Introduction to Computer Algebra

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Room change: Lectures on thursdays now take place at S 110.

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wednesdays 01.15 - 02.45 pm Hs 19
thursdays 09.15 - 10.45 am S 110

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The lecture gives an introduction to basic concepts of computer algebra. In more detail, we will discuss the following topics:
  1. Integer and polynomial arithmetics, fast multiplication, gcd computations, complexity of algorithms, modular techniques
  2. Resultants and extended gcd computations.
  3. Multivariate polynomials, Gröbner bases for ideals and modules, modular methods, Faugère's F4 and F5 algorithm, syzygies, free resolutions.
  4. (Squarefree) Factorization, Hensel lifting, factorization with LLL, primality tests, factorization over algebraic number fields.
Moreover, the lecture will also try to teach you how to use open source computer algebra systems like Singular, Nemo, OSCAR, etc. and how to write your own small algorithms for specific problems.

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Overview julia file jupyter notebook file
Inverse kinematic problem singular file
Introduction to julia julia file jupyter notebook file
Sieve of Eratosthenes julia file
Composite tests julia file
Resultant julia file
Gröbner bases -- Buchberger's algorithm julia file

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The following list is not sorted, but includes books covering some topics of the lecture:
  1. Cohen: A Course in Computational Algebraic Number Theory
  2. Cox, Little, O'Shea: Ideals, Varieties, and Algorithms
  3. von zur Gathen: Modern Computer Algebra
  4. Greuel, Pfister: A SINGULAR introduction to Commutative Algebra
This list might be updated during the course of the lecture.

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Just drop by at my office or write an email to ederc at mathematik dot uni-kl dot de.

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