Development of high performance computer algebra software

高性能计算机代数软件的开发

• 批准号: 14340036
• 负责人: NORO Masayuki
• 金额: $ 5.57万
• 依托单位: KOBE UNIVERSITY
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for Scientific Research (B)
• 财政年份: 2002
• 资助国家: 日本
• 起止时间: 2002 至 2004
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/en/grant/KAKENHI-PROJECT-14340036/
• 关键词: Computer algebra; Groebner Basis; Algebraic analysis; Hypergeometric function; polynomial factorization; Ideal decomposition; Polynomial system solving; Vertex operator algebra; b関数; 多項式因数分解; グレブナー基底; 多項式イデアル; 準素分解; 極小素因子; 最少多項式

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.

我们在Risa/Asir中实现了以下新算法：（1）小有限域上的多项式时间二元多项式因式分解算法，（2）小有限域上多项式理想的最小素因子的计算算法，（3）全局b函数的计算算法，（4）多元超几何函数数值计算的有效算法，（5）广义超几何函数二次关系的推导方法，（6）幂级数环上微分算子环的切锥算法。（1）用新的数据表示计算Groebner基的新程序包，（2）代数数域上有效计算的新程序包. (1)We精确地解决了一个与量子计算有关的多项式系统。(2)We证明了中心荷为6/5的W_3代数可实现为格顶点算子代数的一个子代数，并对其不可约模进行了分类.

项目成果

K.Ohara: "Quadratic Relations for Generalized Hypergeometric Functions _pF_<p-1>"Funkcialaj Ekvacioj. 46. 213-251 (2003)

K.Ohara：“广义超几何函数的二次关系 _pF_<p-1>”Funkcialaj Ekvacioj。

Yet Another Practical Implementation of Polynomial Factorization over Finite Fields

有限域上多项式因式分解的另一种实际实现

• 发表时间: 2002
• 期刊: Proceedings of ISSAC2002
• 作者: M.Noro;K.Yokoyama
• 通讯作者: K.Yokoyama

M.Noro: "Implementation of prime decomposition of polynomial ideals over small finite fields"Journal of Symbolic Computation. (印刷中). (2004)

M.Noro：“小有限域上多项式理想素数分解的实现”符号计算杂志（出版中）。

M.Noro: "A Computer Algebra System : Risa/Asir"Algebra, Geometry and Software, M.Joswig and N.Takayama (eds.), Springer. 147-162 (2002)

M.Noro：“计算机代数系统：Risa/Asir”代数、几何和软件，M.Joswig 和 N.Takayama（编辑），Springer。

K.Yokoyama: "Prime Decomposition of Polynomial Ideals over Finite Fields"Proc. ICMS2002, World Scientific. 217-227 (2002)

K.Yokoyama：“有限域上多项式理想的素数分解”Proc。