2004 Fiscal Year Final Research Report Summary
Development of high performance computer algebra software
| Project/Area Number |
14340036
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| Research Category |
Grant-in-Aid for Scientific Research (B)
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| Allocation Type | Single-year Grants |
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| Section | 一般 |
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| Research Field |
General mathematics (including Probability theory/Statistical mathematics)
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| Research Institution | KOBE UNIVERSITY |
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Principal Investigator |
NORO Masayuki Kobe University, Faculty of Science, Professor, 理学部, 教授 (50332755)
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| Co-Investigator(Kenkyū-buntansha) |
TAKAYAMA Nobuki Kobe University, Faculty of Science, Professor, 理学部, 教授 (30188099)
YOKOYAMA Kazuhiro Kyushu University, Graduate School of Mathematics, Professor, 理学部, 教授 (30333454)
村尾 裕一 電気通信大学, 電気通信学部, 講師 (60174265)
OHARA Katsuyoshi Kanazawa University, Faculty of Science, Research Associate, 理学部, 助手 (00313635)
SAITO Masahiko Kobe University, Faculty of Science, Professor, 理学部, 教授 (80183044)
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| Project Period (FY) |
2002 – 2004
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| Keywords | Computer algebra / Groebner Basis / Algebraic analysis / Hypergeometric function / polynomial factorization / Ideal decomposition / Polynomial system solving / Vertex operator algebra |
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| Research Abstract |
We developed the following new algorithms and implemented them in Risa/Asir :
(1)a polynomial-time bivariate polynomial factorization algorithm over small finite fields,
(2)an algorithm for computing minimal prime divisors of a polynomial ideal over small finite fields,
(3)an algorithm for computing the global b-function,
(4)an efficient algorithm for numerical computation of multivariate hypergeometric functions,
(5)a method for deriving quadratic relations for generalized hypergeometric functions,
(6)a tangent cone algorithm in the ring of differential operators over power series ring.
We implemented the following new facilities in Risa/Asir :
(1)a new package for computing Groebner basis with a new data representation,
(2)a new package for efficient computation in algebraic number fields.
We gave the following applications.
(1)We exactly solved a polynomial system concerned with quantum computing.
(2)We proved that W_3 algebra of central charge 6/5 is realized as a subalgebra of a lattice vertex operator algebra and classify its irreducible modules.
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