Module Handbook

  • Dynamischer Default-Fachbereich geändert auf MAT

Course MAT-41-11-K-7

Computer Algebra (4V+2U, 9.0 LP)

Course Type

SWS Type Course Form CP (Effort) Presence-Time / Self-Study
- K Lecture with exercise classes (V/U) 9.0 CP 186 h
4 V Lecture 56 h
2 U Exercise class (in small groups) 28 h
(4V+2U) 9.0 CP 84 h 186 h

Basedata

SWS 4V+2U
CP, Effort 9.0 CP = 270 h
Position of the semester 1 Sem. irreg. SuSe
Level [7] Master (Advanced)
Language [EN] English
Lecturers
+ further Lecturers of the department Mathematics
Area of study [MAT-AGCA] Algebra, Geometry and Computer Algebra
Additional informations
Livecycle-State [NORM] Active

Contents

  • normal forms and standard bases of ideals and modules,
  • syzygies, free resolutions and the proof of the Buchberger criterion,
  • computation of normalization of Noetherian rings,
  • computation of primary decomposition of ideals,
  • Hilbert function,
  • Ext and Tor.

Literature

  • G.-M. Greuel, G. Pfister: A SINGULAR Introduction to Commutative Algebra,
  • W. Decker, C. Lossen: Computing in Algebraic Geometry - A Quick Start using Singular,
  • W. Decker, F.-O. Schreyer: Varieties, Gröbner bases, and algebraic curves,
  • W. Decker, G. Pfister: A First Course in Computational Algebraic Geometry,
  • D. Cox, J. Little, D. O'Shea: Ideals, Varieties, and Algorithms.

Materials

Further literature will be announced in the lecture; Exercise material is provided.

Registration

Registration for the exercise classes via the online administration system URM (https://urm.mathematik.uni-kl.de)

References to Course [MAT-41-11-K-7]

Module Name Context
[MAT-41-11-M-7] Computer Algebra P: Obligatory 4V+2U, 9.0 LP