[ in English (英語で) ]

こんにちわ (高山信毅)

Last update is Nov 7, 2017.

講義, 講演 video を公開するプロジェクト, OpenXM Video Help (Attachement)

kan/sm1 : 解析のための計算代数システム

OpenXM project : 数学ソフトウエアシステムの統合化計画

論文の投稿案内 : Risa/Asir Journal (Journal of Free Mathematical Software へのステップです)

International Congress on Mathematical Software

Applying for the Graduate School: information for foreign students (外国人学生)

論文その他 (2017, academic year).

  1. non-central complex Wishart 行列の最大固有値の CDF の数値計算 (slides), 2017/11/09 松本
  2. random matrix と多変数特殊関数の数値計算 (slides), 2017/11/04 熊本
  3. F.H.Danufane, K.Ohara, N.Takayama, Holonomic Gradient Method for the Distribution Function of the Largest Root of Complex Non-central Wishart Matrices, arxiv:1707.02564

論文その他 (2016, academic year).

  1. 常微分(差分)方程式用有理数対応数値解析パッケージ (slides) 2017.03.28
  2. R の HGM パッケージ (設計と実装) (slides), 数理統計ひこね2016. 2016/12/02. 参考: ひこにゃん (ライセンス情報).
  3. hgm: Holonomic Gradient Method and Gradient Descent, hgm 1.17 (R-package for HGM) on cran . 新機能: Warning on q0, err パラメータ. hgm.p2wishart.
  4. H.Hashiguchi, N.Takayama, A.Takemura, Distribution of Ratio of two Wishart Matrices and Evaluation of Cumulative Probability by Holonomic Gradient Method, arxiv:1610.09187

論文その他 (2015, academic year).

  1. 熊本発表(2016-03-23) (期間限定)
  2. N.Takayama, S.Kuriki, A.Takemura, A-Hpergeometric Distributions and Newton Polytopes, arxiv:1510.02269
  3. K.Ohara, N.Takayama, Pfaffian Systems of A-Hypergeometric Systems II --- Holonomic Gradient Method, arxiv:1505.02947
  4. hgm: Holonomic Gradient Method and Gradient Descent, hgm 1.11 (R-package for HGM) on cran

論文その他 (2014, academic year).

  1. T.Koyama, H.Nakayama, K.Ohara, T.Sei, N.Takayama, Software Packages for Holonomic Gradient Method, Lecture Notes in Computer Science 8592 (2014), 606--712. DOI
  2. T.Hibi, K.Nishiyama, N.Takayama Computing Bases of Twisted Cohomology Groups for Sparse Polynomials, ACM Communications in Computer Algebra, 48 (2014),118--120. DOI

論文 (2013年度).

  1. T.Hibi, K.Nishiyama, N.Takayama, Pfaffian Systems of A-Hypergeometric Equations I, Bases of Twisted Cohomology Groups, arxiv:1212.6103 (major revision v2 of arxiv:1212.6103). Accepted version is at DOI
  2. Chapter 6 (Groebner basis for rings of differential operators and applications) of T.Hibi et al, Groebner Bases : Statistics and Software Systems , Springer.

その他(2013年度).

  1. Introduction to HGM and recent advances , Talks at CASTA 2014.
  2. Introduction to the Holonomic Gradient Method (movie), 2013. movie at youtube

論文 (2012年度).

  1. T.Hibi, K.Nishiyama, N.Takayama, Pfaffian Systems of A-Hypergeometric Equations, arxiv:1212.6103
  2. F.Castro-Jimenez, M.C.Fernandez-Fernandez, T.Koike, N.Takayama, Irregularity of Modified $A$-Hypergeometric Systems arxiv:1207.1533
  3. T. Koyama, H. Nakayama, K. Nishiyama, N. Takayama, Holonomic Rank of the Fisher-Bingham System of Differential Equations, arxiv:1205.6144

その他 (2012年度)

  1. Wishart行列の最大固有値の分布関数のホロノミック勾配法による計算. 講演資料 板書, movie (15分)
  2. Irregularity of modified hypergeometric systems. 講演資料 板書, movie (45分)
  3. HGD(holonomic gradient descent), HGM (holonomic gradient method), Fisher-Bigham 分布 (2012.07.03, IMA). 講演資料(板書,slides), movie (19分).
  4. HGD(holonomic gradient descent), HGM (holonomic gradient method)の入門 (2012.05.26). 講演資料(板書,slides), movie.

論文 (2011年度).

  1. T. Koyama, H. Nakayama, K. Nishiyama, N. Takayama, Holonomic Gradient Descent for the Fisher-Bingham Distribution on the $n$-dimensional Sphere 1201.3239
  2. Hiroki Hashiguchi, Yasuhide Numata, Nobuki Takayama, Akimichi Takemura, Holonomic gradient method for the distribution function of the largest root of a Wishart matrix 1201.0472
  3. Ryohei Hattori, Nobuki Takayama, The singular locus of Lauricella's F_C 1110.6675 , Journal of Mathematical Society of Japan, 66 (2014), 981--995.
  4. Tomonari Sei, Hiroki Shibata, Akimichi Takemura, Katsuyoshi Ohara, Nobuki Takayama, Properties and applications of Fisher distribution on the rotation group, 1110.0721

その他 (2011年度)

  1. グレブナー道場 (本)

論文 (2010年度).

  1. Tomonari Sei, Nobuki Takayama, Akimichi Takemura ; Hiromasa Nakayama, Kenta Nishiyama, Masayuki Noro, Katsuyoshi Ohara, Holonomic Gradient Descent and its Application to Fisher-Bingham Integral arxiv:1005.5273 , Advances in Applied Mathematics 47 (2011), 639--658
  2. Hiromasa Nakayama, Nobuki Takayama, Computing Differential Equations for Integrals Associated to Smooth Fano Polytopes arxiv:1012.5353

その他 (2010年度)

論文 (2009年度).

  1. Kenta Nishiyama, Nobuki Takayama, Incomplete A-Hypergeometric Systems, arxiv:0907.0745 , Editor T.Hibi, Harmony of Groebner Bases and the Modern Industrial Society, (The Second CREST-SBM International Conference, Osaka, Japan, 2010), 193--212, World Scientific.

その他 (2009年度)

  1. crest グレブナスクール資料
  2. Hankel 関数の Stokes 係数と数値計算 (講義参考資料)
  3. 野呂正行, 高山信毅, Risa/Asir の QUOTE 型 (解説記事)

論文 (2008年度).

  1. Martin Mevissen, Kosuke Yokoyama, Nobuki Takayama, Solutions of Polynomial Systems Derived from the Steady Cavity Flow Problem, math.NA, arXiv:0811.2249v1 , Proceedings of the 2009 International Symposium of Symbolic and Algebraic Computation, ACM Press, 255--262. ACM Portal

その他 (2008年度)

  1. Editors M.Stillman, N.Takayama, J.Verschelde, Software for Algebraic Geometry, (The IMA volumes in Mathematics and its applications, 148), 2008, Springer.
  2. mtg (asir 用 3D graph) についての紹介スライド , mtg-demo.rr

論文 (2007年度).

  1. Katsuyoshi Ohara, Nobuki Takayama, Holonomic Rank of A-Hypergeometric Differential-Difference Equations (PDF, 15pages)(A-超幾何微分差分方程式のランク, 英語), Journal of Pure and Applied Algebra, 213 (2009) 1501--1642. math.CA/0706.2706v1
  2. Nobuki Takayama, Modified A-Hypergeometric System (PDF, 8pages) (変形版 A-超幾何方程式, 英語), Kyushu Journal of Mathematics 63 (2009), 113--122. math.CA/0707.0043v1 ビデオによる講演(日本語)
  3. Mertin Mevissen, Masakazu Kojima, Jiawang Nie, Nobuki Takayama, Solving Partial Differential Equations via Sparse SDP Relaxations , (疎な半正定値プログラミングの緩和法による偏微分方程式の解法, 英語), Pacific Journal of Optimization, 4 (2008), 213--241.
  4. Francisco-Jesus Castro-Jimenez, Nobuki Takayama, The Computation of the Logarithmic Cohomology for Plane Curves (曲線に対する logarithmic コホモロジーの計算), preprint. math.AG/0712.0001 , ビデオによる講演(日本語).

その他 (2007年度)

  1. 超幾何方程式研究会2007
  2. スライド. 解析的グレブナ扇とその応用 (英語)
  3. 科研費報告書 (超幾何微分方程式の計算解析)
  4. スライド: 疎な半正定値プログラミングの緩和法による偏微分方程式の解法 (日本語)
  5. 超幾何方程式研究会2008
  6. 計算による数理科学の展開2008
  7. スライド: cfep と texmacs インタフェースの内部構造 (日本語)

論文 (2006).

  1. Rouchdi Bahloul and Nobuki Takayama, Local Grobner Fan, (局所グレブナ扇の簡潔なサーベイ) PDF (preprint), C.R. Acad.Sci. Paris, Ser. I. 344 (2007), 147--152.

その他 (2006)

  1. 超幾何方程式研究会 (Program, 2006.01.06--2006.01.07)
  2. cfep/asir (MacOS 用 Asir, OpenXM フロントエンド)および入門書(Free Document)
  3. The second International Congress of Mathematical Software (icms2006, developer's meeting, 第2回国際数学ソフトウエア会議 2006.09.01--09.03). 講演のビデオアーカイブ, 会議 knoppix/math DVD, mathsoftware.org , Local organizer's page .
  4. Risa/Asir ドリル, 2006 年版 (PDF, 2.93M)

論文 (2005).

  1. Rouchdi Bahloul and Nobuki Takayama, Local Grobner fan: polyhedral and computational approach, 2005, math.AG/0412044 PS/PDF
  2. 高山信毅 (Nobuki Takayama), OpenXM プロジェクトの過去,現在,未来. 数式処理 (Journal of Japan Society for Symbolic and Algebraic Computation) 12, No. 1 (2005), 51--56. PDF
  3. Katsuyoshi Ohara and Nobuki Takayama, Dimension formula of solution spaces of ${\cal A}$-hypergeometric differential-difference systems (extended abstract), Proceedings of ASCM 2005, KIAS, Seoul, PDF

その他 (2005)

  1. OoHG プロトコル (OX-RFC-104) 解説資料 (OHP, PDF) : 3rd OpenXM committers meeting 2005年2月 (研究集会)
  2. 研究集会プログラム : Risa/Asir Conference 2005
  3. HTMl 入門 / Java Script 入門
  4. レポート提出方法
  5. Nobuki Takayama, Papers in Computatinal Methods for D-Modules (D-module のアルゴリズムについての 論文のリスト), PDF

論文 (2004).

  1. Nobuki Takayama, ディジタル数学公式集の現状と未来 (解説), 情報処理, 2004年7月号

その他 (2004)

  1. 研究集会プログラム : 超幾何方程式研究会 (2004.11.4 -- 2004.11.6)
  2. kan/sm1 の開発の歴史 (PDF), 数式処理, 原稿
  3. Program : Risa/Asir Conference 2004 (conference, 2004.3.22 -- 2004.3.24 )
  4. 研究集会プログラム : 複素領域の微分方程式 (conference, 2004.1.12 -- 2004.1.14 )
  5. 講義資料.
    1. JavaScript 入門
    2. Risa/Asir ドリル 2004 , Risa/Asir binary for the asir book including Prog directory.
    3. 10進Basicのインストールの説明 . 10進Basic(51G)は ここ にも置いてあります.

論文 (2003).

  1. Yasushi Tamura, Isao Hasegawa, Hiromasa Nakayama, Nobuki Takayama, Shuhei Todo, Design and Implementation of a Digital Formula Book for Generalized Hypergeometric Functions, in Proceedings of IAMC 2003 (symbolicnet.org), 2003 [ PDF file ], [ ビデオによるプレゼンテーション ]
  2. Nobuki Takayama, An Algorithm of Constructing Cohomological Series Solutions of Holonomic Systems, PS/PDF
    Journal of Japan Society for Symbolic and Algebraic Computation, {\bf 10}, No.4, 2--11.
  3. T.Oaku, Y.Shiraki, N.Takayama, Algebraic Algorithms for D-modules and Numerical Analysis, Z.M.Li, W.Sit (editors), Computer Mathematics, Proceedings of the sixth asian symposium, 23--39, World scientific, 2003. PDF file, preliminary version .
    Typos
  4. G.Granger, T.Oaku, N.Takayama, Tangent cone algorithm for homogenized differential operators, Journal of Symbolic Computation 39 (2005), 417--431. PDF file (proof reading version)

その他 (2003)

  1. RisaCon II Program : RisaCon II (workshop, 2003.3.18 -- 2003.3.20 )
  2. 2変数の Bessel 関数のグラフ (JavaView)
  3. Slides at ASCM 2003 : ASCM 2003 (Conference, 2003.10.23 -- 2003.10.25 )

論文 (2002).

  1. Nobuki Takayama, Generating Kummer Type Formulas for Hypergeometric Functions, "Algebra, Geometry and software systems", 2003, Springer, pp131--145. [ (preliminary version) Paper in PDF , PDF file generated by pdflatex ].
  2. Katsuyoshi Ohara, Yuichi Sugiki, and Nobuki Takayama, Quadratic Relations for Generalized Hypergeometric Functions ${}_p F _{p-1}$. [ (Funkcialaj Ekvacioj 46, 2003) Paper in PDF ].

その他 (2002)

  1. 情報科学序論について , ffftp の使い方
  2. 情報科学序論の講義ノート.

Papers (2001).

  1. Slopes of a Hypergeometric System Associated to a Monomial Curve, with F. Castro-Jimenez. Transaction of the American Mathematica Society, 355 (2003), 3761--3775. Paper (preliminary version)
  2. The Design and Implementation of OpenXM-RFC 100 and 101, with M.Maekawa, M.Noro, K.Ohara, K.Tamura. Computer Mathematics, Proceedings of the Fifth Asian Symposium (ASCM 2001), edited by Shirayanagi and Yokoyama, World Scientific, 102--111, 2001. [ (Preliminary version) Paper in HTML ].
  3. OpenXM --- an Open System to Integrate Mathematical Software. with Maekawa, M., Noro, M., Ohara, K., Okutani, Y., Tamura, Y., Kerber, M. and Kohlhase, M., eds, Symbolic Computation and Automated Reasoning: The Calculemus ---2000 Symposium. AK Peters, 2001. ISBN: 1-56881-145-4.

Papers (2000).

  1. Minimal free resolutions of homogenized D-modules. with T.Oaku. To appear in Journal of Symbolic Computation. [ Preliminary version : in PS , in PDF ]
  2. Study on the family of $K3$ surfaces induced from the lattice $(D_4)^3\oplus \langle -2\rangle \oplus \langle 2\rangle$, with K.Koike, H.Shiga, and T.Tsutsui. [ math.AG/0003145 ].
  3. Systems for D-modules (Tutorial at Sevilla, OHP sheets) [ dvi file ]
  4. OpenXM --- an Open System to Integrate Mathematica Softwares (with Maekawa, Noro, Ohara, Okutani, Tamura) [ PS file ]
  5. Polynomial and Rational Solutions of Holonomic Systems (with T.Oaku and H.Tsai), to appear in Journal of Pure and Applied Algebra. [ (Preliminary version) math.AG/0001064 ].
  6. Majima, H., Matsumoto, K., Takayama, N., Quadratic relations for confluent hypergeometric functions. To appear in Tohoku Math. J. [ PS file ]

Papers (1999).

  1. Grobner Deformations of Hypergeometric Differential Equations. By Saito, Sturmfels, Takayama. Springer.
    A computer program to find starting terms is here.
  2. An algorithm for de Rham cohomology groups of the complement of an affine variety via D-module computation (with T.Oaku), Journal of Pure and Applied Algebra 139 (1999), 201--233. [ (Preliminary version) math.AG/9801114 ].
  3. Hypergeometric polynomials and Integer Programming (with Mitsumi Saito and Bernd Sturmfels), 18 pages, [ (Preliminary version) LaTeX source , Postscript (657K)]. Compositio Mathematica, {\bf 115}, (1999) 185--204.

Papers (1998).

  1. Comming papers: (1) Computation of intersection numbers with a differential equation and a computer. (2) Writing a computer algebra system I, II, ... (both in English and Japanese).
  2. A Localization Algorithm for D-modules, (with T.Oaku and U.Walther) to appear in Journal of Symbolic Computation. [ math.AG/9811030 ].
  3. Algorithms for D-modules --- restriction, tensor product, localization, and local cohomology groups, (with T.Oaku) to appear in Journal of Pure and Applied Algebra. [ math.AG/9805006 ].
  4. Algebraic Geometry and Computer Algebra. (in Japanese, Exposition), 8 pages. Surikagaku [ pLaTeX source ].

Papers (1997).

  1. Grobner basis and Hypergeometric functions, (with Bernd Sturmfels), 15 pages [ (Preliminary version) LaTeX source , Postscript (538K)]. in "Grobner Bases and Applications" B.Buchberger and F.~Winkler (eds.), Cambridge University Press, London Mathematical Society Lecture Notes Series,f 251, (1998), pp.246--258.
  2. Twisted period relations associated with confluent hypergeometric functions, (with Keiji Matsumoto), 8 pages [ LaTeX source , Postscript (184K)].
  3. Design of the computer algebra system kan/k0. (in Japanese), 7 pages [ LaTeX source ].
  4. Compactifications of the configuration space of $6$ points of the projective plane and fundamental solutions of the hypergeometric system of type $(3,6)$ (with J.Sekiguchi). Tohoku Mathematical Journal (1997), 49-3.

Papers (1996).

  1. CR-geometry on the configuration space of 5 points on the projective line , with M.Yoshida, Figures of this paper. Funkcialaj Ekvacioj (1996), 8 pages.
  2. Construction of voronoi diagram on the upper half plane , (with K.Onishi). IEICE Transaction on Fundamentals, April (1996), 8 pages.

Papers (1995).

  1. Algorithm finding recurrence relations of binomial sums and its complexity. Journal of Symbolic Computation 20 (1995), 637-651.
  2. Keiji Matsumoto and Nobuki Takayama, Braid group and a confluent hypergeometric function, Journal of Mathematical Sciences, The university of Tokyo, 2-3 (1995), 589-610.

Papers (1994).

  1. Mutsumi Saito and Nobuki Takayama, Restrictions of A-hypergeometric systems and connection formulas of the $\Delta_1 \times \Delta_{n-1}$-hypergeometric function, International Journal of Mathematics {\bf 5} (1994), 537-560. preliminary version

Publications before 1993.

  1. Mathematica ドリル (1991年版) PDF . これは Risa/Asir ドリル の前身です.
  2. An algorithm of constructing the integral of a module --- an infinite dimensional analog of Grobner basis, Proceedings of the international symposium on symbolic and algebraic computation, Edited by Watanabe and Nagata, ACM press and Addison-Wesley (1990), 206-211. PDF
  3. Grobner basis and the problem of contiguous relations, Japan Journal of Applied Mathematics, 6-1 (1989), 147-160. PDF
(Others are in preparation)

Papers provided only by WWW.

  1. A benchmark test for Grobner basis systems of differential operators I February 10, 1995, (LaTeX).

    See also kan: a computer algebra system for algebraic analysis.

  2. (pdf, scanned) A global representation of the solutions of the system of hypergeometric equations $E_2,5$ and the Appell function $F_1$ with J. Sekiguchi (1991), 38 pages. (ps, original).

Guides, OHP sheets, etc.

  1. Groebner basis and differential equations --- an example of mathematical software October 15, 1995. OHP sheets for AMC95 at Thailand. 16 pages.
  2. Special functions and Combinatorics. Introduction to the theory of A-determinant, regular triangulations and A-hypergeometric systems in Japanese. Suurikagaku, 1995, July.

SmallPrograms

  1. Computer programs cited from my papers.


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