Algorithmische Aspekte zur Theorie der Gröbner-Basen
Algorithms for permutability in finite groups
In this paper we describe some algorithms to identify permutable and Sylow-permutable subgroups of finite groups, Dedekind and Iwasawa finite groups, and finite T-groups (groups in which normality is transitive), PT-groups (groups in which permutability is transitive), and PST-groups (groups in which Sylow permutability is transitive). These algorithms have been implemented in a package for the computer algebra system GAP.
Almost curvature continuous fitting of B-spline surfaces.
An algorithm for calculation of (+, *) - expressions with natural numbers
An algorithm to calculate the kernel of certain polynomial ring homomorphisms.
An implementation of Karr's summation algorithm in Mathematica.
An implementation of the Neumann-Praeger algorithm for the recognition of special linear groups.
An integral geometry problem along geodesics and a computational approach.
An upper bound on the number of monomials in determinants of sparse matrices with symbolic entries.
Apéry's double sum is plain sailing indeed.
Application of symbolic computation in nonlinear differential-difference equations.
Arrow's Impossibility Theorem
A formalization of the first proof from [6].
Automated proofs for some Stirling number identities.
Automatic differentiation and its program realization
Automatic differentiation is an effective method for evaluating derivatives of function, which is defined by a formula or a program. Program for evaluating of value of function is by automatic differentiation modified to program, which also evaluates values of derivatives. Computed values are exact up to computer precision and their evaluation is very quick. In this article, we describe a program realization of automatic differentiation. This implementation is prepared in the system UFO, but its...
Automatic differentiation platform : design
Automatic differentiation (AD) has proven its interest in many fields of applied mathematics, but it is still not widely used. Furthermore, existing numerical methods have been developed under the hypotheses that computing program derivatives is not affordable for real size problems. Exact derivatives have therefore been avoided, or replaced by approximations computed by divided differences. The hypotheses is no longer true due to the maturity of AD added to the quick evolution of machine capacity....
Automatic Differentiation Platform: Design
Automatic differentiation (AD) has proven its interest in many fields of applied mathematics, but it is still not widely used. Furthermore, existing numerical methods have been developed under the hypotheses that computing program derivatives is not affordable for real size problems. Exact derivatives have therefore been avoided, or replaced by approximations computed by divided differences. The hypotheses is no longer true due to the maturity of AD added to the quick evolution of machine capacity....
Axiomatisation des manipulations symboliques en calcul des prédicats
Beispiele zur Anwendung eines Computeralgebrasystems in der Geometrie.
BERGMAN under MS-DOS and Anick's resolution.
Binomial residues
A binomial residue is a rational function defined by a hypergeometric integral whose kernel is singular along binomial divisors. Binomial residues provide an integral representation for rational solutions of -hypergeometric systems of Lawrence type. The space of binomial residues of a given degree, modulo those which are polynomial in some variable, has dimension equal to the Euler characteristic of the matroid associated with .