Christian Eder: Introduction to Computer Algebra

  • Lecturer: Christian Eder
  • Date and Room:
    • Wednesday 13:15 - 14:45, Leipzig University, Hörsaalgebäude, room HS-19
    • Thursday 9:15 - 10:45, Leipzig University, Seminargebäude, room SG 3-20
  • Language: English
  • Target audience: MSc students, PhD students, Postdocs
  • Keywords: Arithmetics, Systems of (non-)linear equations, lattices, resultants, Gröbner bases, factorization
  • Prerequisites: Basic knowledge about algebra and the usage of computer algebra systems
  • Remarks: Literature and up to date infos

Abstract

The lecture gives an introduction to basic concepts of Computer algebra. In more detail, we will discuss the following topics:

  • Integer and polynomial arithmetics, fast multiplication, gcd computations, complexity of algorithms.
  • Systems of equations, Hermite- and Smith-normal form, p-adic approximation, lattices, LLL algorithm.
  • Resultants and extended gcd computations.
  • Multivariate polynomials, Gröbner bases for ideals and modules, modular methods, Faugère's F4 and F5 algorithm, syzygies, free resolutions.
  • (Squarefree) Factorization, Hensel lifting, factorization with LLL, primality tests, factorization over algebraic number fields.

Regular Lectures (Summer 2019)

07.05.2019, 09:16