大阿久 俊則 (おおあく としのり)

東京女子大学文理学部数理学科教授

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専門：代数解析学と記号計算

研究テーマ

  1. 線型偏微分方程式系(D加群)と超関数
  2. D加群のアルゴリズム
  3. 数式処理（記号計算）

略歴

研究集会等

数式処理用フリーソフト

数学講究（4年ゼミ）の内容

著書および解説記事

  1. 日比孝之(編) 「グレブナー基底の現在」数学書房 2006年7月発行，3,800円+税 (分担執筆).
  2. 「D加群と計算数学」 朝倉書店 （シリーズ：すうがくの風景 5）2002年2月発行, 3,000円+税. (正誤表(PDFファイル)) (正誤表(dviファイル))
  3. 数式処理と数学--ホロノミックパラダイム. 数理科学 1998年11月号, pp.32-38.
  4. 計算の視点から見たD加群理論. 数学 50巻2号(1998年4月), pp.203-211.
  5. 「グレブナ基底と線型偏微分方程式系(計算代数解析入門)」 上智大学数学講究録 No.38 (1994年11月).

プレプリント

  1. T. Oaku: An algorithm to compute the differential equations for the logarithm of a polynomial arXiv:1201.3198v1[cs.SC]
  2. T. Oaku: Algorithms for integrals of holonomic functions over domains defined by polynomial inequalities. arXiv:1108.4853v2[cs.SC]

発表論文

  1. R. Bahloul, T. Oaku: Local Bernstein-Sato ideals: algorithm and examples. J. Symbolic Computation 45 (2010), 46-59. arXiv:0806.4869
  2. T. Oaku: Regular b-functions of D-modules. J. Pure and Applied Algebra 213 (2009), 1545-1557. PDF file
  3. M. Granger, T. Oaku, N. Takayama: Tangent cone algorithm for homogenized differential operators. J. Symbolic Computation 39 (2005), 417-431. PDF file
  4. M. Granger, T. Oaku: Minimal filtered free resolutions for analytic D-modules. J. Pure and Applied Algebra 191 (2004), 157-180. PDF file
  5. T.Oaku, Y.Shiraki, N.Takayama: Algebraic algorithms for D-modules and numerical analysis. Computer mathematics (Proceedings of ASCM 2003), 23--39, Lecture Notes Ser. Comput., 10, World Sci. Publ., River Edge, NJ, 2003. PDF file .
  6. T.Oaku: Minimal free resolutions of analytic D-modules. Proceedings of the 10th International Conference on Complex Analysis, Pusan, Korea, 2002, pp. 145-151. PDF file
  7. T. Oaku, N. Takayama: Minimal free resolutions of homogenized D-modules. J. Symbolic Computation 32 (2001), 575-595.
  8. T. Oaku, N. Takayama, H. Tsai: Polynomial and rational solutions of holonomic systems. J. Pure and Applied Algebra 164 (2001), 199-220. arXiv:math/0001064
  9. T. Oaku, N. Takayama: Algorithms for D-modules --restriction, tensor product, localization, and local cohomology groups. J. Pure and Applied Algebra 156 (2001), 267-308. PDF file
  10. T. Oaku, N. Takayama, U. Walther: A localization algorithm for D-modules. J. Symbolic Computation 29 (2000), 721-728. arXiv:math/9811030
  11. T. Oaku, N. Takayama: An algorithm for de Rham cohomology groups of the complement of an affine variety. J. Pure and Applied Algebra 139 (1999), 201-233. . arXiv:math/9801114
  12. T. Oaku, S. Yamazaki: Higher-codimensional boundary value problems and F-mild microfunctions --Local and microlocal uniqueness--. Publication of the Research Institute for Mathematical Sciences, Kyoto Univ. 34 (1998), 383-437.
  13. T. Oaku: Algorithms for b-functions, restrictions, and algebraic local cohomology groups of D-modules. Advances in Applied Math. 19 (1997), 61-105. PDF file
  14. T. Oaku: Algorithms for the b-function and D-modules associated with a polynomial. J. Pure Appl. Algebra 117 & 118 (1997), 495-518. PDF file
  15. T. Oaku: An algorithm of computing b-functions. Duke Math. J. 87 (1997), 115-132. PDF file
  16. T. Oaku: Groebner bases for D-modules on a non-singluar affine algebraic variety. Tohoku Math. J. 48 (1996), 575-600.
  17. T. Oaku: Algorithmic methods for Fuchsian systems of linear partial differential equations. J. Math. Soc. Japan 47 (1995), 297-328.
  18. T. Oaku, T. Shimoyama: A Groebner basis method for modules over rings of differential operators. J. Symbolic Computation 18 (1994), 223-248.
  19. T. Oaku: Computation of the characteristic variety and the singular locus of a system of differential equations with polynomial coefficients. Japan J. Indust. Appl. Math. 11 (1994), 485-497.
  20. T. Oaku: Boundary value problem for Fuchsian partial differential equations and reflection of singularities. Banach Center Publications 27 (1992), 337-348.
  21. T. Oaku: Some remarks on local solvability of Fuchsian partial differential equations for hyperfunctions. Yokohama Math. J. 37 (1989), 139-143.
  22. T. Oaku: Local solvability of Fuchsian elliptic equations for hyperfunctions. Yokohama Math. J. 36 (1988), 109-114.
  23. T. Oaku: Higher codimensional boundary value problem and F-mild hyperfunctions. In: Algebraic Analysis, eds M. Kashiwara, T. Kawai, Academic Press, 1988, pp. 571-586.
  24. T. Oaku: Boundary value problems for systems of linear partial differential equations and propagation of micro-analyticity. J. Fac. Sci. Univ. Tokyo 33 (1986), 175-232.
  25. T. Oaku: Microlocal boundary value problem for Fuchsian operators, I. -F-mild microfunctions and uniqueness theorem. J. Fac. Sci. Univ. Tokyo 32 (1985), 287-317.
  26. T. Oaku: F-mild hyperfunctions and Fuchsian partial differential equations. Advanced Studies in Pure Mathematics 4 (1984), 223-242.
  27. T. Oaku: Analytic hypo-ellipticity and propagation of regularity for a system of microdifferential equations with non-involutory characteristics. Math. Ann. 269 (1984), 145-168.
  28. T. Oaku: A canonical form of a system of microdifferential equations with non-involutory characteristics and branching of singularities. Inventiones Math. 65 (1982), 491-525.
  29. T. Oaku: Micro-local Cauchy problems and local boundary value problems. Proc. Japan Acad. 55 (1979), 136-140.