[ 日本語で (in Japanese)]

Hi! (Nobuki Takayama)

Last update is August 30, 2013

kan/sm1 : a computer algebra system for algebraic analysis.

OpenXM project : integration of mathematical software systems.

Call for Papers : Risa/Asir Journal (which is a step to "Journal of Free Mathematical Software")

Applying for the Graduate School: information for foreign students

Papers (2013, academic year).

  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)
  2. Chapter 6 (Groebner basis for rings of differential operators and applications) of T.Hibi et al, Groebner Bases : Statistics and Software Systems , Springer.

misc (2013, academic year).

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

Papers (2012, academic year).

  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

misc (2012, academic year).

Papers (2011, academic year).

  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
  4. Tomonari Sei, Hiroki Shibata, Akimichi Takemura, Katsuyoshi Ohara, Nobuki Takayama, Properties and applications of Fisher distribution on the rotation group, 1110.0721

Papers (2010, academic year).

  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

misc (2010, academic year).

Papers (2009, academic year).

  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.

misc (2009, academic year).

Papers (2008, academic year).

  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

misc (2008, academic year).

  1. Editors M.Stillman, N.Takayama, J.Verschelde, Software for Algebraic Geometry, (The IMA volumes in Mathematics and its applications, 148), 2008, Springer.

Papers (2007, academic year).

  1. Katsuyoshi Ohara, Nobuki Takayama, Holonomic Rank of A-Hypergeometric Differential-Difference Equations (PDF, 15pages), Journal of Pure and Applied Algebra, 213 (2009) 1501--1642. math.CA/0706.2706v1
  2. Nobuki Takayama, Modified A-Hypergeometric System (PDF, 8pages), Kyushu Journal of Mathematics 63 (2009), 113--122. math.CA/0707.0043v1 , talk (video, in Japanese)
  3. Mertin Mevissen, Masakazu Kojima, Jiawang Nie, Nobuki Takayama, Solving Partial Differential Equations via Sparse SDP Relaxations , Pacific Journal of Optimization, 4 (2008), 213--241.
  4. Francisco-Jesus Castro-Jimenez, Nobuki Takayama, The Computation of the Logarithmic Cohomology for Plane Curves , preprint. math.AG/0712.0001 , talk (video, in Japanese)

Misc. (2007, academic year)

  1. Workshop on hypergeometric equations 2007 (in Japanese)
  2. slides, Analytic Grobner fan and its applications

Papers (2006).

  1. Rouchdi Bahloul and Nobuki Takayama, Local Grobner Fan, (a short survey) PDF (preprint), C.R. Acad.Sci. Paris, Ser. I. 344 (2007), 147--152.

Misc. (2006)

  1. Workshop on hypergeometric equations (Program, 2006.01.06--2006.01.07)
  2. The second International Congress of Mathematical Software (icms2006, developer's meeting, 2006.09.01--09.03). Video archive of lectures, knoppix/math for icms2006, mathsoftware.org , Local organizer's page .

Papers (2005).

  1. Rouchdi Bahloul and Nobuki Takayama, Local Grobner fan: polyhedral and computational approach, 2005, math.AG/0412044 PS/PDF
  2. Nobuki Takayama, Past, Present and Future of the OpenXM Project (in Japanese), 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

Misc. (2005)

  1. OoHG Protocol (OX-RFC-104) (OHP, PDF, in Japanese) : 3rd OpenXM committers meeting 2005.02
  2. Program : Risa/Asir Conference 2005
  3. Introduction to HTMl/JavaScript
  4. Nobuki Takayama, Papers in Computatinal Methods for D-Modules, PDF

Papers (2004).

  1. Nobuki Takayama, Present and Future for Digital Formula Book Systems for Mathematics (in Japanse, Exposition), in Jyoho Shyori (Information Processing Society of Japan), June 2004

Misc. (2004)

  1. Program : Workshop on hypergeometric equations. (2004.11.4 -- 2004.11.6)
  2. History of kan/sm1 (PDF, in Japanese)
  3. Program : Risa/Asir Conference 2004 (conference, 2004.3.22 -- 2004.3.24 )
  4. Program : Differential Equations in the Complex Domain (conference, 2004.1.12 -- 2004.1.14 )
  5. Handouts for Courses.
    1. Introduction to JavaScript
    2. Risa/Asir drill (in Japanese) , Risa/Asir binary for the asir book including Prog directory.
  6. Assignments

Papers (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 ], [ a video presentation ]
  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)

Misc. (2003)

  1. RisaCon II Program : RisaCon II (workshop, 2003.3.18 -- 2003.3.20 )
  2. JavaView picture of the Bessel function in 2 variables.
  3. Slides at ASCM 2003 : ASCM 2003 (Conference, 2003.10.23 -- 2003.10.25 )
  4. A video on the OpenXM/fb project (A digital formula book project)

Papers (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 ].

Misc. (2002)

  1. Jyoron MEMO , How to use ffftp
  2. Handouts for "Jyoho Kagaku Jyoron"

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. 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
  2. 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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