Some algorithmic questions on ideals of differential operators

  • André Galligo
Algebraic Algorithms V
Part of the Lecture Notes in Computer Science book series (LNCS, volume 204)


Differential Operator Standard Basis Left Ideal Polynomial Ideal Hilbert Function 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. [BA]
    D.A.Bayer, Ph.D., Harvard University, 1982Google Scholar
  2. [BA-St 1]
    D.A.Bayer & M.Stillman,On the complexity of computing syzygies, Preprint (1984)Google Scholar
  3. [Ba-St 2]
    —, A criterion for detecting m-regularity, Preprint (1984)Google Scholar
  4. [Be 1]
    I.N. Bernstein,The analytic continuation of generalised functions w.r.t. a parameter, in Funct. Anal. Akademia Nauk CCP 6(4) (1972), pp.26–40Google Scholar
  5. [BJ 1]
    I.E.Bjork,Rings of differential operators, North Holland Mathematical library (1979)Google Scholar
  6. [BJ 2]
    —, Differential systems on algebraic manifolds, preprint U. of Stockholm (1984)Google Scholar
  7. [Bu 3]
    —, Gröbner bases: an algorithm method in polynomial ideal theory, preprint, Univ. of Linz (1983), to appearGoogle Scholar
  8. [Br-Ga]
    J.Briançon & A.Galligo, Detormations de points de IR2ou C, in Astérisque no7 et 8 (1973)Google Scholar
  9. [Br-Ma]
    J.Briançon & Ph.Maisonobe,Idéaux d'opérateurs différentiels à 1 variable, in Enseignement Mathématique (1984) T.23Google Scholar
  10. [BU 1]
    B.Buchberger,A criterion for detecting unnecessary reductions in the construction of Gröbner bases, Proc. Eurosam 79, Lecture Notes in C.S. 72 (1979)Google Scholar
  11. [BU 2]
    —, Note on the complexity of constructing Gröbner-Bases, in Proc. Eurocal 83, Lecture Notes in C.S. (1983)Google Scholar
  12. [CA]
    F.Castro, Thèse de 3o cycle, Paris VII, oct.1984Google Scholar
  13. [DA-Gal 1]
    J.Damon & A.Galligo,A topological invariant for stable map germs, Invent. Math. 32 (1976)Google Scholar
  14. [DA-Gal 2]
    —, On the Hilbert-Samuel partition of stable map germs, Bull. Soc. Math. France 111 (1983)Google Scholar
  15. [Gae]
    M.Gaetano,Ceyx a good tool for computer algebra constructions in these proceedingsGoogle Scholar
  16. [Gae-Gal]
    M.Gaetano & A.Galligo,Presentation du projet BASTA, Preprint (1984) U. de NiceGoogle Scholar
  17. [Gal 1]
    A.Galligo,A propos du théorème de préparation de Weierstrass, in Springer Lecture Notes in Mathematics no409 (1974)Google Scholar
  18. [Gal 2]
    —, Théorème de préparation et stabilité en géométrie analytique in Ann. Inst. Fourier, T.29, 2 (1979Google Scholar
  19. [Gal 3]
    —, Algorithmes de construction de bases standard, preprint U. de Nice (1983)Google Scholar
  20. [Gi]
    M.Giusti,Some effectivity problems in polynomial ideal theory, in Eurosam 84, Lect. Notes in C.S., 174 (1984)Google Scholar
  21. [Hi]
    H.Hironaka,Resolution of singularities, local theory, informal talks ∼1970Google Scholar
  22. [Ka]
    M.Kashiwara,B-functors and holonomic systems, Invent. Math. 38 (1976)Google Scholar
  23. [La 1]
    D.Lazard,Gröbner bases, Gaussian elimination and resolution of systems of algebraic equations, in Eurocal 83, Lect. Notes in C.S. 162, (1983)Google Scholar
  24. [La 2]
    —, Ideal basis and primary decomposition: case of 2 variables, preprint Paris VI (1984)Google Scholar
  25. [Le-Me]
    Lê D.T. & Z.Mebkhout,Introduction to linear differential systems, in A.M.S. Proceedings 40, (1983)Google Scholar
  26. [Lu 1]
    Colloque "Analyse et Topologie" Luminy 1981, Astérisque no100 (1983)Google Scholar
  27. [Lu 2]
    Colloque "Systèmes Différentiels et Singularités Luminy 1983, in Astérisque (1985), to appearGoogle Scholar
  28. [Ma]
    B.Malgrange, Sur les polynômes de Bernstein, in Uspelaki Mat. Nauk 29 (4) (1974)Google Scholar
  29. [Ma-Ma]
    E.Mayr & A.Meyer, The complexity of the word problem for commutative, semigroups and polynomial ideals, in Adv. in Math, 46, (1982)Google Scholar
  30. [Mu-Mo]
    Muller & Mora, New constructive methods in classical ideal theory preprint (1983)Google Scholar
  31. [Ph]
    F.Pham, Singularités des systèmes de Gauss-Manin, Progress in Math. 2, Progresso in Math.2, Birkhauser (1979)Google Scholar
  32. [S.K.K.]
    M.Sato, M.Kashiwara, T.Kawai, Hyperfunctions and pseudo-differential operators, in Lect.Notes in Math., vol.287, Springer (1973)Google Scholar
  33. [Stf]
    J.T.Stafford, Module structure of Weyl algebras, in J.London Math.Soc. 18, (1978)Google Scholar
  34. [Stn]
    R.P.Stanley, Hilbert functions of graded algebras, in Adv. in Math.28, (1978)Google Scholar
  35. [Wi]
    F.Winkler, On the complexity of the Gröbner bases algorithm over K[x,y,z] in Eurosam'84, Lect.Notes in C.S., no174 (1984)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1985

Authors and Affiliations

  • André Galligo
    • 1
  1. 1.Département de MathématiquesFaculté des SciencesNice Cedex

Personalised recommendations