Viktor Levandovskyy WS0708
Seminar CA

Seminar on Computational Algebra

Prof. Dr. Eva Zerz
Dr. Viktor Levandovskyy

Time and Place: Thursday, 17-15 - 18-30, Room 203 of the Lehrstuhl D
Plan and Schedule:
8.11 (A very personal view on) Non-commutative Gröbner bases for Weyl, shift and their homogenized algebras. Viktor Levandovskyy
15.11 Introduction to SINGULAR . Using and programming. Viktor Levandovskyy (more SINGULAR examples in the files ex-live.tst, ex-primdec.tst, ex-latex.tst, ex-surf.tst; example on writing simple procedures write-proc.tst).
22.11 Annihilator of a Power of a Polynomial (Ann(f^A) (where f is a polynomial and A a complex number) in general and the Oaku-Takayama algorithm. Univariate and multivariate situations.) Viktor Levandovskyy (examples, used in slides: ex1.tst, ex2.tst).
29.11 Brianson-Maisonobe algorithm and the theory behind. Univariate and multivariate situations. Florian Eisele
6.12 Localization. Markus Lange-Hegermann. Notes.
11.12 (A) The algorithm of Noro. Daniel Andres. (B) LOT algorithm (multivariate situation) and examples session. Viktor Levandovskyy
18.12 Restriction and integration modules. Mohamed Barakat
27.12 (:-) All and everything Father Christmas
10.01.08 de Rham cohomology for the complement of affine variety . Arne Lorenz
11.01.08 Enhancing the classical algorithm by Oaku for the computation of Bernstein-Sato polynomial. Jorge Morales
17.01.08 Weyl closure. Thomas Bächler
24.01.08 Ext^i_D(M,N) for holonomic modules M,N. Polynomial, rational and holonomic solutions to holonomic systems. Kristina Schindelar and Moritz Schröer
31.01.08 Submission of results to the Nobel Prize Committee.
07.02.08 Computer Algebra methods for holonomic functions. Christoph Koutschan (RISC Linz)


[T99] H.Tsai Weyl Closure of a Linear Differential Operator (1999)
[OT99] T. Oaku, N. Takayama An algorithm for de Rham cohomology groups of the complement of an affine variety via D-module computation (1999)
[W00] U. Walther Algorithmic Computation of de Rham Cohomology of Complements of Complex Affine Varieties (2000)
[OTW00] T. Oaku, N. Takayama, U. Walther A Localization Algorithm for D-modules (2000)
[OT01] T. Oaku, N. Takayama Algorithms for D-modules: restriction, tensor product, localization, and local cohomology groups (2001)
[TW01] H. Tsai, U. Walther Computing Homomorphisms Between Holonomic D-modules (2001)
[OTT01] T. Oaku, N. Takayama, H. Tsai  Polynomial and rational solutions of holonomic systems (2001)
[OST03] T. Oaku, Y. Shiraki, N. Takayama, Algebraic algorithms for D-modules and numerical analysis. (2003)
Books and Theses
[SST] B. Sturmfels, M. Saito, N. Takayama. "Gröbner Deformations of Hypergeometric Differential Equations" (Springer, 2000)
[GPS] G.-M. Greuel, G. Pfister "A SINGULAR Introduction to Commutative Algebra" (Springer, 2002; 2nd edition 2007)
[VL05] (Thesis) V. Levandovskyy, "Non-commutative Computer Algebra for polynomial algebras: Gröbner bases, applications and implementation" (2005)
[T00] (Thesis) H. Tsai, "Algorithms for Algebraic Analysis" (2000)
[S] SINGULAR:, see dmod.lib in PLURAL Libraries
[M2] Macaulay2:
[M2D] D-modules for Macaulay2:
[OXM] OpenXM (includes kan/sm1 and Risa/Asir):
RWTH Aachen University Division of Mathematics Lehrstuhl D für Mathematik