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Data Computation and Software Development in Number Theory by Computers

Research Project

Project/Area Number 10440012
Research Category

Grant-in-Aid for Scientific Research (B)

Allocation TypeSingle-year Grants
Section一般
Research Field Algebra
Research InstitutionTokyo Metropolitan University

Principal Investigator

NAKAMULA Ken  Graduate School of Science, 理学研究科, 教授 (80110849)

Co-Investigator(Kenkyū-buntansha) KURIHARA Masato  Graduate School of Science, 理学研究科, 助教授 (40211221)
NAKAMURA Hiroaki  Graduate School of Science, 理学研究科, 助教授 (60217883)
MIYAKE Katsuya  Graduate School of Science, 理学研究科, 教授 (20023632)
KURATA Toshihiko  Graduate School of Science, 理学研究科, 助手 (40311899)
MIYAZAKI Takuya  Graduate School of Science, 理学研究科, 助手 (10301409)
岡崎 龍太郎  同志社大学, 工学部, 講師 (20268113)
川崎 健  東京都立大学, 理学研究科, 助手 (40301410)
寺尾 宏明  東京都立大学, 理学研究科, 教授 (90119058)
Project Period (FY) 1998 – 1999
Project Status Completed (Fiscal Year 1999)
Budget Amount *help
¥4,400,000 (Direct Cost: ¥4,400,000)
Fiscal Year 1999: ¥2,400,000 (Direct Cost: ¥2,400,000)
Fiscal Year 1998: ¥2,000,000 (Direct Cost: ¥2,000,000)
Keywordsnumber theory / computer / algorithm / software / database / network / mailing list / TNT
Research Abstract

The objects of this study are to compute invariants on elementary number theory, algebraic number fields and elliptic curves computers using already known theorems and methods, then to gain realistic accumulation of data and to establish theoretical fundamentals in order to construct general-purpose system Tools on Number Theory, or TNT. The progress of this study for these two years spread, beyond the fields which was first planed mainly in number theory, widely to the study of computation by computers in general algebra including ring theory or algebraic geometry.
A significant feature of our study is practical use of the mailing list TNT-ML in addition to file transfer service. In the first year, we collected several data and programs computed and written up to present, and reinstalled the TNT-SERVER for distribution of the results through network. New TNT-SERVER combines three servers for mailing list, anonymous ftp and world wide web together. In the second year, we sorted and classified these data and softwares, designed a method to link them with each other, and we organized a symposium "The 3rd Conference on Algebra and Computation" in order to discuss about the basic design for the TNT-SYSTEM (pre-release).
Summarizing the computation and study above, we have almost finished fundamental preparation for a database on basic algorithms and tables on number theory. Moreover, we are ready to analyze necessary algorithms and important tables in this field, and have shown actual possibility to construct a general-purpose computer algebra system TNT-SYSTEM for software and database.

Report

(3 results)
  • 1999 Annual Research Report   Final Research Report Summary
  • 1998 Annual Research Report

Research Products

(55 results)

All Other

All Publications (55 results)

  • [Publications] Ken Nakamura, Attila Petho: "Squares in Binary Recurrence Sequences"Proceedings of Number Theory Conference, Eger 1996. 409-421 (1999)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1999 Final Research Report Summary
  • [Publications] Ken Nakamula: "Recent Developments of Computational Number Theory"Number theory and its application, Kyoto 1997. 176-184 (1998)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1999 Final Research Report Summary
  • [Publications] Ken Nakamula: "A Survey on the Number Field Sieve"Number Theory and its Application. 263-272 (1999)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1999 Final Research Report Summary
  • [Publications] K. Hashimoto, K. Miyake: "Inverse Galois Problem for Dihedral Groups"Number Theory and its Applications. 165-181 (1999)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1999 Final Research Report Summary
  • [Publications] N. Takao, H. Nakamura: "Galois rigidity of pro-l pure braid groups on algebraic curves"trans. Amer. Math. Soc.. 350. 1079-1102 (1998)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1999 Final Research Report Summary
  • [Publications] S. Garoufalidis, H. Nakamura: "Some IHX-type relations on trivalent graphs and symplectic representation theory"Math. Res. Letters. 5. 391-402 (1998)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1999 Final Research Report Summary
  • [Publications] A. Tamagawa, S. Mochizuki and H. Nakamura: "The Grothendieck conjecture on fundamental groups of algebraic curves"Sugaku. 50・2. 113-129 (1998)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1999 Final Research Report Summary
  • [Publications] L. Solomon, H. Terao: "The double Coxeter arrangements"Comment. Math. Helv.. 73. 237-258 (1998)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1999 Final Research Report Summary
  • [Publications] 寺尾宏明: "超平面配置と超幾何積分"代数幾何学シンポジウム(城崎)記録. 1-9 (1998)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1999 Final Research Report Summary
  • [Publications] T. Kawasaki: "On Macaulayfication of certain quasi-projective schemes"J. Math. Soc. Japan. 50. 969-991 (1998)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1999 Final Research Report Summary
  • [Publications] R. Okazaki, S. Louboutin: "The class number one problem for some non-abelian normal CM-fields of 2-power degrees"Proc. London Math. Soc.. 3(76). 523-548 (1998)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1999 Final Research Report Summary
  • [Publications] R. Okazaki: "On a Shintani decomposition for a cubic field defined by X^3+kX-1=0"in "Number Theory-Diophantine, computational and algebraic aspects". 445-451 (1998)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1999 Final Research Report Summary
  • [Publications] 足立恒雄、 三宅克哉: "類体論講義"日本評論社. (1998)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1999 Final Research Report Summary
  • [Publications] K. Miyake: "Class Field Theory-Its Gentenary and Prospect (to appear as a volume in The Advanced Studies in Pure Mathematics Series of Math. Soc. Japan)"Math. Soc. Japan.

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1999 Final Research Report Summary
  • [Publications] Ken Nakamula and Attila Petho: "Squares in Binary Recurrence Sequences"Proceedings of the Number Theory Conference. Eger 1996. 409-421 (1998)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1999 Final Research Report Summary
  • [Publications] Ken Nakamula: "Recent Developments of Computational Number Theory"Number Theory and its Application. Kyoto 19997. 176-184 (1998)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1999 Final Research Report Summary
  • [Publications] Ken Nakamula: "A Survey on the Number Field Sieve"Number Theory and its Application. 263-272 (1999)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1999 Final Research Report Summary
  • [Publications] K. Hashimoto and K. Miyake: "Inverse Galois Problem for Dihedral Groups"Number Theory and its Applications. 165-181 (1999)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1999 Final Research Report Summary
  • [Publications] N. Takao and H. Nakamura: "Galois rigidity of pro-l pure braid groups on algebraic curves"Trans. Amer. Math. Soc.. 350. 1079-1102 (1998)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1999 Final Research Report Summary
  • [Publications] S. Garoufalidis and H. Nakamura: "Some IHX-type relations on trivalent graphs and symplectic representation theory"Math. Res. Letters. 5. 391-402 (1998)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1999 Final Research Report Summary
  • [Publications] Adachi Norio and Miyake Katsuya: "Lecture on Class Field Theroy (in Japanese)"Nihon Hyoronsha. (1998)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1999 Final Research Report Summary
  • [Publications] K. Miyake: "Math. Soc. Japan, Class Field Theory-Its Centenary and Prospect"The Advanced Studies in Pure Mathematics Series of Math. Soc. Japan.

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1999 Final Research Report Summary
  • [Publications] A. Tamagawa, S. Mochizuki and H. Nakamura: "The Grothendieck conjecture on fundamental groups of algebraic curves"Sugaku. 50.2. 113-129 (1998)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1999 Final Research Report Summary
  • [Publications] L. Solomon and H. Terao: "The double Coxeter arrangements"Comment. Math. Helv.. 73. 237-258 (1998)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1999 Final Research Report Summary
  • [Publications] T. Kawasaki: "On Macaulayfication of certain quasi-projective schemes"J. Math. Soc. Japan. 50. 969-991 (1998)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1999 Final Research Report Summary
  • [Publications] R. Okazaki an dS. Louboutin: "The class number one problem for some non-abelian normal CM-fields of 2-power degrees"Proc. London Math. Soc.. 3(76). 523-548 (1998)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1999 Final Research Report Summary
  • [Publications] R. Okazaki: "On a Shintani decomposition for a cubic field defined by XィイD13ィエD1+kX-1=0"Number Theory - Diophantine, computational and algebraic aspects. 445-451 (1998)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1999 Final Research Report Summary
  • [Publications] Ken Nakamula, Attila Petho: "Squares in Binary Recurrence Sequences"Proceedings of the Number Theory Conference, Eger 1996. 409-421 (1998)

    • Related Report
      1999 Annual Research Report
  • [Publications] Ken Nakamula: "Recent Developements of Computational Number Theory"Number Theory and its application, Kyoto 1997. 176-184 (1998)

    • Related Report
      1999 Annual Research Report
  • [Publications] Ken Nakamula: "A Survery on the Number Field Sieve"Number Theory and its Application. 263-272 (1999)

    • Related Report
      1999 Annual Research Report
  • [Publications] K.Hashimoto, K.Miyake: "Inverse Galois Problem for Dihedral Groups"Number Theory and its Applications. 165-181 (1999)

    • Related Report
      1999 Annual Research Report
  • [Publications] N.Takao: "Galois rigidity of pro-1 pure braid groups on algebraic curves"Trans. Amer. Math. Soc.. 350. 1079-1102 (1998)

    • Related Report
      1999 Annual Research Report
  • [Publications] S.Garoufalidis, H.Nakamura: "Some IHX-type relations on trivalent graphs and symplectic representation theory"Math. Res. Letters. 5. 391-402 (1998)

    • Related Report
      1999 Annual Research Report
  • [Publications] A.Tamagawa, S.Mochizuki, and H.Nakamura: "The Grothendieck conjecture on fundamental groups of algebraic curves"Sugaku. 50・2. 113-129 (1998)

    • Related Report
      1999 Annual Research Report
  • [Publications] L.Solomon, H.Terao: "The double Coxeter arrangements"Comment. Math. Helv.. 73. 237-258 (1998)

    • Related Report
      1999 Annual Research Report
  • [Publications] 寺尾宏明: "超平面配置と超幾何積分"代数幾何学シンポジウム(城崎)記録. 1-9 (1998)

    • Related Report
      1999 Annual Research Report
  • [Publications] T.Kawasaki: "On Macaulayfication of certain quasi-projective schemes"J.Math. Soc. Japan. 50. 969-991 (1998)

    • Related Report
      1999 Annual Research Report
  • [Publications] R.Okazaki, S.Louboutin: "The class number one problem for some non-abelian normal CM-fields of 2-power degrees"Proc. London Math. Soc.. 3(76). 523-548 (1998)

    • Related Report
      1999 Annual Research Report
  • [Publications] R.Okazaki: "On a Shintani decomposition for a cubic field defined by X^3+κX-1=0"in "Number Theory―Diophantine, computational and algebraic aspects". 445-451 (1998)

    • Related Report
      1999 Annual Research Report
  • [Publications] 足立恒雄,三宅克哉: "類体論講義"日本評論社. (1998)

    • Related Report
      1999 Annual Research Report
  • [Publications] K.Miyake: "Class Field Theory-Its Centenary and Prospect (to appear as a volume in The Advanced Studies in Pure Mathematics Series of Math. Soc. Japan)"Math. Soc. Japan.

    • Related Report
      1999 Annual Research Report
  • [Publications] Ken Nakamula Attila Petho: "Squares in Binary Recurrence Sequences" Proceedings of the Number Theory Conference, Eger 1996. 409-421 (1998)

    • Related Report
      1998 Annual Research Report
  • [Publications] Ken Nakamula: "Recent Developements of Computational Number Theory" Number Theory and its application, Kyoto 1997. 176-184 (1998)

    • Related Report
      1998 Annual Research Report
  • [Publications] Ken Nakamula: "A Survey on the Number Field Sieve" Number Theory and its Application. (1999)

    • Related Report
      1998 Annual Research Report
  • [Publications] L.Solomon H.Terao: "The double Coxeter arrangements" Comment.Math.Helv.73. 237-258 (1998)

    • Related Report
      1998 Annual Research Report
  • [Publications] 寺尾宏明: "超平面配置と超幾何積分" 代数幾何学シンポジウム(城崎)記録. 1-9 (1998)

    • Related Report
      1998 Annual Research Report
  • [Publications] K.Hashimoto K.Miyake: "Inverse Galois Problem for Dihedral Groups" to be appear in Number Theory and its Applications. (1998)

    • Related Report
      1998 Annual Research Report
  • [Publications] N.Takao, H.Nakamura: "Galois rigidity of pro-l pure braid groups on algebraic curves" Trans.Amer.Math.Soc.350. 1079-1102 (1998)

    • Related Report
      1998 Annual Research Report
  • [Publications] S.Garoufalidis, H.Nakamura: "Some IHX-type relations on trivalent graphs and symplectic representation theory" Math.Res.Letters. 5. 391-402 (1998)

    • Related Report
      1998 Annual Research Report
  • [Publications] A.Tamagawa, S.Mochizuki and H.Nakamura: "The Grothendieck conjecture on fundamental groups of algebraic curves" Sugaku. 50・2. 113-129 (1998)

    • Related Report
      1998 Annual Research Report
  • [Publications] T.Kawasaki: "On Macaulayfication of certain quasi-projective schemes" J.Math.Soc.Japan. 50. 969-991 (1998)

    • Related Report
      1998 Annual Research Report
  • [Publications] R.Okazaki, S.Louboutin: "The class unmber one problem for some non-abelian normal CM-fields of 2-power degrees" Proc.London Math.Soc.3(76). 523-548 (1998)

    • Related Report
      1998 Annual Research Report
  • [Publications] R.Okazaki: "On a Shintani decomposition for a cubic field defined by X^3+kX-1=0" in "Number Theory-Diophantine, computational and algebraic aspects". 445-451 (1998)

    • Related Report
      1998 Annual Research Report
  • [Publications] 足立恒雄 三宅克哉: "類体論講義" 日本評論社, (1998)

    • Related Report
      1998 Annual Research Report
  • [Publications] K.Miyake: "Class Field Theory-Its Centenary and Prospect (to appear as a volume in The Advanced Studies in Pure Mathematics Series of Math.Soc.Japan)" Math.Soc.Japan,

    • Related Report
      1998 Annual Research Report

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Published: 1998-03-31   Modified: 2019-02-28  

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