• Publications
  • Influence
Risa/Asir—a computer algebra system
Risa’s subroutine libraries include basic arithmetic subroutines, parser, evaluator and storage manager, and each of them can be used individually. Expand
Holonomic Gradient Descent and its Application to Fisher-Bingham Integral
We give a new algorithm to find local maximum and minimum of a holonomic function and apply it for the Fisher-Bingham integral on the sphere $S^n$, which is used in the directional statistics. TheExpand
A Computer Algebra System
Risa/Asir consists of the Risa engine for performing operations on mathematical objects and an interpreter for programs written in the Asir user language. In Risa/Asir, polynomials are represented inExpand
Solutions of Systems of Algebraic Equations and Linear Maps on Residue Class Rings
It is found that many ideal-theoretical arguments for the problem can be translated into their counterparts in the theory of linear maps and this translation succeeds in giving a new description for the U-resultant and forms of solutions of systems straightforwardly. Expand
A Computer Algebra System: Risa/Asir
  • M. Noro
  • Computer Science
  • Algebra, Geometry, and Software Systems
  • 2003
This paper explains an overview of Risa/Asir, its functions and implemented algorithms with their performances, the OpenXM API and the way to add built-in functions. Expand
Efficient Implementation of Schoof's Algorithm
By realizing efficient combination of several improvements, such as Atkin-Elkies's method, the isogeny cycles method, and trial search by match-and-sort techniques, the number of rational points on an elliptic curve over GF(p) in a reasonable time is counted. Expand
Computation of the splitting fields and the Galois groups of polynomials
This study is a continuation of Yokoyama et al. [22], which improved the method by Landau and Miller [11] for the determination of solvability of a polynomial over the integers. In both methods, theExpand
Stratification associated with local b-functions
A new method for computing such a stratification and a primary ideal decomposition of an ideal in C[x,s] is needed and the primary decomposition can be a bottleneck for computing the stratification. Expand
Modular Algorithms for Computing Minimal Associated Primes and Radicals of Polynomial Ideals
This paper applies Chinese Remainder Theorem (CRT) to Laplagne's algorithm which computes minimal associated primes without producing redundant components and computes radicals, and proposes algorithms for computing minimal associatedPrimes of ideals in polynomial rings over Q and computing radicals of ideals over a field. Expand