[ 201COMACALV18 ] VL Computer Algebra

(*) Unfortunately this information is not available in english.
Workload Education level Study areas Responsible person Hours per week Coordinating university
3 ECTS B3 - Bachelor's programme 3. year Mathematics Carsten Schneider 2 hpw Johannes Kepler University Linz
Detailed information
Original study plan Bachelor's programme Technical Mathematics 2022W
Objectives In the last decades big parts of mathematics has been algorithmized and many mathematical problems (or problems coming from natural and technical sciences that can be modeled in mathematics) can be solved with the computer. A major contribution for this algorithmic revolution is the computer algebra. This lecture aims at introducing the most crucial algorithms in this field and illustrating how they can be used for non-trivial applications.
Subject We discuss constructive symbolic methods for simplification of expressions and solving algebraic (i.e., polynomial) systems of equations. Among others, the following algorithms are explored:

  • basic structures and algorithms
  • the extended Euclidean algorithm, polynomial remainder sequences and applications
  • modular methods based on Hensel lifting and the Chinese Reemainder Theorem (resultants, gcd, factorization)
  • a gentle introduction to Gröbner bases
  • symbolic summation and integration
Criteria for evaluation Depending on the needs of the participants there will be a written or oral exam.
Methods The different algorithms will be presented on the blackboard. Concrete examples will be carried out with the computer.
Language English
Study material Joachim von zur Gathen and Jürgen Gerhard, "Modern Computer Algebra", Cambridge University Press, 2013 (or earlier versions).
Changing subject? No
Corresponding lecture (*)ist gemeinsam mit 201ALGECALU12 bzw. 201COMACALU18: UE Computer Algebra (1,5 ECTS)
äquivalent zu

TM1WHKVCASY: KV Computeralgebra (4,5 ECTS)
On-site course
Maximum number of participants -
Assignment procedure Direct assignment