Computer Algebra

Course guarantor:

Lecturer:

Tutor:

Supervisor:

Department of Laser Physics and Photonics

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:

Further information:

No time-table has been prepared for this course

The course is a part of the following study plans:

• Fyzikální inženýrství - Počítačová fyzika (PS)
• Matematické inženýrství - Matematická informatika (elective course)
• Physical Engineering - Computational physics (PS)