differential dimension
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A Bound for a Typical Differential Dimension of Systems of Linear Differential Equations

Journal of Mathematical Sciences ◽

10.1007/s10958-021-05647-1 ◽

2021 ◽

Author(s):

M. V. Kondratieva

Keyword(s):

Differential Equations ◽

Linear Differential Equations ◽

Differential Dimension ◽

Linear Differential

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Some properties of multivariate differential dimension polynomials and their invariants

Proceedings of the 45th International Symposium on Symbolic and Algebraic Computation ◽

10.1145/3373207.3404013 ◽

2020 ◽

Author(s):

Alexander Levin

Keyword(s):

Differential Dimension

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Multivariate Difference–Differential Dimension Polynomials

Mathematics in Computer Science ◽

10.1007/s11786-019-00436-1 ◽

2020 ◽

Vol 14 (2) ◽

pp. 361-374

Author(s):

Alexander Levin

Keyword(s):

Differential Dimension

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Estimates for the coefficients of differential dimension polynomials

Mathematics of Computation ◽

10.1090/mcom/3429 ◽

2019 ◽

Vol 88 (320) ◽

pp. 2959-2985 ◽

Author(s):

Omar León Sánchez

Keyword(s):

Differential Dimension

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The Differential Dimension Polynomial for Characterizable Differential Ideals

Algorithmic and Experimental Methods in Algebra, Geometry, and Number Theory ◽

10.1007/978-3-319-70566-8_18 ◽

2017 ◽

pp. 443-453 ◽

Author(s):

Markus Lange-Hegermann

Keyword(s):

Differential Dimension ◽

Differential Dimension Polynomial ◽

Dimension Polynomial

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Termination of algorithm for computing relative Gröbner bases and difference differential dimension polynomials

Frontiers of Mathematics in China ◽

10.1007/s11464-015-0439-1 ◽

2015 ◽

Vol 10 (3) ◽

pp. 635-648 ◽

Author(s):

Guanli Huang ◽

Meng Zhou

Keyword(s):

Gröbner Bases ◽

Grobner Bases ◽

Differential Dimension

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Multivariate difference-differential dimension polynomials and new invariants of difference-differential field extensions

Proceedings of the 38th international symposium on International symposium on symbolic and algebraic computation - ISSAC '13 ◽

10.1145/2465506.2465521 ◽

2013 ◽

Author(s):

Alexander B. Levin

Keyword(s):

Field Extensions ◽

Differential Field ◽

Differential Dimension

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Computing difference-differential dimension polynomials by relative Gröbner bases in difference-differential modules

Journal of Symbolic Computation ◽

10.1016/j.jsc.2008.02.001 ◽

2008 ◽

Vol 43 (10) ◽

pp. 726-745 ◽

Author(s):

Meng Zhou ◽

Franz Winkler

Keyword(s):

Gröbner Bases ◽

Grobner Bases ◽

Differential Dimension ◽

Differential Modules

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Gröbner bases in difference-differential modules and difference-differential dimension polynomials

Science in China Series A Mathematics ◽

10.1007/s11425-008-0081-4 ◽

2008 ◽

Vol 51 (9) ◽

pp. 1732-1752 ◽

Author(s):

Meng Zhou ◽

Winkler Franz

Keyword(s):

Gröbner Bases ◽

Grobner Bases ◽

Differential Dimension ◽

Differential Modules

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Multivariable dimension polynomials and new invariants of differential field extensions

International Journal of Mathematics and Mathematical Sciences ◽

10.1155/s0161171201006767 ◽

2001 ◽

Vol 27 (4) ◽

pp. 201-214 ◽

Author(s):

Alexander B. Levin

Keyword(s):

Field Extension ◽

Differential Polynomials ◽

Finitely Generated ◽

Field Extensions ◽

Differential Field ◽

Differential Dimension ◽

Characteristic Sets ◽

Differential Dimension Polynomial ◽

Dimension Polynomial

We introduce a special type of reduction in the ring of differential polynomials and develop the appropriate technique of characteristic sets that allows to generalize the classical Kolchin's theorem on differential dimension polynomial and find new differential birational invariants of a finitely generated differential field extension.

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