InformaApp - Publikationen

Finite fields play an important role for many applications (e.g. coding theory, cryptography). There are different ways to construct a finite field for a given prime power. The paper describes the different constructions implemented in AXIOM. These are polynomial basis representation, cyclic group representation, and normal basis representation. Furthermore, the concept of the implementation, the used algorithms and the various datatype coercions between these representations are discussed.

Angewandte Wirtschaftswissenschaften

Buch (Monographie)

U. Krieger, Johannes Grabmeier, K. Huber

Das Computeralgebrasystem AXIOM bei kryptologischen und verkehrstheoretischen Untersuchungen des Forschungsinstituts der Deutschen Bundespost TELEKOM

1991

Angewandte Wirtschaftswissenschaften

Zeitschriftenartikel

M. Clausen, M. Karpinski, Johannes Grabmeier, A. Dress

On zero-testing and interpolation of k-sparse multivariate polynomials over finite fields

Theoretical Computer Science, vol. 84, no. 2, pp. 151-164

1991

DOI: 10.1016/0304-3975(91)90157-W

Angewandte Wirtschaftswissenschaften

Zeitschriftenartikel

Johannes Grabmeier, A. Dress

The Interpolation Problem for k-sparse Polynomials and Character Sums

Advances in Applied Mathematics, vol. 12, no. 1, pp. 57-75

1991

Abstract anzeigen

Motivated by a remarkable result of D. Y. Grigoriev and M. Karpinski, the interpolation problem for k-sparse multivariate polynomials has received some attention in recent years. In this note we want to show that essentially all of the results obtained so far hold more generally for k-sparse sums of characters of abelian monoids, thereby providing a useful unified approach to this active field of research. As it turns out, there are basically two different situations, in the first one reduction to the (rather trivial) case of cyclic monoids is possible, in the general case we can handle direct products of abelian monoids by using informations about the factors. Basic ingredients of these approaches are the construction of distinction sets for characters and zero-test sets for k-sparse character sums.

Angewandte Wirtschaftswissenschaften

Zeitschriftenartikel

Johannes Grabmeier, H. Gollan

Algorithms in Representation Theory and their Realization in the Computer Algebra

Bayreuther Mathematische Schriften, no. 33, pp. 1-23

1990

Angewandte Wirtschaftswissenschaften

Buch (Monographie)

Johannes Grabmeier, G. Dueck, G. Jaeschke

VLSI Complexity of Basic Arithmetic Operations

1988

Angewandte Wirtschaftswissenschaften

Zeitschriftenartikel

Johannes Grabmeier

On the socle of Weyl modules

Archiv der Mathematik, vol. 50, no. 4, pp. 319-322

1988

Angewandte Wirtschaftswissenschaften

Zeitschriftenartikel

Johannes Grabmeier, A. Kerber

The evaluation of irreducible polynomial representations of the general linerar groups and of the unitary groups over fields of characteristic 0

Acta Applicandae Mathematicae, no. 8, pp. 271-291

1987

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We describe an efficient method for the computer evaluation of the ordinary irreducible polynomial representations of general linear groups using an integral form of the ordinary irreducible representations of symmetric groups. In order to do this, we first give an algebraic explanation of D. E. Littlewood's modification of I. Schur's construction. Then we derive a formula for the entries of the representing matrices which is much more concise and adapted to the effective use of computer calculations. Finally, we describe how one obtains — using this time an orthogonal form of the ordinary irreducible representations of symmetric groups — a version which yields a unitary representation when it is restricted to the unitary subgroup. In this way we adapt D. B. Hunter's results which heavily rely on Littlewood's methods, and boson polynomials come into the play so that we also meet the needs of applications to physics.

Angewandte Wirtschaftswissenschaften

Zeitschriftenartikel

Johannes Grabmeier

Kombinatorische Probleme aus der Darstellungstheorie der GLm(k)

Publications de l'I.R.M.A., Seminaire Lotharingien de Combinatoire, no. 314/S-12, pp. 131-136

1986

Angewandte Wirtschaftswissenschaften

Zeitschriftenartikel

Johannes Grabmeier

Unzerlegbare Moduln mit trivialer Youngquelle und Darstellungstheorie der Schuralgebra

Bayreuther Mathematische Schriften, no. 20, pp. 9-152

1985