Bibliography on Geometric Reasoning


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Books and Special Issues

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Arnon, D. S., Buchberger, B. (eds.): Algorithms in real algebraic geometry. Special Issue of J. Symb. Comput. 5(1-2), Academic Press, London (1988).

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Balbiani, P., Dugat, V., Fariñas del Cerro, L., Lopez, A.: Eléments de géométrie mécanique. Hermès, Paris (1994).

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Boissonnat, J.-D., Laumond, J.-P. (eds.): Geometry and robotics. Springer, Berlin Heidelberg (1988).

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Bokowski, J., Sturmfels, B.: Computational synthetic geometry. LNM 1355, Springer, Berlin Heidelberg (1989).

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Chen, F., Wang, D. (eds.): Geometric computation. World Scientific, Singapore (2004).

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Chou, S.-C.: Mechanical geometry theorem proving. Reidel, Dordrecht Boston (1988).

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Chou, S.-C., Gao, X.-S., Zhang, J.-Z.: Machine proofs in geometry. World Scientific, Singapore (1994).

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Crapo, H. (ed.): Computer-aided geometric reasoning. Proc. INRIA Workshop (INRIA Sophia-Antipolis, June 22-26, 1987), INRIA Rocquencourt, France.

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Du, D.-Z., Hwang, F. (eds.): Computing in Euclidean geometry. World Scientific, Singapore (1992). 2nd edition (1995).

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Gao, X.-S., Wang, D., Yang, L. (eds.): Automated deduction in geometry - ADG '98 proceedings. LNAI 1669, Springer, Berlin Heidelberg (1999).

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Hoffmann, C. M.: Geometric and solid modeling: An introduction. Morgan Kaufmann, San Mateo (1989).

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Hoffmann, C. M. (ed.): Issues in robotics and nonlinear geometry. JAI Press, Greenwich (1992).

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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).

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Kapur, D., Mundy, J. L. (eds.): Geometric reasoning. Special issue of Artif. Intell. 37(1-3), The MIT Press, Cambridge (1989).

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Kramer, G.: Solving geometric constraint systems. The MIT Press, Cambridge (1992).

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Kueker, D., Smith, C. (eds.): Learning and geometry: Computational approaches. Birkhäuser, Boston (1996).

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Laborde, J.-M. (ed.): Intelligent learning environments - The case of geometry. Springer, Berlin New York (1996).

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McCune, W., Padmanabhan, R.: Automated deduction in equational logic and cubic curves. Springer, Berlin Heidelberg (1996).

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MMRC (ed.): Mathematics mechanization research preprints (1-15). Academia Sinica, China (1987-1997).

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Richter-Gebert, J., Kortenkamp, U. H.: The interactive geometry software Cinderella. Springer, Berlin Heidelberg (1999).

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Richter-Gebert, J., Kortenkamp, U. H.: User manual for the interactive geometry software Cinderella. Springer, Berlin Heidelberg (2000).

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Richter-Gebert, J., Kortenkamp, U. H.: Cinderella: Die interaktive Geometrie-Software. Springer, Berlin Heidelberg (2001).

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Richter-Gebert, J., Kortenkamp, U. H.: Benutzerhandbuch fr die interaktive Geometrie-Software Cinderella. Springer, Berlin Heidelberg (2001).

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Richter-Gebert, J., Kortenkamp, U. H.: Cinderella: Software interattivo di geometria. Springer, Berlin Heidelberg (2001).

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Richter-Gebert, J., Wang, D. (eds.): Proceedings of ADG 2000 - The third international workshop on automated deduction in geometry (Zurich, Switzerland, September 25-27, 2000). 290 pages, available from Theoretische Informatik, ETH Zentrum, Zurich, Switzerland.

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Richter-Gebert, J., Wang, D. (eds.): Automated deduction in geometry - ADG 2000 revised papers. LNAI 2061, Springer, Berlin Heidelberg (2001).

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Sturmfels, B., White, N. L. (eds.): Invariant-theoretic algorithms in geometry. Special issue of J. Symb. Comput. 11(5-6), Academic Press, London (1991).

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Tarski, A.: A decision method for elementary algebra and geometry. The RAND Corporation, Santa Monica (1948). 2nd edition, Univ. of California Press, Berkeley Los Angeles (1951).

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Wang, D. (ed. in cooperation with R. Caferra, L. Fariñas del Cerro and H. Shi): Automated deduction in geometry. LNAI 1360, Springer, Berlin Heidelberg (1997).

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Wang, D.: Elimination methods. Springer, Wien New York (2001).

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Wang, D.: Elimination practice: Software tools and applications. Imperial College Press, London (2004).

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Woodwark, J. (ed.): Geometric reasoning. Oxford Univ. Press, Oxford (1990).

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Wu, W.-t.: Basic principles of mechanical theorem proving in geometries - Part on elementary geometries. Science Press, Beijing (1984) [in Chinese].

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Wu, W.-t. Mechanical theorem proving in geometries: Basic principles (translated from the Chinese by X. Jin and D. Wang). Springer, Wien New York (1994).

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Wu, W.-t., Lü, X.-L.: Triangles with equal bisectors. People's Education Press, Beijing (1985) [in Chinese].

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Yang, L., Zhang, J.-Z., Hou, X.-R.: Nonlinear algebraic equation system and automated theorem proving. Shanghai Sci & Tech Education Publ. House, Shanghai (1996) [in Chinese].

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Zhang, J.-Z.: How to solve geometry problems using areas. Shanghai Education Publ. Inc., Shanghai (1982) [in Chinese].

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Zhang, J.-Z.: A new approach to plane geometry. Sichuan Education Publ. Inc., Chengdu (1992) [in Chinese].

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Zhang, J.-Z., Cao, P.-S.: From education of mathematics to mathematics for education. Sichuan Education Publ. Inc., Chengdu (1988) [in Chinese].

Articles

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Alberti, M. A., Carrà Ferro, G., Lammoglia, B., Torelli, M.: The dimension method in elementary and differential geometry. Ann. Math. Artif. Intell. 13: 47-71 (1995).

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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.

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Anderson, J. R., Boyle, C. F., Yost, G.: The geometry tutor. In: Proc. IJCAI '85 (Los Angeles, August 18-23, 1985), pp. 1-7.

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Arbab, F., Wang, B.: Reasoning about geometric constraints. In: Intelligent CAD II (Yoshikawa, H., Holden, T., eds.), Elsevier, North-Holland, pp. 93-107 (1990).

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Arnon, D. S.: Algorithms for the geometry of semi-algebraic sets. Ph.D thesis, Comput. Sci. Dept., Univ. of Wisconsin-Madison, USA (1981).

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Arnon, D. S.: Geometric reasoning with logic and algebra. Artif. Intell. 37: 37-60 (1988).

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Arnon, D. S., Mignotte, M.: On mechanical quantifier elimination for elementary algebra and geometry. J. Symb. Comput. 5: 237-259 (1988).

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Aubry, P., Wang, D.: Reasoning about surfaces using differential zero and ideal decomposition. In: Springer's LNAI 2061, pp. 154-174 (2001).

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Balbiani, P.: Equation solving in projective planes and planar ternary rings. In: Springer's LNCS 850, pp. 95-113 (1994).

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Balbiani, P.: Equation solving in geometrical theories. In: Springer's LNCS 968, pp. 31-55 (1995).

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Balbiani, P., Dugat, V., Lopez, A.: Le raisonnement sur les figures de la géométrie projective. Rapport Irit/94-5-R, IRIT, Univ. Paul Sabatier, France (1994).

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Balbiani, P., Fariñas del Cerro, L.: Affine geometry of collinearity and conditional term rewriting. In: Springer's LNCS 909, pp. 196-213 (1995).

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Balbiani, P., Lopez, A.: Simplification des figures de la géométrie affine plane d'incidence. In: 9e congrès reconnaissance des formes et intell. artif. (Paris, January 11-14, 1994), pp. 341-351.

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Barry, M., Cyrluk, D., Kapur, D, Mundy, J.: Multi-level geometric reasoning system for vision. In: Proc. Int. Workshop Geom. Reason. (Oxford, June 30 - July 3, 1986).

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Bazzotti, L., Dalzotto, G., Robbiano, L.: Remarks on geometric theorem proving. In: Springer's LNAI 2061, pp. 104-128 (2001).

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Beutelspacher, A., Ueberberg, J.: Symbolic incidence geometry: Proposal for doing geometry with a computer. ACM SIGSAM 27(2): 19-29; 27(3): 9-24 (1992).

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Bokowski, J.: Effective methods in computational synthetic geometry. In: Springer's LNAI 2061, pp. 175-192 (2001).

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Bondyfalat, D., Mourrain, B., Papadopoulo, T.: An application of automatic theorem proving in computer vision. In: Springer's LNAI 1669, pp. 207-231 (1999).

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Botana, F.: A web-based intelligent system for geometric discovery. In: Springer's LNCS 2657, pp. 801-810 (2003).

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Botana, F., Valcarce, J. L.: A software tool for the investigation of plane loci. Math. Comput. Simulation 61(2): 139-152 (2003).

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Bouhineau, D.: Solving geometrical constraint systems using CLP based on linear constraint solver. In: Springer's LNCS 1138, pp. 274-288 (1996).

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Boy de la Tour, T., Fèvre, S., Wang, D.: Clifford term rewriting for geometric reasoning in 3D. In: Springer's LNAI 1669, pp. 130-155 (1999).

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Brüderlin, B.: Using Prolog for constructing geometric objects defined by constraints. In: Springer's LNCS 204, p. 448 (1985).

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Brüderlin, B.: Automatizing geometric proofs and constructions. In: Springer's LNCS 333, pp. 232-252 (1988).

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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).

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Buchberger, B., Collins, G. E., Kutzler, B.: Algebraic methods for geometric reasoning. Ann. Rev. Comput. Sci. 3: 85-119 (1988).

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Bulmer, M., Fearnley-Sander, D., Stokes, T.: The kinds of truth of geometry theorems. In: Springer's LNAI 2061, pp. 129-142 (2001).

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Caferra, R., Peltier, N., Puitg, F.: Emphasizing human techniques in automated geometry theorem proving: A practical realization. In: Springer's LNAI 2061, pp. 269-306 (2001).

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Carrà Ferro, G.: An extension of a procedure to prove statements in differential geometry. J. Automat. Reason. 12: 351-358 (1994).

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Carrà Ferro, G., Gallo, G.: A procedure to prove geometrical statements. In: Springer's LNCS 356, pp. 141-150 (1987).

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Carrà Ferro, G., Gallo, G.: A procedure to prove statements in differential geometry. J. Automat. Reason. 6: 203-209 (1990).

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Carrà Ferro, G., Gallo, G., Gennaro, R.: Probabilistic verification of elementary geometry statements. In: Springer's LNAI 1360, pp. 87-101 (1997).

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Cerutti, E., Davis, P. J.: Formac meets Pappus: Some observations on elementary analytic geometry by computer. Amer. Math. Monthly 76: 895-905 (1969).

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Chou, S.-C.: Proving elementary geometry theorems using Wu's algorithm. In: Automated theorem proving: After 25 years (Bledsoe, W. W., Loveland, D. W., eds.), AMS, Providence, pp. 243-286 (1984).

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Chou, S.-C.: Proving and discovering theorems in elementary geometries using Wu's method. Ph.D thesis, Univ. of Texas at Austin, USA (1985).

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Chou, S.-C.: GEO-prover - A geometry theorem prover developed at UT. In: Springer's LNCS 230, pp. 679-680 (1986).

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Chou, S.-C.: A method for the mechanical derivation of formulas in elementary geometry. J. Automat. Reason. 3: 291-299 (1987).

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Chou, S.-C.: An introduction to Wu's method for mechanical theorem proving in geometry. J. Automat. Reason. 4: 237-267 (1988).

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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.

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Chou, S.-C.: A geometry theorem prover for Macintoshes. In: Springer's LNCS 607, pp. 687-690 (1992).

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Chou, S.-C., Gao, X.-S.: A collection of 120 computer solved geometry problems in mechanical formula derivation. Tech. Rep. TR-89-22, Dept. of Comput. Sci., Univ. of Texas at Austin, USA (1989).

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Chou, S.-C., Gao, X.-S.: Methods for mechanical geometry formula deriving. In: Proc. ISSAC '90 (Tokyo, August 20-24, 1990), pp. 265-270.

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Chou, S.-C., Gao, X.-S.: Ritt-Wu's decomposition algorithm and geometry theorem proving. In: Springer's LNCS 449, pp. 207-220 (1990).

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Chou, S.-C., Gao, X.-S.: Theorems proved automatically using Wu's method - Part on differential geometry (space curves) and mechanics. Math. Mech. Res. Preprints 6: 37-55 (1991).

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Chou, S.-C., Gao, X.-S.: Proving geometry statements of constructive type. In: Springer's LNCS 607, pp. 20-34 (1992).

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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).

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Chou, S.-C., Gao, X.-S.: Mechanical theorem proving in Riemann geometry using Wu's method. In: Computer mathematics (Tianjin, 1991), Nankai Ser. Pure Appl. Math. Theoret. Phys. 5, World Scientific, River Edge, pp. 136-157 (1993).

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Chou, S.-C., Gao, X.-S.: Automated reasoning in differential geometry and mechanics using the characteristic set method I & II. J. Automat. Reason. 10: 161-189 (1993).

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Chou, S.-C., Gao, X.-S.: Automated reasoning in differential geometry and mechanics using the characteristic method IV. Syst. Sci. Math. Sci. 6: 186-192 (1993).

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Chou, S.-C., Gao, X.-S.: The computer searches for Pascal conics. Comput. Math. Appl. 29: 63-71 (1995).

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Chou, S.-C., Gao, X.-S.: A survey of geometric reasoning using algebraic methods. In: Learning and geometry: Computational approaches (Kueker, D. W., Smith, C., eds.), Birkhäuser, Boston, pp. 97-119 (1996).

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Chou, S.-C., Gao, X.-S., Arnon, D. S.: On the mechanical proof of geometry theorems involving inequalities. In: Issues in robotics and nonlinear geometry (Hoffmann, C. M., ed.), JAI Press, Greenwich, pp. 139-181 (1992).

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Chou, S.-C., Gao, X.-S., Liu, Z., Wang, D.-K., Wang, D.: Geometric theorem provers and algebraic equation solvers. In: Mathematics mechanization and applications (Gao, X.-S., Wang, D., eds.), Academic Press, London, pp. 491-505 (2000).

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Chou, S.-C., Gao, X.-S., Yang, L., Zhang, J.-Z.: A collection of 90 automatically proved geometry theorems in non-Euclidean geometries. Tech. Rep. TR-WSU-94-10, Wichita State Univ., USA (1994).

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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.

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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.

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Chou, S.-C., Gao, X.-S., Zhang, J.-Z.: The area method and affine geometries over any fields. Math. Mech. Res. Preprints 10: 92-100 (1993).

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Chou, S.-C., Gao, X.-S., Zhang, J.-Z.: A rule based geometry theorem prover using full angles. Math. Mech. Res. Preprints 11: 72-103 (1994).

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Chou, S.-C., Gao, X.-S., Zhang, J.-Z.: Vectors and automated geometry reasoning. Math. Mech. Res. Preprints 11: 104-127 (1994).

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Chou, S.-C., Gao, X.-S., Zhang, J.-Z.: Automated production of traditional proofs in solid geometry. J. Automat. Reason. 14: 257-291 (1995).

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Chou, S.-C., Gao, X.-S., Zhang, J.-Z.: Automated geometry theorem proving and geometry education. In: Proc. 1st Asian Tech. Conf. Math. (Singapore, December 18-21, 1995), pp. 319-328.

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Chou, S.-C., Gao, X.-S., Zhang, J.-Z.: A fixpoint approach to automated geometry theorem proving. Tech. Rep. WSUCS-95-2, Wichita State Univ., USA (1995).

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Chou, S.-C., Gao, X.-S., Zhang, J.-Z.: Automated generation of readable proofs with geometric invariants I & II. J. Automat. Reason. 17: 325-370 (1996).

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Chou, S.-C., Gao, X.-S., Zhang, J.-Z.: An introduction to geometry expert. In: Springer's LNAI 1104, pp. 235-239 (1996).

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Chou, S.-C., Gao, X.-S., Zhang, J.-Z.: Recent advances of automated geometry theorem proving with high level geometry invariants. In: Proc. ASCM '96 (Kobe, 1996), pp. 173-186.

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Chou, S.-C., Gao, X.-S., Zhang, J.-Z.: Automated solution of two-dimensional geometric constraint problems. In: Proc. ASCM '96 (Kobe, 1996), pp. 153-164.

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Chou, S.-C., Gao, X.-S., Zhang, J.-Z.: Automated generation of construction steps for geometric constraint problems. In: Automated reasoning and its applications (Veroff, R., ed.), The MIT Press, Cambridge, pp. 49-69 (1997).

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Chou, S.-C., Gao, X.-S., Zhang, J.-Z.: A deductive database approach to automated geometry theorem proving and discovering. J. Automat. Reason. 25: 219-246 (1996).

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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.

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Chou, S.-C., Lin, D.: Wu's method for automated geometry theorem proving and discovering. In: Mathematics mechanization and applications (Gao, X.-S., Wang, D., eds.), Academic Press, London, pp. 125-146 (2000).

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Chou, S.-C., Rathi, M.: Machine proofs of geometry theorems. In: Computing in Euclidean geometry (Du, D.-Z., Hwang, F. K., eds.), World Scientific, Singapore, pp. 91-115 (1992).

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Chou, S.-C., Schelter, W. F.: Proving geometry theorems with rewrite rules. J. Automat. Reason. 2: 253-273 (1986).

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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 (Aït-Kaaci, H., Nivat, M., eds.), Academic Press, San Diego, pp. 33-92 (1989).

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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).

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Chou, S.-C., Yang, J.-G.: On the algebraic formulation of certain geometry statements and mechanical geometry theorem proving. Algorithmica 4: 237-262 (1989).

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Coelho, H., Pereira, L. M.: GEOM: A Prolog geometry theorem prover. Laboratório Nacional de Engenhaaria Civil Memória no. 525, Ministerio de Habitacao e Obrass Publicas, Portugal (1979).

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Coelho, H., Pereira, L. M.: Automated reasoning in geometry theorem proving with Prolog. J. Automat. Reason. 2: 329-390 (1986).

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Collins, G. E.: Quantifier elimination for real closed fields by cylindrical algebraic decomposition. In: Springer's LNCS 33, pp. 134-165 (1975).

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Connolly, C. I., Kapur, D., Mundy, J. L., Weiss, R.: GEometer: A system for modeling and algebraic manipulation. In: Proc. DARPA Workshop Image Understanding (Palo Alto, May 1989), pp. 797-804.

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Conti, P., Traverso, C.: A case of automatic theorem proving in Euclidean geometry: The Maclane 8_3 theorem. In: Springer's LNCS 948, pp. 183-193 (1995).

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Conti, P., Traverso, C.: Algebraic and semialgebraic proofs: Methods and paradoxes. In: Springer's LNAI 2061, pp. 83-103 (2001).

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Cox, D., Little, J., O'Shea, D.: Robotics and automated geometric theorem proving. Chapter 6 in: Ideals, varieties and algorithms, Springer, New York Berlin (1992). 2nd edition (1997).

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Crapo, H., Richter-Gebert, J.: Automatic proving of geometric theorems. In: Invariant methods in discrete and computational geometry (White, N. L., ed.). Kluwer, Dordrecht, pp. 167-196 (1995).

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Cyrluk, D. A., Harris, R. M., Kapur, D.: GEOMETER: A theorem prover for algebraic geometry. In: Springer's LNCS 310, pp. 770-771 (1988).

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de Alwis, T.: Normal lines drawn to a parabola and geometric constructions. In: Proc. ATCM98 (Tsukuba, August 24-28, 1998), pp. 389-398.

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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.

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Dehlinger, C., Dufourd, J.-F., Schreck, P.: Higher-order intuitionistic formalization and proofs in Hilbert's elementary geometry. In: Springer's LNAI 2061, pp. 307-324 (2001).

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Deng, M.-K.: The parallel numerical method of proving the constructive geometric theorem. Chinese Sci. Bull. 34: 1066-1070 (1989).

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Dolzmann, A.: Solving geometric problems with real quantifier elimination. In: Springer's LNAI 1669, pp. 14-29 (1999).

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Dolzmann, A., Sturm, T., Weispfenning, V.: A new approach for automatic theorem proving in real geometry. J. Automat. Reason. 21: 357-380 (1998).

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Elcock, E. W.: Representation of knowledge in a geometry machine. Machine Intell. 8: 11-29 (1977).

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Evans, T. G.: A heuristic program to solve geometry analogy problems. In: Semantic information processing (Minsky, M. L., ed.), The MIT Press, Cambridge (1969).

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Fearnley-Sander, D.: The idea of a diagram. In: Resolution of equations in algebraic structures (Aït-Kaaci, H., Nivat, M., eds.), Academic Press, San Diego, pp. 27-150 (1989).

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Fearnley-Sander, D.: Using and computing symmetry in geometry proofs. In: Proc. Conf. AI Simul. Behav. (Ross, P., ed.).

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Fearnley-Sander, D.: Plane Euclidean reasoning. In: Springer's LNAI 1669, pp. 86-110 (1999).

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Fearnley-Sander, D., Stokes, T.: Area in Grassmann geometry. In: Springer's LNAI 1360, pp. 141-170 (1997).

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Fèvre, S.: A hybrid method for proving theorems in elementary geometry. In: Proc. ASCM '95 (Beijing, August 18-20, 1995), pp. 113-123.

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Fèvre, S.: Integration of reasoning and algebraic calculus in geometry. In: Springer's LNAI 1360, pp. 218-234 (1997).

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Fèvre, S., Peltier, N.: Two problems in geometry solved by using automated model builders. AAR Newsletter 38 (1997).

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Fèvre, S., Wang, D.: Proving geometric theorems using Clifford algebra and rewrite rules. In: Springer's LNAI 1421, pp. 17-32 (1998).

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Fèvre, S., Wang, D.: Combining algebraic computing and term-rewriting for geometry theorem proving. In: Springer's LNAI 1476, pp. 145-156 (1998).

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Fèvre, S., Wang, D.: Combining Clifford algebraic computing and term-rewriting for geometric theorem proving. Fundamenta Informaticae 39 (1-2): 85-104 (1999).

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Fleuriot, J. D.: Nonstandard geometric proofs. In: Springer's LNAI 2061, pp. 246-268 (2001).

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Fleuriot, J. D., Paulson, L. C.: A combination of nonstardard analysis and geometry theorem proving, with application to Newton's principia. In: Springer's LNAI 1421, pp. 3-16 (1998).

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Fleuriot, J. D., Paulson, L. C.: Proving Newton's Propositio Kepleriana using geometry and nonstandard analysis in Isabelle. In: Springer's LNAI 1669, pp. 47-66 (1999).

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Gao, X.-S.: Trigonometric identities and mechanical theorem proving in elementary geometry. J. Syst. Sci. Math. Sci. 7: 264-272 (1987) [in Chinese].

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Gao, X.-S.: Constructive methods for polynomial sets and their applications. Ph.D thesis, Academia Sinica, China (1988) [in Chinese].

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Gao, X.-S.: Transcendental functions and mechanical theorem proving in elementary geometries. J. Automat. Reason. 6: 403-417 (1990).

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Gao, X.-S.: Transformation theorems among Cayley-Klein geometries. Syst. Sci. Math. Sci. 5: 263-273 (1992).

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Gao, X.-S.: An introduction to Wu's method of mechanical geometry theorem proving. In: Automated reasoning (Shi, Z., ed.), Elsevier, North-Holland, pp. 13-21 (1992).

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Gao, X.-S.: Automated geometry diagram construction and engineering geometry. In: Springer's LNAI 1669, pp. 232-257 (1999).

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Gao, X.-S.: Building dynamic mathematical models with Geometry Expert - III. A geometry deductive batabase. In: Proc. ATCM '99 (Guangzhou, December 17-21, 1999), pp. 153-162.

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Gao, X.-S.: Search methods revisited. In: Mathematics mechanization and applications (Gao, X.-S., Wang, D., eds.), Academic Press, London, pp. 253-271 (2000).

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Gao, X.-S., Chou, S.-C.: Solving geometric constraint systems I & II. J. CAD (to appear).

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Gao, X.-S., Huang, L.-D., Jiang, K.: A hybrid method for solving geometric constraint problems. In: Springer's LNAI 2061, pp. 16-25 (2001).

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Gao, X.-S., Li, Y.-L., Lin, D.-D., Lü, X.-S.: A geometric theorem prover based on Wu's method. In: Proc. IWMM '92 (Beijing, July 16-18, 1992), pp. 201-205.

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Gao, X.-S., Wang, D.-K.: On the automatic derivation of a set of geometric formulae. J. Geom. 53: 79-88 (1995).

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Gao, X.-S., Zhu, C., Huang, Y.: Building dynamic mathematical models with Geometry Expert - I. Geometric transformations, funtions and plane curves. In: Proc. ATCM98 (Tsukuba, August 24-28, 1998), pp. 216-224.

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Gelernter, H.: Realization of a geometry theorem proving machine. In: Proc. Int. Conf. Info. Process. (Paris, June 15-20, 1959), pp. 273-282.

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Gelernter, 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.

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Gehrke, W., Pfalzgraf, J.: Computer-aided construction of finite geometric spaces: Automated verification of geometric constraints. J. Automat. Reason. 26: 139-160 (2001).

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Gilmore, P. C.: An examination of the geometry theorem machine. Artif. Intell. 1: 171-187 (1970).

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Goguen, J. A.: Modular algebraic specification of some basic geometrical constructions. Artif. Intell. 37: 121-156 (1988).

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Goldstein, I.: Elementary geometry theorem proving. MIT AI Memo no. 28, MIT, USA (1973).

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Grünbaum, B., Shephard, G. C.: From Menelaus to computer assisted proofs in geometry. Preprint, Washington State Univ., USA (1993).

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Guergueb, A.: Exemples de démonstration automatique en géométrie réelle. Ph.D thesis, Univ. de Rennes I, France (1994).

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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.

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Hadzikadic, M., Lichtenberger, F., Yun, D. Y. Y.: An application of knowledge-base technology in education: A geometry theorem prover. In: Proc. SYMSAC '86 (Waterloo, July 21-23, 1986), pp. 141-147.

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Havel, T. F.: Some examples of the use of distances as coordinates for Euclidean geometry. J. Symb. Comput. 11: 579-593 (1991).

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Havel, T. F.: Computational synthetic geometry with Clifford algebra. In: Springer's LNAI 1360, pp. 102-114 (1997).

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Yang, L., Zeng, Z.: Equi-Cevaline points of triangle. In: Proc. ASCM 2000 (Chiang Mai, December 17-21, 2000), pp. 130-137.

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Yang, L., Zhang, J.: A practical program of automated proving for a class of geometric inequalities. In: Springer's LNAI 2061, pp. 41-57 (2001).

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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).

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Yang, L., Zhang, J.-Z., Hou, X.-R.: A criterion of dependency between algebraic equations and its applications. In: Proc. IWMM '92 (Beijing, July 16-18, 1992), pp. 110-134.

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Yang, L., Zhang, J.-Z., Hou, X.-R.: A note on Wu Wen-tsün's nondegenerate condition. Chinese Sci. Bull. 38: 86-87 (1993). Also in: Computer mathematics (Tianjin, 1991), Nankai Ser. Pure Appl. Math. Theoret. Phys. 5, World Scientific, River Edge, pp. 127-135 (1993).

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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.

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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.

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Zhang, J.-Z.: Points elimination methods for geometric problem solving. In: Mathematics mechanization and applications (Gao, X.-S., Wang, D., eds.), Academic Press, London, pp. 175-204 (2000).

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Zhang, J.-Z., Chou, S.-C., Gao, X.-S.: Automated production of traditional proofs for theorems in Euclidean geometry I. Ann. Math. Artif. Intell. 13: 109-137 (1995).

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Zhang, J.-Z., Li, C.: Automated reasoning in ICAI. In: Proc. ATCM98 (Tsukuba, August 24-28, 1998), pp. 36-44.

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Zhang, J.-Z., Yang, L.: Principles of parallel numerical method and single-instance method of mechanical theorem proving. Math. Practice Theory 1: 34-43 (1989) [in Chinese].

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Zhang, J.-Z., Yang, L., Deng, M.-K.: The parallel numerical method of mechanical theorem proving. Theoret. Comput. Sci. 74: 253-271 (1990).

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Zhang, J.-Z., Yang, L., Gao, X.-S., Chou, S.-C.: Automated production of readable proofs for geometry theorems. Chinese J. Comput. 18(5): 380-393 (1995).

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Zhang, J.-Z., Yang, L., Hou, X.-R.: A criterion for dependency of algebraic equations and its applications to automated theorem proving. In: Proc. Asian Math. Conf. (Hong Kong, 1990), pp. 548-553.

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Zhang, J.-Z., Yang, L., Hou, X.-R.: A criterion for dependency of algebraic equations with applications to automated theorem proving. Sci. China (Ser. A) 37: 547-554 (1994).

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Zhang, J.-Z., Yang, L., Hou, X.-R.: The subresultant method for automated theorem proving in geometry. J. Syst. Sci. Math. Sci. 15: 10-15 (1995) [in Chinese].

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Zhang, J.-Z., Yang, L., Hou, X.-R.: The WE complete algorithm for automated theorem proving in geometry. J. Syst. Sci. Math. Sci. 15: 200-207 (1995) [in Chinese].

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