Welcome to the web page of Katsuyoshi Ohara.

• Katsuyoshi OHARA
  Faculty of Mathematics and Physics, Kanazawa University

• Publications
  1. J. Kaneko, K. Matsumoto, K. Ohara, T. Terasoma: A system of hypergeometric differential equations in m variables of rank p^m, preprint. (arXiv:2404.00295 [math.CA])
  2. Ari Dwi Hartanto, K. Ohara: An F5 algorithm for tropical Gröbner bases in the Weyl algebras, preprint. (arXiv:2312.14419 [cs.CS])
  3. Ari Dwi Hartanto, K. Ohara: Computing Gröbner bases on Weyl algebras over fields with valuations, Journal of Algebra 659(2024), 902--926. (DOI)
  4. S. Tajima, K. Nabeshima, K. Ohara, Y. Umeta: Computing holonomic D-modules associated to a family of non-isolated hypersurface singularities via comprehensive Groebner systems of PBW algebra, Mathematics in Computer Science, 17 (2023) (DOI) (full paper)
  5. S. Tajima, K. Ohara, A. Terui: Exact Algorithms for Computing Generalized Eigenspaces of Matrices via Annihilating Polynomials, preprint. (arXiv:2209.04807 [math.RA])
  6. S. Tajima, K. Ohara, K. Nabeshima: Computing holonomic D-modules associated to a family of non-isolated hypersurface singularities via comprehensive Groebner systems of PBW algebra, Proceedings of 26th Conference on Applications of Computer Algebra --- ACA 2021, 241--242, 2021. (proceeding)
  7. K. Ohara, S. Tajima: An algorithm for computing Grothendieck local residues II: general case, Mathematics in Computer Science 14 (2020), 483--496. (DOI) (full paper)
  8. J. Kaneko, K. Matsumoto, K. Ohara: The structure of a local system associated with a hypergeometric system of rank 9, International Journal of Mathematics 31-3 (2020) (DOI)
  9. S. Tajima, K. Ohara, A. Terui: Fast Algorithm for Computing Eigenvectors of Matrices via Pseudo Annihilating Polynomials, preprint, (arXiv:1811.09149 [math.NA])
  10. K. Ohara, S. Tajima: An algorithm for computing Grothendieck local residues II --- general case ---, Proceedings of 24th Conference on Applications of Computer Algebra --- ACA 2018, 245--248, 2018. (proceeding)
  11. S. Tajima, K. Ohara, A. Terui: Fast Algorithm for Calculating the Minimal Annihilating Polynomials of Matrices via Pseudo Annihilating Polynomials, preprint. (arXiv:1801.08437 [math.AC])
  12. K. Ohara, S. Tajima: An algorithm for computing Grothendieck local residues I: shape basis case, Mathematics in Computer Science 13 (2019), 205--216. (DOI) (full paper)
  13. K. Ohara, S. Tajima: An algorithm for computing Grothendieck local residues I --- shape base case ---, Abstracts of 23rd Conference on Applications of Computer Algebra --- ACA 2017, 226--227, 2017.
  14. K. Nabeshima, K. Ohara, S. Tajima: Comprehensive Gröbner systems in PBW algebras, Bernstein-Sato ideals and holonomic D-modules, Journal of Symbolic Computation 89 (2018), 146--170. (DOI)
  15. F. H. Danufane, K. Ohara, N. Takayama, C. Siriteanu: Holonomic Gradient Method-Based CDF Evaluation for the Largest Eigenvalue of a Complex Noncentral Wishart Matrix, preprint. (arXiv:1707.02564 [math.ST])
  16. K. Ohara, N. Takayama: Pfaffian Systems of A-Hypergeometric Systems II --- Holonomic Gradient Method, preprint. (arXiv:1505.02947 [cs.SC])
  17. J. Kaneko, K. Matsumoto, K. Ohara: A system of hypergeometric differential equations in two variables of rank 9, International Journal of Mathematics 28-3 (2017) (DOI)
  18. K. Nabeshima, K. Ohara, S. Tajima: Comprehensive Gröbner systems in rings of differential operators, holonomic D-modules and b-functions, Proceedings of the ACM on International Symposium on Symbolic and Algebraic Computation (ISSAC 2016), 349--356.
  19. M. Z. Almuzakki, K. Ohara: Computing general error locator polynomial of 3-error-correcting BCH codes via syndrome varieties using minimal polynomial, Recent Development in Computational Science 6 (2015), 80--85.
  20. T. Koyama, H. Nakayama, K. Ohara, T. Sei, N. Takayama: Software Packages for Holonomic Gradient Method, The proceedings of ICMS 2014, Lecture Notes in Computer Science 8592, 706--712, Springer, 2014.
  21. K. Ohara, S. Tajima, A. Terui: Developing linear algebra packages on Risa/Asir for eigenproblems, The proceedings of ICMS 2014, Lecture Notes in Computer Science 8592, 321--324, Springer, 2014.
  22. S. Tajima, K. Ohara, A. Terui: An extension and efficient calculation of the Horner's rule, The proceedings of ICMS 2014, Lecture Notes in Computer Science 8592, 346--351, Springer, 2014.
  23. T. Sei, H. Shibata, A. Takemura, K. Ohara and N. Takayama: Properties and applications of Fisher distribution on the rotation group, Journal of Multivariate Analysis 116 (2013), 440--455.
  24. P. H. Gunawan, S. Omata, K. Ohara and M. Kazama: Droplet collision via the SPH method with surface tension, Gakuto Intern. Ser. Math. Sci. Appl. 34 (2011), 151--156.
  25. H. Nakayama, K. Nishiyama, M. Noro, K. Ohara, T. Sei, N. Takayama and A. Takemura: Holonomic Gradient Descent and its Application to Fisher-Bingham Integral, Advances in Applied Mathematics 47-3 (2011), 639--658.
  26. K. Ohara and S. Tajima: Spectral Decomposition and Eigenvectors of Matrices by Residue Calculus, Proceedings of the Joint Conference of ASCM 2009 and MACIS 2009, COE Lecture Note 22, Kyushu University, 137--140.
  27. K. Matsumoto and K. Ohara: Some transformation formulas for Lauricella's hypergeometric functions F_D, Funkcialaj Ekvacioj, 52-2 (2009), 203--212.
  28. K. Ohara and N. Takayama: Holonomic rank of A-hypergeometric differential-difference equations, Journal of Pure and Applied Algebra 213-8 (2009), 1536--1544.
  29. H. Yoshiuchi, S. Omata, K. Svadlenka and K. Ohara: Numerical solution of film vibration with obstacle, Adv. Math. Sci. Appl. 16-1 (2006), 33--43.
  30. T. Yamazaki, S. Omata, K. Svadlenka and K. Ohara: Construction of approximate solution to a hyperbolic free boundary problem with volume constraint and its numerical computation, Adv. Math. Sci. Appl. 16-1 (2006), 57--67.
  31. K. Ohara and N. Takayama: Dimension formula of solution spaces of A-hypergeometric differential-difference systems, Proceedings of the Seventh Asian Symposium on Computer Mathematics (ASCM2005), edited by Sung-il Pae and Hyungju Park, Korea Institute for Advanced Study, 100--102, 2005.
  32. T. Yamazaki, S. Omata, H. Yoshiuchi and K. Ohara: Bubble motion on water surface, Gakuto Intern. Ser. Math. Sci. Appl. 23 (2005), 209--216.
  33. H. Iwasaki, K. Ohara, S. Omata and T. Zhou: Numerical computations for interfaces motion related to a triple potential well problem, Adv. Math. Sci. Appl. 14-2 (2004), 457--464.
  34. K. Mimachi, K. Ohara and M. Yoshida: Intersection numbers for loaded cycles associated with Selberg-type integrals, Tohoku Math. J. 56-4 (2004), 531--551.
  35. K. Ohara, Y. Sugiki and N. Takayama: Quadratic Relations for Generalized Hypergeometric Functions _pF_p-1, Funkcialaj Ekvacioj 46-2 (2003), 213--251.
  36. M. Maekawa, M. Noro, K. Ohara, N. Takayama and Y. Tamura: OpenXM --- an Open System to Integrate Mathematical Software:
      Kerber, M. and Kohlhase, M., eds, Symbolic Computation and Automated Reasoning: The Calculemus 2000 Symposium. AK Peters, 2001.
  37. M. Maekawa, M. Noro, K. Ohara, N. Takayama and K. Tamura: The Design and Implementation of OpenXM-RFC 100 and 101, Computer Mathematics, Proceedings of the Fifth Asian Symposium (ASCM 2001), edited by Shirayanagi and Yokoyama, World Scientific, 102--111, 2001.
  38. K. Ohara: Computation of the monodromy of the generalized hypergeometric function _pF_p-1(a₁, ..., a_p; b₂, ..., b_p; z), Kyushu J. Math. 51(1997), 101--124.
• software
  • A unofficial source distribution of the OpenXM project.
  • Risa/Asir binary (32bit or 64bit) for Windows7.
  • yang --- a package for hypergeometric functions and Groebner bases of rings of differential-difference operators. (it is idistributed with the OpenXM softwares above)
  • Table of Pfaffian differential equations of 34 hypergeometric functions in Horn's List, Lauricella's 3-variate hypergeometric functions and the hypergeometric function of type (3,6).
    This table is computed by yang.