof of geometry theorems involving inequalities. In: Issues in robotics and nonlinear geometry (Hoffmann, C., ed.), JAI Press, Greenwich, pp. 139-181 (1992).
32. Chou, S.-C., Gao, X.-S., Yang, L., Zhang, J.-Z.: Automated production of readable proofs for theorems in non-Euclidean geometries. Tech. Rep. TR-WSU-94-9, Wichita State Univ., USA (1994).
33. Chou, S.-C., Gao, X.-S., Zhang, J.-Z.: Automated production of traditional proofs for constructive geometry theorems. In: Proc. 8th IEEE Symp. LICS (Montreal, June 19-23, 1993), pp. 48-56.
34. 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.
35. Chou, S.-C., Gao, X.-S., Zhang, J.-Z.: Machine proofs in geometry. World Scientific, Singapore (1994).
36. Chou, S.-C., Gao, X.-S., Zhang, J.-Z.: Automated production of traditional proofs in solid geometry. JAR 14: 257-291 (1995).
37. Chou, S.-C., Ko, H.-P.: On mechanical theorem proving in Minkowskian plane geometry. In: Proc. IEEE Symp. LICS (Cambridge, June 16-18, 1986), pp. 187-192.
38. Chou, S.-C., Schelter, W. F.: Proving geometry theorems with rewrite rules. JAR 2: 253-273 (1986).
39. Chou, S.-C., Schelter, W. F., Yang, J.-G.: Characteristic sets and Gröbner bases in geometry theorem proving. In: Resolution of equations in algebraic structures (Ait-Kaaci, H., Nivat, M., eds.), Academic Press, San Diego, pp. 33-92 (1989).
40. Chou, S.-C., Schelter, W. F., Yang, J.-G.: An algorithm for constructing Gröbner bases from characteristic sets and its application to geometry. Algorithmica 5: 147-154 (1990).
41. Chou, S.-C., Yang, J. G.: On the algebraic formulation of certain geometry statements and mechanical geometry theorem proving. Algorithmica 4: 237-262 (1989).
42. Coelho, H., Pereira, L. M.: GEOM: A Prolog geometry theorem prover. Laboratório Nacional de Engenhaaria Civil Memoria no. 525, Ministerio de Habitacao e Obrass Publicas, Portugal (1979).
43. Coelho, H., Pereira, L. M.: Automated reasoning in geometry theorem proving with Prolog. JAR 2: 329-390 (1986).
44. Collins, G. E.: Quantifier elimination for real closed fields by cylindrical algebraic decomposition. In: LNCS 33, pp. 134-165 (1975).
45. Conti, P., Traverso, C.: A case of automatic theorem proving in Euclidean geometry: The Maclane 83 theorem. In: LNCS 948, pp. 183-193 (1995).
46. Crapo, H. (ed.): Computer-aided geometric reasoning. Proc. INRIA Workshop (INRIA Sophia-Antipolis, June 22-26, 1987), INRIA Rocquencourt, France.
47. Cyrluk, D. A., Harris, R. M., Kapur, D.: GEOMETER: A theorem prover for algebraic geometry. In: LNCS 310, pp. 770-771 (1988).
48. Deguchi, K.: An algebraic framework for fusing geometric constraints of vision and range sensor data. In: Proc. IEEE Int. Conf. MFI ‘94 (Las Vegas, October 2-5, 1994), pp. 329-336.
49. Deng, M.-K.: The parallel numerical method of proving the constructive geometric theorem. Chinese Sci. Bull. 34: 1066-1070 (1989).
50. Elcock, E. W.: Representation of knowledge in a geometry machine. Machine Intell. 8: 11-29 (1977).
51. Feamley-Sander, D.: The idea of a diagram. In: Resolution of equations in algebraic structures (Ait-Kaaci, H,, Nivat, M., eds.), Academic Press, San Diego, pp. 27-150 (1989).
52. Fevre, S.: A hybrid method for proving theorems in elementary geometry. In: Proc. ASCM ‘95 (Beijing, August 18-20, 1995), pp. 113-123.
53. Gao, X.-S.: Transcendental functions and mechanical theorem proving in elementary geometries. JAR 6: 403-417 (1990).
54. Gao, X.-S.: Transformation theorems among Cayley-Klein geometries. SSMS 5: 263-273 (1992).
55. Gao, X.-S., Chou, S.-C.: Computations with parametric equations. In: Proc. IS- SAC ‘91 (Bonn, July 15-17, 1991), pp. 122-127.
56. Gao, X.-S., Li, Y.-L., Lin, D.-D., Lii, X.-S.: A geometric theorem prover based on Wu’s method. In: Proc. IWMM ‘92 (Beijing, July 16-18, 1992), pp. 201-205.
57. Gao, X.-S., Wang, D.-K.: On the automatic derivation of a set of geometric formulae. J. Geom. 53: 79-88 (1995).
58. Gelemter, H.: Realization of a geometry theorem proving machine. In: Proc. Int. Conf. Info. Process. (Paris, June 15-20, 1959), pp. 273-282.
59. Gelemter, H., Hansen, J. R., Loveland, D. W.: Empirical explorations of the geometry-theorem proving machine. In: Proc. Western Joint Comput. Conf. (San Francisco, May 3-5, 1960), pp. 143-147.
60. Gilmore, P. C.: An examination of the geometry theorem machine. Artif. Intell. 1: 171-187 (1970).
61. Goldstein, I.: Elementary geometry theorem proving. MIT AI Memo no. 28, MIT, USA (1973).
62. Guergueb, A., Mainguené, J., Roy, M.-F.: Examples of automatic theorem proving in real geometry. In: Proc. ISSAC ‘94 (Oxford, July 20-22, 1994), pp. 20-24.
63. Hadzikadic, M., Lichtenberger, F., Yun, D. Y. Y.: An application of knowledgebase technology in education: A geometry theorem prover. In: Proc. SYMSAC ‘86 (Waterloo, July 21-23, 1986), pp. 141-147.
64. Havel, T. F.: Some examples of the use of distances as coordinates for Euclidean geometry. JSC 11: 579-593 (1991).
65. Hilbert, D.: Grundlagen der Geometrie. Teubner, Stuttgart (1899).
66. Hong, H., Wang, D., Winkler, F. (eds.): Algebraic approaches to geometric reasoning. Special issue of Ann. Math. Artif. Intell 13(1-2), Baltzer, Basel (1995).
67. Hong, J.: Can we prove geometry theorems by computing an example? Sci. Sinica 29: 824-834 (1986).
68. Hong, J.: Proving by example and gap theorems. In: Proc. 27th Ann. Symp. Foundations Comput. Sci. (Toronto, October 27-29, 1986), pp. 107-116.
69. Hussain, M. A., Drew, M. A., Noble, B.: Using a computer for automatic proving of geometric theorems. Comput. Mech. Eng. 5: 56-69 (1986).
70. Kalkbrener, M.: A generalized Euclidean algorithm for geometry theorem proving. In [66]: 73-95 (1995).
71. Kandri-Rody, A., Weispfenning, V.: Non-commutative Gröbner bases in algebras of solvable type. JSC 9: 1-26 (1990).
72. Kapur, D.: Geometry theorem proving using Hilbert’s Nullstellensatz. In: Proc. SYMSAC ‘86 (Waterloo, July 21-23, 1986), pp. 202-208.
73. Kapur, D.: Using Gröbner bases to reason about geometry problems. JSC 2: 399-408 (1986).
74. Kapur, D.: A refutational approach to geometry theorem proving. Artif. Intell. 37: 61-93 (1988).
75. Kapur, D., Mundy, J. L.: Wu’s method and its application to perspective viewing. Artif. Intell. 37: 15-26 (1988).
76. Kapur, D., Mundy, J. L. (eds.): Geometric reasoning. Special issue of Artif. Intell. The MIT Press, Cambridge (1989).
77. 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.
78. Kapur, D., Wan, H. K.: Refutational proofs of geometry theorems via characteristic set computation. In: Proc. ISSAC ‘90 (Tokyo, August 20-24, 1990), pp. 277-284.
79. Kelanic, T. J.: Theorem-proving with EUCLID. Creative Comput. 4/4: 60-63 (1978).
80. Ko, H.-P.: ALGE-prover II: A new edition of ALGE-prover. Tech. Rep. 86CRD-081, General Electric Co., Schenectady, USA (1986).
81. Ko, H.-P.: Geometry theorem proving by decomposition of quasi-algebraic sets: An application of the Ritt-Wu principle. Artif. Intell. 37: 95-122 (1988).
82. Ko, H.-P., Chou, S.-C.: A decision method for certain algebraic geometry problems. Rocky Mountain J. Math. 19: 709-724 (1989).
83. Ko, H.-P., Hussain, M. A.: A study of Wu’s method - A method to prove certain theorems in elementary geometry. Congr. Numer. 48: 225-242 (1985).
84. Ko, H.-P., Hussain, M. A.: ALGE-prover: An algebraic geometry theorem proving software. Tech. Rep. 85CRD139, General Electric Co., Schenectady, USA (1985).
85. Kusche, K., Kutzler, B., Stifter, S.: Implementation of a geometry theorem proving package in Scratchpad II. In: LNCS 387, pp. 246-257 (1989).
86. Kutzler, B.: Algebraic approaches to automated geometry theorem proving. Ph.D thesis, RISC-LINZ, Johannes Kepler Univ., Austria (1988).
87. Kutzler, B.: Careful algebraic translations of geometry theorems. In: Proc. ISSAC ‘89 (Portland, July 17-19, 1989), pp. 254-263.
88. Kutzler, B., Stifter, S.: Automated geometry theorem proving using Buchberger’s algorithm. In: Proc. SYMSAC ‘86 (Waterloo, July 21-23., 1986), pp. 209-214.
89. Kutzler, B., Stifter, S.: On the application of Buchberger’s algorithm to automated geometry theorem proving. JSC 2: 389-397 (1986).
90. Kutzler, B., Stifter, S.: A geometry theorem prover based on Buchberger’s algorithm. In: LNCS 230, pp. 693-694 (1986).
91. Kutzler, B., Stifter, S.: Collection of computerized proofs of geometry theorems. Tech. Rep. 86-12, RISC-LINZ, Johannes Kepler Univ., Austria (1986).
92. Laborde, J.-M. (ed.): Intelligent learning environments - The case of geometry. Springer, Berlin-New York (1996).
93. Li, H.: Clifford algebra and area method. In [99] no. 14: 37-69 (1996).
94. Li, H., Cheng, M.: Proving theorems in elementary geometry with Clifford algebraic method. Preprint, MMRC, Academia Sinica, China (1995).
95. Li, Z.: Automatic implicitization of parametric objects. In [99] no. 4: 54-62 (1989).
96. Li, Z.: Mechanical theorem proving in the local theory of surfaces. In [66]: 25-46 (1995).
97. Lin, D., Liu, Z.: Some results on theorem proving in geometry over finite fields. In: Proc. ISSAC ‘93 (Kiev, July 6-8, 1993), pp. 292-300.
98. McPhee, N. F., Chou, S.-C., Gao, X.-S.: Mechanically proving geometry theorems using a combination of Wu’s method and Collins’ method. In: LNCS 814, pp. 401-415 (1994).
99. MMRC (ed.): Mathematics-Mechanization Research Preprints, nos. 1-14. Academia Sinica, China (1987-1996).
100. Mundy, J. L.: Reasoning about 3-D space with algebraic deduction. In: Robotics research: The third international symposium, The MIT Press, Cambridge- London, pp. 117-124 (1986).
101. Nevins, A. J.: Plane geometry theorem proving using forward chaining. Artif. Intell. 6: 1-23 (1975).
102. Pfalzgraf, J.: A category of geometric spaces: Some computational aspects. In [66]: 173-193 (1995).
103. Pfalzgraf, J., Stokkermans, K., Wang, D.: The robotics benchmark. In: Proc. 12-Month MEDLAR Workshop (Weinberg Castle, November 4-7, 1990), DOC, Imperial College, Univ. of London, England.
104. Quaife, A.: Automated development of Tarski’s geometry. JAR 5: 97-118 (1989).
105. Rege, A.: A complete and practical algorithm for geometric theorem proving. In: Proc. 11th Ann. Symp. Comput. Geom. (Vancouver, June 5-7, 1995), pp. 277-286.
106. Richter-Gebert, J.: Mechanical theorem proving in projective geometry. In [66]: 139-172 (1995).
107. Ritt, J. F.: Differential algebra. Amer. Math. Soc., New York (1950).
108. Shi, H.: On the resultant formula for mechanical theorem proving. In [99] no. 4: 77-86 (1989).
109. Smietanski, F.: Systèmes de réécriture sur des idèaux de polynômes, géométrie et calcul formel. RAPPORT de DEA, E.N.S., Université de Jussieu Paris 7, France (1986/87).
110. Starkey, J. D.: EUCLID: A program which conjectures, proves and evaluates theorems in elementary geometry. Order no. 75-2780, Univ. Microfilms (1975).
111. 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.
112. Swain, M. J., Mundy, J. L.: Experiments in using a theorem prover to prove and develop geometrical theorems in computer vision. In: Proc. IEEE Int. Conf. Robotics Automat. (San Francisco, April 7-10, 1986), pp. 280-285.
113. Tarski, A.: A decision method for elementary algebra and geometry. The RAND Corporation, Santa Monica (1948).
114. Ueberberg, J.: Interactive theorem proving and computer algebra. In: LNCS 958, pp. 1-9 (1995).
115. Ullmen, S.: A model-driven geometry theorem prover. AI Lab Memo no. 321, MIT, Cambridge, USA (1975).
116. Wang, D.-K.: Mechanical solution of a group of space geometry problems. In: Proc. IWMM‘92 (Beijing, July 16-18, 1992), pp. 236-243.
117. Wang, D.: Mechanical approach for polynomial set and its related fields. Ph.D thesis, Academia Sinica, China (1987) [in Chinese].
118. Wang, D.: Proving-by-examples method and inclusion of varieties. Kexue Tongbao 33: 1121-1123 (1988).
119. Wang, D.: A new theorem discovered by computer prover. J. Geom. 36: 173-182 (1989).
120. Wang, D.: On Wu’s method for proving constructive geometric theorems. In: Proc. IJCAI‘89 (Detroit, August 20-25, 1989), pp. 419-424.
121. Wang, D.: Reasoning about geometric problems using algebraic methods. In: Medlar 24-month deliverables, DOC, Imperial College, Univ. of London, England (1991).
122. Wang, D.: Irreducible decomposition of algebraic varieties via characteristic sets and Gröbner bases. Comput. Aided Geom. Design 9: 471-484 (1992).
123. Wang, D.: Geometry theorem proving with existing technology. In: Medlar II Report PPRl, DOC, Imperial College, Univ. of London, England (1993). Also in: Proc. 1st Asian Tech. Conf. Math. (Singapore, December 18-21, 1995), 561-570.
124. Wang, D.: Algebraic factoring and geometry theorem proving. In: LNCS 814, pp. 386-400 (1994).
125. Wang, D.: Reasoning about geometric problems using an elimination method. In: Automated practical reasoning: Algebraic approaches (Pfalzgraf, J., Wang, D., eds.), Springer, Wien-New York, pp. 147-185 (1995).
126. Wang, D.: Elimination procedures for mechanical theorem proving in geometry. In [66]: 1-24 (1995).
127. Wang, D.: A method for proving theorems in differential geometry and mechanics. J. Univ. Comput. Sci. 1: 658-673 (1995).
128. Wang, D.: GEOTHER: A geometry theorem prover. In: Proc. CADE-13 (New Brunswick, July 30 - August 3, 1996), to appear.
129. Wang, D., Gao, X.-S.: Geometry theorems proved mechanically using Wu’s method - Part on Euclidean geometry. In [99] no. 2: 75-106 (1987).
130. Wang, D., Hu, S.: A mechanical proving system for constmctible theorems in elementary geometry. J. SSMS 7: 163-172 (1987) [in Chinese].
131. Winkler, F.: A geometrical decision algorithm based on the Gröbner bases algorithm. In: LNCS 358, pp. 356-363 (1988).
132. Winkler, F.: Gröbner bases in geometry theorem proving and simplest degeneracy conditions. Math. Pannonica 1: 15-32 (1990).
133. Winkler, F.: Automated theorem proving in nonlinear geometry. In: Issues in robotics and nonlinear geometry (Hoffmann, C., ed.), JAI Press, Greenwich, pp. 183-197 (1992).
134. Wong, R.: Construction heuristics for geometry and a vector algebra representation of geometry. Tech. Memo. 28, Project MAC, MIT, Cambridge, USA (1972).
135. Wu, T.-J.: On a collision problem. In [99] no. 7: 96-104 (1991).
136. Wu, W.-t.: On the decision problem and the mechanization of theorem-proving in elementary geometry. Sci. Sinica 21: 159-172 (1978). Also in [9], pp. 213-234 (1984).
137. Wu, W.-t.: On the mechanization of theorem-proving in elementary differential geometry. Sci. Sinica Special Issue on Math. (I): 94-102 (1979) [in Chinese].
138. Wu, W.-t.: Mechanical theorem proving in elementary geometry and elementary differential geometry. In: Proc. 1980 Beijing Symp. Diff. Geom. Diff. Eqs. (Beijing, August 18 - September 21, 1980), pp. 1073-1092.
139. Wu, W.-t.: Toward mechanization of geometry - Some comments on Hilbert’s “Grundlagen der Geometrie”. Acta Math. Scientia 2: 125-138 (1982).
140. Wu, W.-t.: Some remarks on mechanical theorem-proving in elementary geometry. Acta Math. Scientia 3: 357-360 (1983).
141. Wu, W.-t.: Basic principles of mechanical theorem proving in elementary geometries. J. SSMS 4: 207-235 (1984). Also in JAR 2: 221-252 (1986).
142. Wu, W.-t.: Basic principles of mechanical theorem proving in geometries (part on elementary geometries). Science Press, Beijing (1984) [in Chinese]. English Translation, Springer, Wien-New York (1994).
143. Wu, W.-t.: Some recent advances in mechanical theorem-proving of geometries. In [9], pp. 235-241 (1984).
144. Wu, W.-t.: A mechanization method of geometry I. Chinese Quart. J. Math. 1: 1-14 (1986).
145. Wu, W.-t.: A mechanization method of geometry and its applications I. J. SSMS 6: 204-216 (1986).
146. Wu, W.-t.: A report on mechanical theorem proving and mechanical theorem discovering in geometries. Adv. Sci. China Math. 1: 175-198 (1986).
147. Wu, W.-t.: A constructive theory of differential algebraic geometry. In: Lecture Notes in Math. 1255, pp. 173-189 (1987).
148. Wu, W.-t.: A mechanization method of geometry and its applications II. Kexue Tongbao 32: 585-588 (1987).
149. Wu, W.-t.: On reducibility problem in mechanical theorem proving of elementary geometries. Chinese Quart. J. Math. 2: 1-20 (1987).
150. Wu, W.-t.: A mechanization method of geometry and its applications III. SSMS 1: 1-17 (1988).
151. Wu, W.-t.: A mechanization method of geometry and its applications IV. SSMS 2: 97-109 (1989).
152. Wu, W.-t.: Equations-solving and theorems-proving - Zero-set formulation and ideal formulation. In: Proc. Asian Math. Conf. (Hong Kong, August 14-18, 1990), pp. 1-10.
153. Wu, W.-t.: Mechanical theorem proving of differential geometries and some of its applications in mechanics. JAR 7: 171-191 (1991).
154. Wu, W.-t.: A report on mechanical geometry theorem proving. Progr. Natur. Sci. 2: 1-17 (1992).
155. Wu, W.-t.: A mechanization method of equations solving and theorem proving. In: Issues in robotics and nonlinear geometry (Hoffmann, C., ed.), JAI Press, Greenwich, pp. 103-138 (1992).
156. Wu, W.-t.: On problems involving inequalities. In [99] no. 7: 1-13 (1992).
157. Wu, W.-t.: On a finiteness theorem about problems involving inequalities. SSMS 7: 193-200 (1994).
158. Wu, W.-t.: Centred configurations in planet motions and vortex motions. In [99] no. 13: 1-14 (1995).
159. Wu, W.-t., Lii, X.-L.: Triangles with equal bisectors. People’s Edu. Press, Beijing [in Chinese].
160. Wu, W.-t., Wang, D.-K.: The algebraic surface fitting problem in CAGD. Math. Practice Theory no. 3: 26-31 (1994) [in Chinese]
161. Xu, C., Shi, Q., Cheng, M.: A globed stereo vision method based on Wu-solver. In: Proc. GMICV‘95 (Xi’an, April 27-29, 1995), pp. 198-205.
162. Xu, L., Chen, J.: AUTOBASE: A system which automatically establishes the geometry knowledge base. In: Proc. COMPINT: Computer aided technologies (Montreal, September 8-12, 1985), pp. 708-714.
163. Xu, L., Chen, J., Yang, L.: Solving plane geometry problem by learning. In: Proc. IEEE 1st Int. Conf. Comput. Appl. (Beijing, June 20-22, 1984), pp. 862-869.
164. Yang, L.: A new method of automated theorem proving. In: The mathematical revolution inspired by computing (Johnson, J., Loomes, M., eds.), Oxford Univ. Press, New York, pp. 115-126 (1991).
165. Yang, L., Zhang, J.-Z.: Searching dependency between algebraic equations: An algorithm applied to automated reasoning. In: Artificial intelligence in mathematics (Johnson, J., McKee, S., Vella, A., eds.), Oxford Univ. Press, Oxford, pp. 147-156 (1994).
166. Yang, L., Zhang, J.-Z., Hou, X.-R.: A criterion for dependency of algebraic equations, with applications to automated theorem proving. Sci. China Ser. A 37: 547-554 (1994).
167. Yang, L., Zhang, J.-Z., Hou, X.-R.: An efficient decomposition algorithm for geometry theorem proving without factorization. In: Proc. ASCM‘95 (Beijing, August 18-20, 1995), pp. 33-41.
168. Yang, L., Zhang, J.-Z., Li, C.-Z.: A prover for parallel numerical verification of a class of constructive geometry theorems. In: Proc. IWMM‘92 (Beijing, July 16-18, 1992), pp. 244-250.
169. Zhang, J.-Z.: How to solve geometry problems using areas. Shanghai Edu. Publ., Shanghai (1982) [in Chinese].
170. Zhang, J.-Z., Chou, S.-C., Gao, X.-S.: Automated production of traditional proofs for theorems in Euclidean geometry I. In [66]: 109-137 (1995).
171. Zhang, J.-Z., Yang, L., Deng, M.-K.: The parallel numerical method of mechanical theorem proving. Theoret. Comput. Sci. 74: 253-271 (1990).