Testing the logarithmic comparison theorem for free divisors.
The asymptotic spectrum of tensors.
The construction of orthonormal wavelets using symbolic methods and a matrix analytical approach for wavelets on the interval.
The hyperrings of order 3.
The multiplicity problem for indecomposable decompositions of modules over domestic canonical algebras
Given a module M over a domestic canonical algebra Λ and a classifying set X for the indecomposable Λ-modules, the problem of determining the vector such that is studied. A precise formula for , for any postprojective indecomposable module X, is computed in Theorem 2.3, and interrelations between various structures on the set of all postprojective roots are described in Theorem 2.4. It is proved in Theorem 2.2 that a general method of finding vectors m(M) presented by the authors in Colloq....
The multiplicity problem for indecomposable decompositions of modules over a finite-dimensional algebra. Algorithms and a computer algebra approach
Given a module M over an algebra Λ and a complete set of pairwise nonisomorphic indecomposable Λ-modules, the problem of determining the vector such that is studied. A general method of finding the vectors m(M) is presented (Corollary 2.1, Theorem 2.2 and Corollary 2.3). It is discussed and applied in practice for two classes of algebras: string algebras of finite representation type and hereditary algebras of type . In the second case detailed algorithms are given (Algorithms 4.5 and 5.5).
The optimal lower bound for generators of invariant rings without finite SAGBI bases with respect to any admissible order.
The summation package Sigma: underlying principles and a rhombus tiling application.
The sum-product algorithm: algebraic independence and computational aspects
The sum-product algorithm is a well-known procedure for marginalizing an “acyclic” product function whose range is the ground set of a commutative semiring. The algorithm is general enough to include as special cases several classical algorithms developed in information theory and probability theory. We present four results. First, using the sum-product algorithm we show that the variable sets involved in an acyclic factorization satisfy a relation that is a natural generalization of probability-theoretic...
The tensor product of polynomials.
The use of Schubert polynomials in SYMCHAR.
Towards the automated synthesis of a Gröbner bases algorithm.
We discuss the question of whether the central result of algorithmic Gröbner bases theory, namely the notion of S?polynomials together with the algorithm for constructing Gröbner bases using S?polynomials, can be obtained by ?artificial intelligence?, i.e. a systematic (algorithmic) algorithm synthesis method. We present the ?lazy thinking? method for theorem and algorithm invention and apply it to the ?critical pair / completion? algorithm scheme. We present a road map that demonstrates that, with...
Treating the exceptional cases of the MeatAxe.