Tajima, Shinichi; Nabeshima, Katsusuke; Ohara, Katsuyoshi; Umeta, Yoko Computing holonomic D-modules associated to a family of non-isolated hypersurface singularities via comprehensive Gröbner systems of PBW algebra. (English) Zbl 07700018 Math. Comput. Sci. 17, No. 1, Paper No. 6, 22 p. (2023). MSC: 14H20 PDFBibTeX XMLCite \textit{S. Tajima} et al., Math. Comput. Sci. 17, No. 1, Paper No. 6, 22 p. (2023; Zbl 07700018) Full Text: DOI
Tajima, Shinichi; Umeta, Yoko Algebraic analysis of Siersma’s non-isolated hypersurface singularities. (English) Zbl 1487.32167 Hokkaido Math. J. 51, No. 1, 117-151 (2022). MSC: 32S25 32C38 32C36 PDFBibTeX XMLCite \textit{S. Tajima} and \textit{Y. Umeta}, Hokkaido Math. J. 51, No. 1, 117--151 (2022; Zbl 1487.32167) Full Text: DOI
Tajima, Shinichi; Nabeshima, Katsusuke An effective method for computing Grothendieck point residue mappings. (English) Zbl 1484.32006 J. Algebra 593, 568-588 (2022). MSC: 32A27 32C36 13P10 14B15 PDFBibTeX XMLCite \textit{S. Tajima} and \textit{K. Nabeshima}, J. Algebra 593, 568--588 (2022; Zbl 1484.32006) Full Text: DOI arXiv
Nabeshima, Katsusuke; Tajima, Shinichi Methods for computing \(b\)-functions associated with \(\mu\)-constant deformations: case of inner modality two. (English) Zbl 1509.14116 Kyushu J. Math. 75, No. 1, 55-76 (2021). MSC: 14Q05 13P10 14B05 14F10 14H20 PDFBibTeX XMLCite \textit{K. Nabeshima} and \textit{S. Tajima}, Kyushu J. Math. 75, No. 1, 55--76 (2021; Zbl 1509.14116) Full Text: DOI arXiv
Nabeshima, Katsusuke; Tajima, Shinichi Testing zero-dimensionality of varieties at a point. (English) Zbl 1492.13037 Math. Comput. Sci. 15, No. 2, 317-331 (2021). MSC: 13P10 14H20 14Q10 PDFBibTeX XMLCite \textit{K. Nabeshima} and \textit{S. Tajima}, Math. Comput. Sci. 15, No. 2, 317--331 (2021; Zbl 1492.13037) Full Text: DOI arXiv
Nabeshima, Katsusuke; Tajima, Shinichi A new algorithm for computing logarithmic vector fields along an isolated singularity and Bruce-Roberts Milnor ideals. (English) Zbl 1489.14085 J. Symb. Comput. 107, 190-208 (2021). Reviewer: Alvaro Bustinduy (Madrid) MSC: 14Q10 32S05 32S65 68W30 PDFBibTeX XMLCite \textit{K. Nabeshima} and \textit{S. Tajima}, J. Symb. Comput. 107, 190--208 (2021; Zbl 1489.14085) Full Text: DOI
Ohara, Katsuyoshi; Tajima, Shinichi An algorithm for computing Grothendieck local residues. II: General case. (English) Zbl 1457.32006 Math. Comput. Sci. 14, No. 2, 483-496 (2020). MSC: 32A27 13N10 32C38 PDFBibTeX XMLCite \textit{K. Ohara} and \textit{S. Tajima}, Math. Comput. Sci. 14, No. 2, 483--496 (2020; Zbl 1457.32006) Full Text: DOI arXiv
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
Nabeshima, Katsusuke; Tajima, Shinichi Alternative algorithms for computing generic \(\mu^\ast\)-sequences and local Euler obstructions of isolated hypersurface singularities. (English) Zbl 1423.13097 J. Algebra Appl. 18, No. 8, Article ID 1950156, 13 p. (2019). Reviewer: Gerhard Pfister (Kaiserslautern) MSC: 13D45 32C37 13J05 32A27 PDFBibTeX XMLCite \textit{K. Nabeshima} and \textit{S. Tajima}, J. Algebra Appl. 18, No. 8, Article ID 1950156, 13 p. (2019; Zbl 1423.13097) Full Text: DOI
Tajima, Shinichi; Nabeshima, Katsusuke An implementation of the Lê-Teissier method for computing local Euler obstructions. (English) Zbl 1474.32048 Math. Comput. Sci. 13, No. 1-2, 273-280 (2019). MSC: 32S05 14B05 PDFBibTeX XMLCite \textit{S. Tajima} and \textit{K. Nabeshima}, Math. Comput. Sci. 13, No. 1--2, 273--280 (2019; Zbl 1474.32048) Full Text: DOI
Ohara, Katsuyoshi; Tajima, Shinichi An algorithm for computing Grothendieck local residues. I: Shape basis case. (English) Zbl 1474.32015 Math. Comput. Sci. 13, No. 1-2, 205-216 (2019). MSC: 32A27 13N10 PDFBibTeX XMLCite \textit{K. Ohara} and \textit{S. Tajima}, Math. Comput. Sci. 13, No. 1--2, 205--216 (2019; Zbl 1474.32015) Full Text: DOI
Nabeshima, Katsusuke; Tajima, Shinichi A new method for computing the limiting tangent space of an isolated hypersurface singularity via algebraic local cohomology. (English) Zbl 1420.13044 Izumiya, Shyuichi (ed.) et al., Singularities in generic geometry. Proceedings of the 4th workshop on singularities in generic geometry and applications (Valencia IV), Kobe, Japan, June 3–6, 2015 and Kyoto, Japan, June 8–10, 2015. Tokyo: Mathematical Society of Japan (MSJ). Adv. Stud. Pure Math. 78, 331-344 (2018). MSC: 13D45 32C37 13J05 32A27 PDFBibTeX XMLCite \textit{K. Nabeshima} and \textit{S. Tajima}, Adv. Stud. Pure Math. 78, 331--344 (2018; Zbl 1420.13044)
Nabeshima, Katsusuke; Ohara, Katsuyoshi; Tajima, Shinichi Comprehensive Gröbner systems in PBW algebras, Bernstein-Sato ideals and holonomic \(D\)-modules. (English) Zbl 1428.13047 J. Symb. Comput. 89, 146-170 (2018). Reviewer: Rolf Källström (Gävle) MSC: 13P10 13D45 13J05 14F10 32A27 32C37 PDFBibTeX XMLCite \textit{K. Nabeshima} et al., J. Symb. Comput. 89, 146--170 (2018; Zbl 1428.13047) Full Text: DOI
Nabeshima, Katsusuke; Tajima, Shinichi Computing \(\mu^{*}\)-sequences of hypersurface isolated singularities via parametric local cohomology systems. (English) Zbl 1393.13035 Acta Math. Vietnam. 42, No. 2, 279-288 (2017). Reviewer: Takesi Kawasaki (Tokyo) MSC: 13D45 32C37 13J05 32A27 PDFBibTeX XMLCite \textit{K. Nabeshima} and \textit{S. Tajima}, Acta Math. Vietnam. 42, No. 2, 279--288 (2017; Zbl 1393.13035) Full Text: DOI
Nabeshima, Katsusuke; Tajima, Shinichi Algebraic local cohomology with parameters and parametric standard bases for zero-dimensional ideals. (English) Zbl 1430.13026 J. Symb. Comput. 82, 91-122 (2017). MSC: 13D45 13J05 32A27 32C37 68W30 PDFBibTeX XMLCite \textit{K. Nabeshima} and \textit{S. Tajima}, J. Symb. Comput. 82, 91--122 (2017; Zbl 1430.13026) Full Text: DOI arXiv
Nabeshima, Katsusuke; Tajima, Shinichi Computing Tjurina stratifications of \(\mu \)-constant deformations via parametric local cohomology systems. (English) Zbl 1357.13021 Appl. Algebra Eng. Commun. Comput. 27, No. 6, 451-467 (2016). Reviewer: Gerhard Pfister (Kaiserslautern) MSC: 13D45 32C37 13J05 32A27 PDFBibTeX XMLCite \textit{K. Nabeshima} and \textit{S. Tajima}, Appl. Algebra Eng. Commun. Comput. 27, No. 6, 451--467 (2016; Zbl 1357.13021) Full Text: DOI
Oaku, Toshinori Annihilators of distributions associated with algebraic local cohomology of a hypersurface. (English) Zbl 1301.32007 Complex Var. Elliptic Equ. 59, No. 11, 1533-1546 (2014). MSC: 32C38 46F10 14B15 PDFBibTeX XMLCite \textit{T. Oaku}, Complex Var. Elliptic Equ. 59, No. 11, 1533--1546 (2014; Zbl 1301.32007) Full Text: DOI
Nabeshima, Katsusuke; Tajima, Shinichi An algorithm for computing Tjurina stratifications of \(\mu \)-constant deformations by using local cohomology classes with parameters. (English) Zbl 1437.14011 Hong, Hoon (ed.) et al., Mathematical software – ICMS 2014. 4th international congress, Seoul, South Korea, August 5–9, 2014. Proceedings. Berlin: Springer. Lect. Notes Comput. Sci. 8592, 523-530 (2014). MSC: 14-04 14B07 13D45 PDFBibTeX XMLCite \textit{K. Nabeshima} and \textit{S. Tajima}, Lect. Notes Comput. Sci. 8592, 523--530 (2014; Zbl 1437.14011) Full Text: DOI
Nabeshima, Katsusuke; Tajima, Shinichi An algorithm for computing standard bases by change of ordering via algebraic local cohomology. (English) Zbl 1437.13008 Hong, Hoon (ed.) et al., Mathematical software – ICMS 2014. 4th international congress, Seoul, South Korea, August 5–9, 2014. Proceedings. Berlin: Springer. Lect. Notes Comput. Sci. 8592, 414-418 (2014). MSC: 13-04 13P10 13D45 13F25 PDFBibTeX XMLCite \textit{K. Nabeshima} and \textit{S. Tajima}, Lect. Notes Comput. Sci. 8592, 414--418 (2014; Zbl 1437.13008) Full Text: DOI
Oshima, Toshio Fractional calculus of Weyl algebra and Fuchsian differential equations. (English) Zbl 1269.34003 MSJ Memoirs 28. Tokyo: Mathematical Society of Japan (ISBN 978-4-86497-016-7/pbk). xix, 203 p. (2012). Reviewer: Shun Shimomura (Yokohama) MSC: 34-02 34M35 34A05 34A25 34C20 34M40 34M50 PDFBibTeX XMLCite \textit{T. Oshima}, Fractional calculus of Weyl algebra and Fuchsian differential equations. Tokyo: Mathematical Society of Japan (2012; Zbl 1269.34003) Full Text: DOI arXiv Link
Uchida, Yukihiro Canonical local heights and multiplication formulas for the Jacobians of curves of genus 2. (English) Zbl 1229.11096 Acta Arith. 149, No. 2, 111-130 (2011). Reviewer: Lenny Fukshansky (Claremont) MSC: 11G50 11G20 11G30 14H40 PDFBibTeX XMLCite \textit{Y. Uchida}, Acta Arith. 149, No. 2, 111--130 (2011; Zbl 1229.11096) Full Text: DOI Link
Uchida, Yukihiro Division polynomials and canonical local heights on hyperelliptic Jacobians. (English) Zbl 1226.14039 Manuscr. Math. 134, No. 3-4, 273-308 (2011). Reviewer: Christophe Ritzenthaler (Marseille) MSC: 14H40 11G10 11G50 PDFBibTeX XMLCite \textit{Y. Uchida}, Manuscr. Math. 134, No. 3--4, 273--308 (2011; Zbl 1226.14039) Full Text: DOI Link
Takahasi, Tadashi Deformation of double cusp singularity on an irreducible quartic curve by using the computer algebra system Risa/Asir. (English) Zbl 1018.14021 Shirayanagi, Kiyoshi (ed.) et al., Computer mathematics. Proceedings of the 5th Asian symposium (ASCM 2001), Matsuyama, Japan, September 26-28, 2001. Singapore: World Scientific. Lect. Notes Ser. Comput. 9, 161-164 (2001). MSC: 14Q05 14H20 PDFBibTeX XMLCite \textit{T. Takahasi}, Lect. Notes Ser. Comput. 9, 161--164 (2001; Zbl 1018.14021)
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
Tajima, Shinichi Algebraic analysis of multivariate Hermite interpolation formulas. (English) Zbl 1038.32012 Begehr, Heinrich G. W. (ed.) et al., Proceedings of the second ISAAC congress. Vol. 2. Proceedings of the International Society for Analysis, its Applications and Computation Congress, Fukuoka, Japan, August 16–21, 1999. Dordrecht: Kluwer Academic Publishers (ISBN 0-7923-6598-4/hbk). Int. Soc. Anal. Appl. Comput. 8, 829-838 (2000). MSC: 32E30 32C38 14F43 14F10 PDFBibTeX XMLCite \textit{S. Tajima}, Int. Soc. Anal. Appl. Comput. 8, 829--838 (2000; Zbl 1038.32012)