Automated Deduction in Geometry

1. Front Matter

   Pages I-VII

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2. Automatic Geometry Theorem-Proving and Automatic Geometry Problem-Solving

   • Wen-tsü Wu

   Pages 1-13

3. Solving Geometric Problems with Real Quantifier Elimination

   • Andreas Dolzmann

   Pages 14-29

4. Automated Discovering and Proving for Geometric Inequalities

   • Lu Yang, Xiaorong Hou, Bican Xia

   Pages 30-46

5. Proving Newton’s Propositio Kepleriana Using Geometry and Nonstandard Analysis in Isabelle

   • Jacques D. Fleuriot, Lawrence C. Paulson

   Pages 47-66

6. Readable Machine Solving in Geometry and ICAI Software MSG

   • Chuan-Zhong Li, Jhing-Zhong Zhang

   Pages 67-85

7. Plane Euclidean Reasoning

   • Desmond Fearnley-Sander

   Pages 86-110

8. A Clifford Algebraic Method for Geometric Reasoning

   • Haiquan Yang, Shugong Zhang, Guochen Feng

   Pages 111-129

9. Clifford Term Rewriting for Geometric Reasoning in 3D

   • Thierry Boy de la Tour, Stéphane Fèvre, Dongming Wang

   Pages 130-156

10. Some Applications of Clifford Algebra to Geometries

    • Hongbo Li

    Pages 156-179

11. Decomposing Algebraic Varieties

    • Dongming Wang

    Pages 180-206

12. An Application of Automatic Theorem Proving in Computer Vision

    • Didier Bondyfalat, Bernard Mourrain, Théodore Papadopoulo

    Pages 207-232

13. Automated Geometry Diagram Construction and Engineering Geometry

    • Xiao-Shan Gao

    Pages 232-258

14. A 2D Geometric Constraint Solver for Parametric Design Using Graph Analysis and Reduction

    • Jae Yeol Lee

    Pages 258-274

15. Variant Geometry Analysis and Synthesis in Mechanical CAD

    • Zongying Ou, Jun Liu

    Pages 275-285

16. Back Matter

    Pages 287-287

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The Second International Workshop on Automated Deduction in Geometry (ADG ’98) was held in Beijing, China, August 1–3, 1998. An increase of interest in ADG ’98 over the previous workshop ADG ’96 is represented by the notable number of more than 40 participants from ten countries and the strong tech- cal program of 25 presentations, of which two one-hour invited talks were given by Professors Wen-tsun ¨ Wu and Jing-Zhong Zhang. The workshop provided the participants with a well-focused forum for e?ective exchange of new ideas and timely report of research progress. Insight surveys, algorithmic developments, and applications in CAGD/CAD and computer vision presented by active - searchers, together with geometry software demos, shed light on the features of this second workshop. ADG ’98 was hosted by the Mathematics Mechanization Research Center (MMRC) with ?nancial support from the Chinese Academy of Sciences and the French National Center for Scienti?c Research (CNRS), and was organized by the three co-editors of this proceedings volume. The papers contained in the volume were selected, under a strict refereeing procedure, from those presented at ADG ’98 and submitted afterwards. Most of the 14 accepted papers were carefully revised and some of the revised versions were checked again by external reviewers. We hope that these papers cover some of the most recent and signi?cant research results and developments and re?ect the current state-of-the-art of ADG.

• Automat
• automated deduction
• composing
• computer vision
• problem solving
• proving
• theorem proving

• Academia Sinica, Institute of Systems Science, Beijing, China

  Xiao-Shan Gao

• Laboratoire LEIBNIZ, Institut IMAG, Grenoble Cedex, France

  Dongming Wang

• Laboratory for Automated Reasoning and Programming, Chengdu Institute of Computer Applications, Academia Sinica, Chengdu, China

  Lu Yang

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