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| 研究生： |
姚秉毅 Yao, Ping-Yi |
|---|---|
| 論文名稱： |
Groebner基底與機械手臂 Groebner bases and robotic arms |
| 指導教授： |
柯文峰
Ke, Wen-Fong |
| 學位類別： |
碩士 Master |
| 系所名稱： |
理學院 - 數學系應用數學碩博士班 Department of Mathematics |
| 論文出版年： | 2017 |
| 畢業學年度： | 105 |
| 語文別： | 英文 |
| 論文頁數： | 19 |
| 中文關鍵詞： | Gröbner基底 |
| 外文關鍵詞： | Gröbner basis |
| 相關次數： | 點閱：67 下載：14 |
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在此論文中，我們討論使用Gröbner基底解決平面逆向運動及研究相關的穩定性問題。
We discuss the use of Gröbner bases for solving the inverse kinematics problem of a planar robotic manipulator and examine the stability of Gröbner bases from k(t_1,...,t_m)[x_1,...,x_n] to k[x_1,...,x_n].
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[2] Thomas Becker On Gröbner Bases under Specialization, Applicable Algebra in Engineering, Communication and Computing, Volume 5, pp 1-8, 1994.
[3] Thomas Becker and Volker Weispfenning, Gröbner Bases, Graduate Texts in Mathematics 141, Springer, 1993.
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[6] ______, Ideals, Varieties, and Algorithms, 4th edition, Springer, 2015.
[7] Viviana Ene and Jürgen Herzog, Gröbner Bases in Commutative Algebra, Graduate Studies in Mathematics, Volume 130, American Mathematical Society, 2012.
[8] Patrizia Gianni, Properties of Gröbner Bases under Specializations, in James H. Davenport (eds.), EUROCAL '87, Lecture Notes in Computer Science, Volume 378, Springer, pp 293-297, 1989.
[9] Jaime Gutierrez and Rosario Rubio, CADECOM: Computer Algebra software for functional DECOMposition, in Victor G. Ganzha, Ernst W. Mayr and Evgenii V. Vorozhtsov (eds.), Computer Algebra in Scientific Computing, Springer , pp 233-247, 2000.
[10] Bhubaneswar Mishra, Algorithmic Algebra, Springer, 1993.
[11] Antonio Montes, A New Algorithm for Discussing Gröbner Bases with Parameters, J. Symb. Comput., Volume 33, pp 183-208, 2002.
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