Improved Kolchin–Ritt Algorithm
作者： G. Carra'Ferro , V. P. Gerdt
关键词: Set (abstract data type) 、 Computation 、 Ramer–Douglas–Peucker algorithm 、 Discrete mathematics 、 Wu's method of characteristic set 、 Mathematics 、 Differential (mathematics) 、 Algorithm 、 Reduction (complexity) 、 Rank (linear algebra) 、 Algebra 、 Algebraic number
摘要: An algorithm for computation of an extended characteristic sets finitely generated differential ideals is suggested. This improves the well-known Kolchin–Ritt algorithm. The improvement achieved through computing algebraic Grobner bases on intermediate stages process. rank set obtained less than or equal to that by Examples demonstrating reduction are presented.
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sci-hub.se 参考文章(10)
Giuseppa Carra' Ferro, Gröbner bases and differential algebra Applied Algebra, Algebraic Algorithms and Error-Correcting Codes. pp. 129- 140 ,(1989) , 10.1007/3-540-51082-6_73
François Ollivier, Standard Bases of Differential Ideals Applicable Algebra in Engineering, Communication and Computing. pp. 304- 321 ,(1990) , 10.1007/3-540-54195-0_60
Ellis Kolchin, Differential Algebra and Algebraic Groups ,(2012)
ELIZABETH L. MANSFIELD, PETER A. CLARKSON, Applications of the differential algebra package diffgrob2 to classical symmetries of differential equations Journal of Symbolic Computation. ,vol. 23, pp. 517- 533 ,(1997) , 10.1006/JSCO.1996.0105
F. Boulier, D. Lazard, F. Ollivier, M. Petitot, Representation for the radical of a finitely generated differential ideal Proceedings of the 1995 international symposium on Symbolic and algebraic computation - ISSAC '95. pp. 158- 166 ,(1995) , 10.1145/220346.220367
François Boulier, Daniel Lazard, François Ollivier, Michel Petitot, Computing representations for radicals of finitely generated differential ideals Applicable Algebra in Engineering, Communication and Computing. ,vol. 20, pp. 73- 121 ,(2009) , 10.1007/S00200-009-0091-7
B. Buchberger, Greobner Bases : an algorithmic method in polynomial ideal theory Multidimensional Systems Theory. pp. 184- 232 ,(1985)
Azriel Rosenfeld, Specializations in differential algebra Transactions of the American Mathematical Society. ,vol. 90, pp. 394- 407 ,(1959) , 10.1090/S0002-9947-1959-0107642-2
Evelyne Hubert, Factorization-free decomposition algorithms in differential algebra Journal of Symbolic Computation. ,vol. 29, pp. 641- 662 ,(2000) , 10.1006/JSCO.1999.0344
Donald Ervin Knuth, The Art of Computer Programming ,(1968)