Mathematical Interests
The research group Computational Mathematics is interested in algorithmic and experimental aspects of pure mathematics, in particular in algebra and number theory. Another topic is the implementation of mathematical methods in computer algebra systems.

Software development
(Wolfram Koepf,
Torsten Sprenger)
 Maple packages for power series and algorithmic summation: FPS / hsum / qsum
 SpecialFunctions: Mathematica package for the work with special functions.

Orthogonal Polynomials and Special Functions
(Wolfram Koepf,
Mama Foupouagnigni)
 Representations of classical orthogonal polynomials.
 Properties of hypergeometric functions.
 Formal power series.
 Algorithmic summation (Hypergeometric Summation).

Computer Algebra
(Peter Horn,
Wolfram Koepf,
Werner Seiler,
Torsten Sprenger)
 Algorithms for factorization.
 Ore algebras.
 Gröbner bases, involutive bases.
 Computer algebra in mathematics education.
 Constructive commutative Algebra.

Number Theory
(HansGeorg Rück,
Werner Bley)
 Constructive number theory.
 Function Fields and Drinfeld modules.
 Elliptic curves.
 Lseries, in particular equivariant Tamagawa number conjectures.
 Generalized Stark conjectures.

Coding Theory and Cryptography
(HansGeorg Rück)
 Block codes and finite geometry.
 Convolutional codes.
 Elliptic and hyperelliptic curves.
 Algebraic geometric codes.

Differential equations
(Werner Seiler)
 Completion.
 Geometric theory.
 Symmetry theory.
 Singularities.