By Ilias Kotsireas, Eugene Zima

Книга laptop Algebra 2006: most recent Advances in Symbolic Algorithms machine Algebra 2006: most modern Advances in Symbolic AlgorithmsКниги English литература Автор: Ilias Kotsireas, Eugene Zima Год издания: 2007 Формат: pdf Издат.:World clinical Publishing corporation Страниц: 211 Размер: 1,5 ISBN: 9812702008 Язык: Английский0 (голосов: zero) Оценка:Computer Algebra 2006: newest Advances in Symbolic Algorithms: court cases of the Waterloo Workshop in machine Algebra 2006, Ontario, Canada, 10-12 April 2006By Ilias Kotsireas, Eugene Zima

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11. I. Gohberg, P. Lancaster, and L. Rodman. Matrix polynomials. Academic Press, New York; London; Paris, 1982. 12. D. Grigoriev. Complexity of Irreducibility Testing for a System of Linear Ordinary Diﬀerential Equations. In Proceedings of ISSAC’90. ACM Press, 1990. 13. N. Jacobson. Pseudo-linear transformations. Annals of Mathematics, 38(2):484–507, 1937. 14. N. Jacobson. Basic Algebra II. W. H. Freeman and Company, San Fransisco, 1980. 15. M. Singer. Direct and Inverse Problems in Diﬀerential Galois Theory, pages 527–554.

The eigenring of the matrix pseudo-linear equation [A] is deﬁned as the set of n × n matrices T in K satisfying δT = T A − Aφ(T ). We shall denote by E(A) the eigenring of [A]. It is a C−algebra which has ﬁnite dimension, as vector space over C (cf. Sec. 2). Algorithms for computing eigenrings of a diﬀerential (diﬀerence) systems over C(x) have been presented in Refs. 8 and 6. Our interest in eigenrings arises from the fact we shall establish later that with their aid we can factor matrix pseudo-linear equations.

Rational solutions of linear diﬀerence equations. In Proceedings of ISSAC’98, pages 120–123. ACM Press, 1998. ca GEORGE LABAHN David R. ca We give a modular algorithm to perform row reduction of a matrix of Ore polynomials with coeﬃcients in Z[t]. Both the transformation matrix and the transformed matrix are computed. The algorithm can be used for ﬁnding the rank and left nullspace of such matrices. In the special case of shift polynomials, we obtain algorithms for computing a weak Popov form and for computing a greatest common right divisor (GCRD) and a least common left multiple (LCLM) of matrices of shift polynomials.