Matsubara-Heo, Saiei-Jaeyeong; Takayama, Nobuki An algorithm of computing cohomology intersection number of hypergeometric integrals. (English) Zbl 1510.33014 Nagoya Math. J. 246, 256-272 (2022). MSC: 33C60 33C70 33F99 68W30 32G34 14D05 14J28 14F10 PDFBibTeX XMLCite \textit{S.-J. Matsubara-Heo} and \textit{N. Takayama}, Nagoya Math. J. 246, 256--272 (2022; Zbl 1510.33014) Full Text: DOI arXiv
Matsubara-Heo, Saiei-Jaeyeong; Takayama, Nobuki Algorithms for Pfaffian systems and cohomology intersection numbers of hypergeometric integrals. (English) Zbl 1503.33014 Bigatti, Anna Maria (ed.) et al., Mathematical software – ICMS 2020. 7th international conference, Braunschweig, Germany, July 13–16, 2020. Proceedings. Cham: Springer. Lect. Notes Comput. Sci. 12097, 73-84 (2020). MSC: 33C70 13P10 14F10 68W30 PDFBibTeX XMLCite \textit{S.-J. Matsubara-Heo} and \textit{N. Takayama}, Lect. Notes Comput. Sci. 12097, 73--84 (2020; Zbl 1503.33014) Full Text: DOI
Nakayama, Hiromasa; Takayama, Nobuki Introduction to algorithms for \(D\)-modules with quiver \(D\)-modules. (English) Zbl 1453.14057 Iohara, Kenji (ed.) et al., Two algebraic byways from differential equations: Gröbner bases and quivers. Cham: Springer. Algorithms Comput. Math. 28, 95-114 (2020). MSC: 14F10 32C38 13N10 13P10 14F40 PDFBibTeX XMLCite \textit{H. Nakayama} and \textit{N. Takayama}, Algorithms Comput. Math. 28, 95--114 (2020; Zbl 1453.14057) Full Text: DOI
Iohara, Kenji (ed.); Malbos, Philippe (ed.); Saito, Masa-Hiko (ed.); Takayama, Nobuki (ed.) Two algebraic byways from differential equations: Gröbner bases and quivers. (English) Zbl 1444.14002 Algorithms and Computation in Mathematics 28. Cham: Springer (ISBN 978-3-030-26453-6/hbk; 978-3-030-26454-3/ebook). xi, 371 p. (2020). MSC: 14-06 16-06 62-06 00B15 13P10 14F10 14H60 14L24 14L30 16D40 16G20 16S37 18C10 18N10 18G10 34M35 34M40 35A25 53D20 58A15 68Q42 PDFBibTeX XMLCite \textit{K. Iohara} (ed.) et al., Two algebraic byways from differential equations: Gröbner bases and quivers. Cham: Springer (2020; Zbl 1444.14002) Full Text: DOI
Hashiguchi, Hiroki; Takayama, Nobuki; Takemura, Akimichi Distribution of the ratio of two Wishart matrices and cumulative probability evaluation by the holonomic gradient method. (English) Zbl 1397.62188 J. Multivariate Anal. 165, 270-278 (2018). MSC: 62H10 62E20 62H15 PDFBibTeX XMLCite \textit{H. Hashiguchi} et al., J. Multivariate Anal. 165, 270--278 (2018; Zbl 1397.62188) Full Text: DOI arXiv
Castro-Jiménez, Francisco-Jesús; Fernández-Fernández, María-Cruz; Koike, Tatsuya; Takayama, Nobuki Irregular modified \(A\)-hypergeometric systems. (English) Zbl 1335.32005 Trans. Am. Math. Soc. 367, No. 8, 5415-5445 (2015). Reviewer: Takesi Kawasaki (Tokyo) MSC: 32C38 14F10 33C70 13N10 14M25 PDFBibTeX XMLCite \textit{F.-J. Castro-Jiménez} et al., Trans. Am. Math. Soc. 367, No. 8, 5415--5445 (2015; Zbl 1335.32005) Full Text: DOI arXiv
Hattori, Ryohei; Takayama, Nobuki The singular locus of Lauricella’s \(F_C\). (English) Zbl 1312.33043 J. Math. Soc. Japan 66, No. 3, 981-995 (2014). MSC: 33C65 14F10 32C38 PDFBibTeX XMLCite \textit{R. Hattori} and \textit{N. Takayama}, J. Math. Soc. Japan 66, No. 3, 981--995 (2014; Zbl 1312.33043) Full Text: DOI arXiv Euclid
Koyama, Tamio; Nakayama, Hiromasa; Nishiyama, Kenta; Takayama, Nobuki The holonomic rank of the Fisher-Bingham system of differential equations. (English) Zbl 1295.35196 J. Pure Appl. Algebra 218, No. 11, 2060-2071 (2014). MSC: 35G35 32C38 14F10 PDFBibTeX XMLCite \textit{T. Koyama} et al., J. Pure Appl. Algebra 218, No. 11, 2060--2071 (2014; Zbl 1295.35196) Full Text: DOI arXiv
Nakayama, Hiromasa; Takayama, Nobuki Computing differential equations for integrals associated to smooth Fano polytope. (English) Zbl 1314.13046 Japan J. Ind. Appl. Math. 30, No. 2, 307-319 (2013). Reviewer: Christoph Koutschan (Linz) MSC: 13P10 14Q99 33F10 68W30 47L20 PDFBibTeX XMLCite \textit{H. Nakayama} and \textit{N. Takayama}, Japan J. Ind. Appl. Math. 30, No. 2, 307--319 (2013; Zbl 1314.13046) Full Text: DOI arXiv
Nakayama, Hiromasa; Nishiyama, Kenta; Noro, Masayuki; Ohara, Katsuyoshi; Sei, Tomonari; Takayama, Nobuki; Takemura, Akimichi Holonomic gradient descent and its application to the Fisher-Bingham integral. (English) Zbl 1226.90137 Adv. Appl. Math. 47, No. 3, 639-658 (2011). MSC: 90C52 16Z99 62F10 33F10 32C38 PDFBibTeX XMLCite \textit{H. Nakayama} et al., Adv. Appl. Math. 47, No. 3, 639--658 (2011; Zbl 1226.90137) Full Text: DOI arXiv
Castro-Jiménez, Francisco-Jesús; Takayama, Nobuki The computation of the logarithmic cohomology for plane curves. (English) Zbl 1186.14061 J. Algebra 322, No. 11, 3839-3851 (2009). Reviewer: Juan Gerardo Alcazar (Alcala da Henares) MSC: 14Q05 14F40 PDFBibTeX XMLCite \textit{F.-J. Castro-Jiménez} and \textit{N. Takayama}, J. Algebra 322, No. 11, 3839--3851 (2009; Zbl 1186.14061) Full Text: DOI arXiv
Granger, Michel; Oaku, Toshinori; Takayama, Nobuki Tangent cone algorithm for homogenized differential operators. (English) Zbl 1120.32300 J. Symb. Comput. 39, No. 3-4, 417-431 (2005). MSC: 32C38 16S32 68W30 PDFBibTeX XMLCite \textit{M. Granger} et al., J. Symb. Comput. 39, No. 3--4, 417--431 (2005; Zbl 1120.32300) Full Text: DOI
Oaku, Toshinori; Shiraki, Yoshinao; Takayama, Nobuki Algebraic algorithms for \(D\)-modules and numerical analysis. (English) Zbl 1092.14026 Li, Ziming (ed.) et al., Computer mathematics. Proceedings of the sixth Asian symposium (ASCM 2003), Beijing, China, April 17–19, 2003. River Edge, NJ: World Scientific (ISBN 981-238-220-8/hbk). Lect. Notes Ser. Comput. 10, 23-39 (2003). Reviewer: E. V. Pankrat’ev (Moskva) MSC: 14F10 32C38 33F10 14Q05 68W30 13P05 PDFBibTeX XMLCite \textit{T. Oaku} et al., Lect. Notes Ser. Comput. 10, 23--39 (2003; Zbl 1092.14026)
Castro-Jiménez, Francisco Jesús; Takayama, Nobuki Singularities of the hypergeometric system associated with a monomial curve. (English) Zbl 1060.33023 Trans. Am. Math. Soc. 355, No. 9, 3761-3775 (2003). Reviewer: Gheorghe Gussi (Bucureşti) MSC: 33C99 32C38 PDFBibTeX XMLCite \textit{F. J. Castro-Jiménez} and \textit{N. Takayama}, Trans. Am. Math. Soc. 355, No. 9, 3761--3775 (2003; Zbl 1060.33023) Full Text: DOI
Castro-Jiménez, Francisco Jesús; Takayama, Nobuki GKZ hypergeometric slopes associated to monomial curves. (English) Zbl 1119.32300 RIMS Kokyuroku 1212, 79-94 (2001). MSC: 32C38 16S32 33C70 PDFBibTeX XMLCite \textit{F. J. Castro-Jiménez} and \textit{N. Takayama}, RIMS Kokyuroku 1212, 79--94 (2001; Zbl 1119.32300) Full Text: arXiv
Oaku, Toshinori; Takayama, Nobuki Minimal free resolutions of homogenized \(D\)-modules. (English) Zbl 1028.16015 J. Symb. Comput. 32, No. 6, 575-595 (2001). Reviewer: Masakazu Muro (Yanagido) MSC: 16S32 16E05 PDFBibTeX XMLCite \textit{T. Oaku} and \textit{N. Takayama}, J. Symb. Comput. 32, No. 6, 575--595 (2001; Zbl 1028.16015) Full Text: DOI
Oaku, Toshinori; Takayama, Nobuki; Tsai, Harrison Polynomial and rational solutions of holonomic systems. (English) Zbl 0990.35031 J. Pure Appl. Algebra 164, No. 1-2, 199-220 (2001). Reviewer: Valery V.Karachik (Tashkent) MSC: 35C05 14Q99 35N10 33F10 PDFBibTeX XMLCite \textit{T. Oaku} et al., J. Pure Appl. Algebra 164, No. 1--2, 199--220 (2001; Zbl 0990.35031) Full Text: DOI arXiv
Oaku, Toshinori; Takayama, Nobuki Algorithms for \(D\)-modules – restriction, tensor product, localization, and local cohomology groups. (English) Zbl 0983.13008 J. Pure Appl. Algebra 156, No. 2-3, 267-308 (2001). Reviewer: T.G.Berry (Caracas) MSC: 13N10 13P10 14Q20 32C38 14B15 68W30 PDFBibTeX XMLCite \textit{T. Oaku} and \textit{N. Takayama}, J. Pure Appl. Algebra 156, No. 2--3, 267--308 (2001; Zbl 0983.13008) Full Text: DOI arXiv
Takayama, Nobuki (ed.) Algorithms for \(D\)-modules. Proceedings of a symposium held at the Research Institute for Mathematical Sciences, Kyoto University, Kyoto, Japan, May 16–19, 2000. (English, Japanese) Zbl 0974.14002 RIMS Kokyuroku 1171, vi, 189 p. (2000). MSC: 14-06 00B25 32-06 68-06 PDFBibTeX XMLCite \textit{N. Takayama} (ed.), RIMS Kokyuroku 1171, vi, 189 p. (2000; Zbl 0974.14002)
Oaku, Toshinori; Takayama, Nobuki; Walther, Uli A localization algorithm for \(D\)-modules. (English) Zbl 1012.13010 J. Symb. Comput. 29, No. 4-5, 721-728 (2000). MSC: 13N05 68W30 14F10 PDFBibTeX XMLCite \textit{T. Oaku} et al., J. Symb. Comput. 29, No. 4--5, 721--728 (2000; Zbl 1012.13010) Full Text: DOI arXiv
Saito, Mutsumi; Sturmfels, Bernd; Takayama, Nobuki Gröbner deformations of hypergeometric differential equations. (English) Zbl 0946.13021 Algorithms and Computation in Mathematics. 6. Berlin: Springer. viii, 254 p. (2000). Reviewer: Peter Schenzel (Halle) MSC: 13P10 68W30 13-02 68-02 33D60 13N10 14M25 16S32 14F10 PDFBibTeX XMLCite \textit{M. Saito} et al., Gröbner deformations of hypergeometric differential equations. Berlin: Springer (2000; Zbl 0946.13021)
Oaku, Toshinori; Takayama, Nobuki An algorithm for de Rham cohomology groups of the complement of an affine variety via \(D\)-module computation. (English) Zbl 0960.14008 J. Pure Appl. Algebra 139, No. 1-3, 201-233 (1999). Reviewer: Joos Heintz (Buenos Aires) MSC: 14F40 68W30 14F10 14Q15 PDFBibTeX XMLCite \textit{T. Oaku} and \textit{N. Takayama}, J. Pure Appl. Algebra 139, No. 1--3, 201--233 (1999; Zbl 0960.14008) Full Text: DOI arXiv Backlinks: MO
Oaku, Toshinori; Takayama, Nobuki Integrals of modules and their applications. (Japanese) Zbl 0944.14501 RIMS Kokyuroku 1038, 163-169 (1998). MSC: 14F10 PDFBibTeX XMLCite \textit{T. Oaku} and \textit{N. Takayama}, RIMS Kokyuroku 1038, 163--169 (1998; Zbl 0944.14501)
Saito, Mutsumi; Sturmfels, Bernd; Takayama, Nobuki Gröbner deformations of regular holonomic systems. (English) Zbl 0946.13022 Proc. Japan Acad., Ser. A 74, No. 7, 111-113 (1998). Reviewer: Peter Schenzel (Halle) MSC: 13P10 13N10 68W30 14F10 16S32 PDFBibTeX XMLCite \textit{M. Saito} et al., Proc. Japan Acad., Ser. A 74, No. 7, 111--113 (1998; Zbl 0946.13022) Full Text: DOI