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Bivariate Kolchin-type dimension polynomials of non-reflexive prime difference-differential ideals. The case of one translation. (English) Zbl 1456.12004

See the combined review about four papers by Alexander Levin (one coauthored with Alexander Egrafov) in Zbl 1456.12002.
I: A. Levin, Math. Comput. Sci. 13, No. 1–2, 157–168 (2019);
II: A. Levin, J. Symb. Comput. 102, 173–188 (2021);
III: A. Levin, Math. Comput. Sci. 14, No. 2, 361–374 (2020; Zbl 1456.12001);
IV: A. Evgrafov and A. Levin, Math. Comput. Sci. 14, No. 2, 347–360 (2020; Zbl 1456.12003).

MSC:

12H05 Differential algebra
12H10 Difference algebra
68W30 Symbolic computation and algebraic computation
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References:

[1] Cohn, R., Difference Algebra, Interscience Tracts in Pure and Appl. Math., vol. 17 (1965) · Zbl 0127.26402
[2] Cohn, R., A difference-differential basis theorem, Can. J. Math., 22, 6, 1224-1237 (1970) · Zbl 0206.05104
[3] Einstein, A., The Meaning of Relativity. Appendix II (Generalization of Gravitation Theory), 133-165 (1953), Princeton · Zbl 0050.21208
[4] Hrushovski, E., The elementary theory of the Frobenius automorphisms (2012), 2004, pp. 1-135. The updated version (2012):
[5] Johnson, J., A notion on Krull dimension for differential rings, Comment. Math. Helv., 44, 207-216 (1969) · Zbl 0179.34401
[6] Kolchin, E. R., The notion of dimension in the theory of algebraic differential equations, Bull. Am. Math. Soc., 70, 570-573 (1964) · Zbl 0144.03702
[7] Kolchin, E. R., Differential Algebra and Algebraic Groups (1973), Academic Press: Academic Press New York · Zbl 0264.12102
[8] Kondrateva, M. V.; Levin, A. B.; Mikhalev, A. V.; Pankratev, E. V., Differential and Difference Dimension Polynomials (1999), Kluwer Academic Publishers: Kluwer Academic Publishers Dordrecht, The Netherlands · Zbl 0930.12005
[9] Levin, A. B., Characteristic polynomials of filtered difference modules and of difference field extensions, Russ. Math. Surv., 33, 1, 165-166 (1978) · Zbl 0465.12011
[10] Levin, A. B., Characteristic polynomials of inversive difference modules and some properties of inversive difference dimension, Russ. Math. Surv., 35, 1, 217-218 (1980) · Zbl 0459.12017
[11] Levin, A. B., Reduced Gröbner bases, free difference-differential modules and difference-differential dimension polynomials, J. Symb. Comput., 30, 4, 357-382 (2000) · Zbl 0994.13009
[12] Levin, A. B., Difference Algebra (2008), Springer: Springer Dordrecht, The Netherlands · Zbl 1209.12003
[13] Levin, A. B., Multivariate difference-differential polynomials and new invariants of difference-differential field extensions, (Proceedings of the 38th International Symposium on Symbolic and Algebraic Computation (2013)), 267-274 · Zbl 1360.12006
[14] Levin, A. B., On the ascending chain condition for mixed difference ideals, Int. Math. Res. Not., 2015, 10, 2830-2840 (2015) · Zbl 1380.12008
[15] Levin, A. B., Bivariate dimension polynomials of non-reflexive prime difference-differential ideals. The case of one translation, (Proceedings of the 38th International Symposium on Symbolic and Algebraic Computation (2018)), 255-262 · Zbl 1464.12009
[16] Levin, A. B.; Mikhalev, A. V., Type and dimension of finitely generated G-algebras, Contemp. Math., 184, 275-280 (1995) · Zbl 0840.13004
[17] Ritt, J. F., Differential Equations from the Algebraic Standpoint, Amer. Math. Soc. Colloquium Publ., vol. 14 (1932) · JFM 58.0445.06
[18] Wang, J., Finite basis for radical well-mixed difference ideals generated by binomials, Commun. Algebra, 46, 6, 2589-2599 (2018) · Zbl 1409.12002
[19] Wibmer, M., Algebraic Difference Equations. Lecture Notes (2013), University of Pennsylvania, or
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