Sparse difference resultant

Journal of Symbolic Computation - Tập 68 - Trang 169-203 - 2015
Wei Li1, Chun-Ming Yuan1, Xiao-Shan Gao1
1KLMM, Academy of Mathematics and Systems Science, The Chinese Academy of Sciences, Beijing 100190, China

Tài liệu tham khảo

Bernshtein, 1975, The number of roots of a system of equations, Funct. Anal. Appl., 9, 183, 10.1007/BF01075595 Bouziane, 2001, Unmixed-dimensional decomposition of a finitely generated perfect differential ideal, J. Symb. Comput., 31, 631, 10.1006/jsco.1999.1562 Canny, 1990, Generalized characteristic polynomials, J. Symb. Comput., 9, 241, 10.1016/S0747-7171(08)80012-0 Cohen, 1993 Cohn, 1948, Manifolds of difference polynomials, Trans. Am. Math. Soc., 64, 10.1090/S0002-9947-1948-0025438-X Cohn, 1952, Extensions of difference fields, Am. J. Math., 74, 507, 10.2307/2372012 Cohn, 1965 Cohn, 1983, Order and dimension, Proc. Am. Math. Soc., 87, 1, 10.1090/S0002-9939-1983-0677218-6 Cox, 1998 D'Andrea, 2002, Macaulay style formulas for sparse resultants, Trans. Am. Math. Soc., 354, 2595, 10.1090/S0002-9947-02-02910-0 Eisenbud, 1995 Eisenbud, 2004, Resultants and chow forms via exterior syzygies, J. Am. Math. Soc., 16, 537, 10.1090/S0894-0347-03-00423-5 Emiris, 1996, On the complexity of sparse elimination, J. Complex., 12, 134, 10.1006/jcom.1996.0010 Emiris, 1995, Efficient incremental algorithms for the sparse resultant and the mixed volume, J. Symb. Comput., 20, 117, 10.1006/jsco.1995.1041 Emiris, 1999, Matrices in elimination theory, J. Symb. Comput., 28, 3, 10.1006/jsco.1998.0266 Emiris, 2005, Improved algorithms for computing determinants and resultants, J. Complex., 21, 43, 10.1016/j.jco.2004.03.003 Gao, 1993, On the dimension for arbitrary ascending chains, Chin. Sci. Bull., 38, 396 Gao, 2013, Intersection theory in differential algebraic geometry: generic intersections and the differential Chow form, Trans. Am. Math. Soc., 365, 4575, 10.1090/S0002-9947-2013-05633-4 Gao, 2009, A characteristic set method for ordinary difference polynomial systems, J. Symb. Comput., 44, 242, 10.1016/j.jsc.2007.05.005 Gelfand, 1994 Heintz, 1983, Definability and fast quantifier elimination in algebraically closed fields, Theor. Comput. Sci., 24, 239, 10.1016/0304-3975(83)90002-6 Hodge, 1968 Hoffman, 1971 Hrushovski Jouanolou, 1991, Le formalisme du rèsultant, Adv. Math., 90, 117, 10.1016/0001-8708(91)90031-2 Kapranov, 1992, Chow polytopes and general resultants, Duke Math. J., 67, 189, 10.1215/S0012-7094-92-06707-X Kolchin, 1974, Differential equations in a projective space and linear dependence over a projective variety, 195 Lando, 1970, Jacobi's bound for the order of systems of first order differential equations, Trans. Am. Math. Soc., 152, 119 Levin, 2008 Li, 2011, Sparse differential resultant, 225 Li, 2012, Differential Chow form for projective differential variety, J. Algebra, 370, 344, 10.1016/j.jalgebra.2012.07.047 Li Li, 2013, Sparse difference resultant Pedersen, 1993, Product formulas for resultants and Chow forms, Math. Z., 214, 377, 10.1007/BF02572411 Rueda, 2013, Linear sparse differential resultant formulas, Linear Algebra Appl., 438, 4296, 10.1016/j.laa.2013.01.016 Rueda, 2010, Linear complete differential resultants and the implicitization of linear DPPEs, J. Symb. Comput., 45, 324, 10.1016/j.jsc.2009.09.003 Shen, 2011, Proper reparametrization for inherently improper unirational varieties, J. Syst. Sci. Complex., 24, 367, 10.1007/s11424-010-7221-y Sturmfels, 1993, Sparse elimination theory, 264 Sturmfels, 1994, On the Newton polytope of the resultant, J. Algebr. Comb., 3, 207, 10.1023/A:1022497624378 Vogel, 1984 Wibmer, 2013 Wu, 2003 Zhang