ZHAO Ting
Ban lãnh đạo nghiên cứu : Dongming WANG
Đồng hướng dẫn : AUBRY Philippe
Dynamic Geometry and geometric Constrain Solving
This thesis focuses on the design and implementation of efficient algorithms and software tools for solving parametric geometric constraints involving both equalities and inequalities, with application to automated generation of dynamic diagrams. It introduces a real convention for cubic and quartic polynomial equations that leads to a main advance on Lagrange's formula, under the form of real solution formulas for generic cubic and quartic polynomial equations with constraints. These results are applied to improve an existing approach in terms of stability of numeric computation and quality of generated diagrams. Finally a software package developed with Java, Maple and QEPCAD for automated generation of dynamic diagrams with inequality constraints is presented.
Bảo vệ luận án : 05/03/2012
Hội đồng giám khảo :
Thomas STURM [Rapporteur]
Bican XIA [Rapporteur]
She ZHIKUN
Philippe AUBRY
Annick VALIBOUZE
Dongming WANG
Liu TIEGANG
Lihong ZHI
Bài báo khoa học 2011-2012
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2012
- T. Zhao : “Résolution de systèmes polynomiaux paramétriques par radicaux et ses applicationsgéométriques”, luận án, bảo vệ luận án 05/03/2012, ban lãnh đạo nghiên cứu Wang, Dongming, Đồng hướng dẫn : Aubry, Philippe (2012)
- X. Chen, D. Wang, T. Zhao : “GeoText: An Intelligent Dynamic Geometry Textbook (Extended Abstract)”, ACM Communications in Computer Algebra, vol. 46 (4), pp. 171-175, (Association for Computing Machinery (ACM)) (2012)
- T. Zhao, D. Wang, H. Hong, Ph. Aubry : “Real Solution Formulas of Cubic and Quartic Equations Applied to Generate Dynamic Diagrams with Inequality Constraints”, 27th Annual ACM Symposium on Applied Computing (SAC 2012), Trento, Italy, pp. 94-101 (2012)
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2011
- T. Zhao, D. Wang, H. Hong : “Solution Formulas for Cubic Equations Without or With Constraints”, Journal of Symbolic Computation, vol. 46 (8), pp. 904-918, (Elsevier) (2011)