A.Sakoda, N.Takayama,
An Application of the Holonomic Gradient Method to the Neural Tangent Kernel,
arxiv .
Papers, other (2023, academic year).
Vsevolod Chestnov, Saiei J. Matsubara-Heo, Henrik J. Munch, Nobuki Takayama,
Restrictions of Pfaffian Systems for Feynman Integrals,
DOI: 10.1007/JHEP11(2023)202
Nobuki Takayama, Takaharu Yaguchi, Yi Zhang,
Comparison of Numerical Solvers for Differential Equations for Holonomic Gradient Method in Statistics,
arxiv:2111.10947
Shuhei Mano, Nobuki Takayama,
Algebraic algorithm for direct sampling from toric models,
arxiv:2110.14992
Xavier Caruso, Marc Mezzarobba, Nobuki Takayama, Tristan Vaccon,
Fast evaluation of some p-adic transcendental functions,
arxiv:2106.09315
Saiei-Jaeyeong Matsubara-Heo, Nobuki Takayama,
An algorithm of computing cohomology intersection number of hypergeometric integrals
arxiv: 1904.01253
Yoshihito Tachibana, Yoshiaki Goto, Tamio Koyama, Nobuki Takayama,
Holonomic Gradient Method for Two Way Contingency Tables,
Version 3 (a major update).
arxiv:1803.04170
N.Takayama, L.Jiu, S.Kuriki, Y.Zhang,
Computations of the Expected Euler Characteristic for the Largest Eigenvalue of a Real Wishart Matrix,
arxiv:1903.10099
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
Papers (2016, academic year).
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
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
Papers (2013, academic year).
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)
Introduction to the Holonomic Gradient Method (movie), 2013.
movie at youtube
Papers (2012, academic year).
T.Hibi, K.Nishiyama, N.Takayama,
Pfaffian Systems of A-Hypergeometric Equations,
arxiv:1212.6103
F.Castro-Jimenez, M.C.Fernandez-Fernandez, T.Koike, N.Takayama,
Irregularity of Modified $A$-Hypergeometric Systems
arxiv:1207.1533
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).
T. Koyama, H. Nakayama, K. Nishiyama, N. Takayama,
Holonomic Gradient Descent for the Fisher-Bingham Distribution on the $n$-dimensional Sphere
1201.3239
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
Ryohei Hattori, Nobuki Takayama,
The singular locus of Lauricella's F_C,
1110.6675 ,
Journal of Mathematical Society of Japan,
66 (2014), 981--995
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).
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
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).
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).
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).
Editors M.Stillman, N.Takayama, J.Verschelde,
Software for Algebraic Geometry,
(The IMA volumes in Mathematics and its applications, 148), 2008, Springer.
Rouchdi Bahloul and Nobuki Takayama,
Local Grobner fan: polyhedral and computational approach,
2005, math.AG/0412044
PS/PDF
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
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
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.
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
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 ].
Katsuyoshi Ohara, Yuichi Sugiki, and Nobuki Takayama,
Quadratic Relations for Generalized Hypergeometric
Functions ${}_p F _{p-1}$.
[ (Funkcialaj Ekvacioj 46, 2003) Paper in PDF ].
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)
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 ].
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).
Minimal free resolutions of homogenized D-modules.
with T.Oaku. To appear in Journal of Symbolic Computation.
[ Preliminary version : in PS ,
in PDF ]
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 ].
Systems for D-modules (Tutorial at Sevilla, OHP sheets)
[ dvi file ]
OpenXM --- an Open System to Integrate Mathematica Softwares
(with Maekawa, Noro, Ohara, Okutani, Tamura)
[ PS file ]
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 ].
Majima, H., Matsumoto, K., Takayama, N.,
Quadratic relations for confluent hypergeometric functions.
To appear in Tohoku Math. J.
[ PS file ]
Papers (1999).
Grobner Deformations of Hypergeometric Differential Equations.
By Saito, Sturmfels, Takayama. Springer.
A computer program to find starting terms
is here.
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 ].
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).
A Localization Algorithm for D-modules,
(with T.Oaku and U.Walther)
to appear in Journal of Symbolic Computation.
[ math.AG/9811030 ].
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 ].
Algebraic Geometry and Computer Algebra.
(in Japanese, Exposition), 8 pages. Surikagaku
[ pLaTeX source ].
Papers (1997).
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.
Twisted period relations associated with confluent hypergeometric
functions, (with Keiji Matsumoto), 8 pages
[ LaTeX source ,
Postscript (184K)].
Design of the computer algebra system kan/k0.
(in Japanese), 7 pages
[ LaTeX source ].
Construction of voronoi diagram on the upper
half plane ,
(with K.Onishi).
IEICE Transaction on Fundamentals, April (1996), 8 pages.
Papers (1995).
Algorithm finding recurrence relations of
binomial sums and its complexity.
Journal of Symbolic Computation 20 (1995), 637-651.
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).
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 by ps2pdf
or
preliminary version (removed
old AMS fonts)
Publications before 1993.
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
Grobner basis and the problem of contiguous relations,
Japan Journal of Applied Mathematics,
6-1 (1989), 147-160.
PDF
Special functions and Combinatorics.
Introduction to the theory of A-determinant, regular triangulations
and A-hypergeometric systems in Japanese.
Suurikagaku, 1995, July.
