Computing diagonal form and Jacobson normal form of a matrix using Gröbner bases
نویسندگان
چکیده
منابع مشابه
Computing diagonal form and Jacobson normal form of a matrix using Gröbner bases
In this paper we present two algorithms for the computation of a diagonal form of a matrix over non-commutative Euclidean domain over a field with the help of Gröbner bases. This can be viewed as the preprocessing for the computation of Jacobson normal form and also used for the computation of Smith normal form in the commutative case. We propose a general framework for handling, among other, o...
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In this paper we describe how an idea centered on the concept of self-saturation allows several improvements in the computation of Gröbner bases via Buchberger’s Algorithm. In a nutshell, the idea is to extend the advantages of computing with homogeneous polynomials or vectors to the general case. When the input data are not homogeneous, we use a technique described in Section 2: the main tool ...
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In this note we will discuss the structure theorem for finitely generated modules over a principal ideal domain from the point of view of matrices. We will then give a matrixtheoretic proof of the structure theorem from the point of view of the Smith normal form of a matrix over a principal ideal domain. One benefit from this method is that there are algorithms for finding the Smith normal form...
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In this note we will discuss the structure theorem for finitely generated modules over a principal ideal domain from the point of view of matrices. We will then give a matrixtheoretic proof of the structure theorem from the point of view of the Smith normal form of a matrix over a principal ideal domain. One benefit from this method is that there are algorithms for finding the Smith normal form...
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ژورنال
عنوان ژورنال: Journal of Symbolic Computation
سال: 2011
ISSN: 0747-7171
DOI: 10.1016/j.jsc.2010.10.009