Masayuki Noro

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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 language of asir is a variant of that of C and asir has a built-in dbx-like debugger. Risa’s subroutine libraries include basic arithmetic subroutines, parser, evaluator(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. Multivariate polynomial factorization over finite fields is very important for computations of mathematical object over positive characteristic fields, which(More)
To give an efficiently computable representation of the zeros of a zero-dimensional ideal I, Rouillier (1996) introduced the rational univariate representation (RUR) as an extension of the generalized shape lemma (GSL) proposed by Alonso et al. (1996). In this paper, we propose a new method to compute the RUR of the radical of I, and report on its practical(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 problem can be translated into their counterparts in the theory of linear maps . And by this translation, we succeed in giving a new description for the Uresultant and(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 a “nice” direction, which is usually −(∇f)(p). As textbooks on optimizations present (see, e.g., [5], [16]), we have a lot of achievements on this method and its(More)