Abstract
Denote by A n = A n (F) = F[X 1,…, X n , D 1,…, D n ] the Weyl algebra over a field F([2]) determined by the relations X i X j = X j X i , D i D j = D j D i , X i D i = D i X i − 1, X i D j = D j X i for i ≠ j, and by the algebra of differential operators.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Artin E., “Geometric algebra,” Interscience publishers, 1957.
Björk J.-E., “Rings of differential operators,” North-Holland, 1979.
Chistov A.L., Grigor’ev D.Yu., Subexponential-time solving systems of algebraic equations, Preprints LOMI E-9-83, E-10-83. Leningrad, 1983.
Fitchas N., Galligo A., Nullstellensatz effectif et Conjecture de Serre (Théorème de Quillen-Suslin) pour le Calcul Formel, Séminaire “Structures algébriques ordonnées”, Paris VII, 1988 (to appear in Mathematische Nachrichten).
Galligo A., Some algorithmical questions on ideals of differential operators., in “ Lect. Notes Comput. Sci.,” 204, 1985, pp. 413–421.
Grigor’ev D. Yu., Computational complexity in polynomial algebra, in “Proc. Intern. Congr. Mathem.,” Berkeley, 1986, pp. 1452–1460.
Grigor’ev D. Yu., Complexity of factoring and GCD calculating of linear ordinary differential operators, J. Symbol. Comput. (to appear).
Seidenberg A., Constructions in algebra, Trans. Amer. Math. Soc. 197 (1974), 273–313.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1991 Springer Science+Business Media New York
About this chapter
Cite this chapter
Grigor’ev, D.Y. (1991). Complexity of Solving Systems of Linear Equations over the Rings of Differential Operators. In: Mora, T., Traverso, C. (eds) Effective Methods in Algebraic Geometry. Progress in Mathematics, vol 94. Birkhäuser, Boston, MA. https://doi.org/10.1007/978-1-4612-0441-1_12
Download citation
DOI: https://doi.org/10.1007/978-1-4612-0441-1_12
Publisher Name: Birkhäuser, Boston, MA
Print ISBN: 978-1-4612-6761-4
Online ISBN: 978-1-4612-0441-1
eBook Packages: Springer Book Archive