Computer algebra

Lecturer:

Richard Liska (gar.)

Tutor:

Richard Liska (gar.)

Supervisor:

Department of Physical Electronics

Synopsis:

Lisp, representation of basic objects (integers, rational and algebraic numbers, polynomials, rational functions, radicals, algebraic functions), arithmetics, simplification, greatest common divisor, resultant, derivation, series summation, integration, ordinary differential equations, factorization, equations solving,

quantifier elimination, substitution and pattern matching, algebraic programming, graphics, Maple - detailed introduction and solving of practical examples, applications, overview of other systems (Axiom, Macsyma, Mathematica), miniproject.

Requirements:

Syllabus of lectures:

1. Basic characteristics of computer algebra.

2. Algebraic structures and their representation.

3. Aritmetics and simplification.

4. Greatest common divisor, resultant.

5. Summation, integration.

6. Factorization, quantifier elimination.

7. Integrated computational systems.

Syllabus of tutorials:

1. Maple, basics.

2. Maple, data structures and simplification.

3. Maple, calculus and substitutions.

4. Maple, programming.

5. Maple, simple exercises.

6. Maple, more complicated exercises.

7. Miniproject.

Study Objective:

Knowledge:

Knowledge of computer algebra algorithms.

Skills:

Ability to use system Maple for symbolic computation.

Study materials:

Key references:

[1] R. Liska etal. Computer Algebra, Algorithms, Systems and Applications.

http://www-troja.fjfi.cvut.cz/~liska/ca

Recommended references:

[2] K.O. Geddes, S.R. Czapor and G. Labahn: Algorithms For Computer Algebra. Kluwer Academic Publishers, Boston, 1992.

[3] F. Wright: Computing with Maple, Chapman and Hall/CRC, Boca Raton, 2002.

Study aids:

Computer classroom Unix with integrated mathematical system Maple.

Note:

Time-table for winter semester 2011/2012:

Time-table is not available yet

Time-table for summer semester 2011/2012:

Time-table is not available yet

The course is a part of the following study plans: