A computer algebra system risa/asir consists of a command asir for interactive use and several subroutine libraries which can be used as the parts of other programs. The grammar of the user languageâ€¦ (More)

Polynomial factorization plays a significant role in computational mathematics and its application to engineering, since it forms a fundamental part of algorithms for higher algebraic computations.â€¦ (More)

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 inâ€¦ (More)

In this paper, we present new mathematical results and several new algorithms for solving a system of algebraic equations algebraically . We find that many ideal-theoretical arguments for the problemâ€¦ (More)

The gradient descent is a general method to find a local minimum of a smooth function f(z1, . . . , zd). The method utilizes the observation that f(p) decreases if one goes from a point z = p to aâ€¦ (More)

In this paper we propose an efficient modular method for Dynamic Evaluation (DE) [2][3][5]. For efficient computation over algebraic number fields, we have to design algorithms very carefully. Forâ€¦ (More)