77 citations · 337 across the 28 of their papers we have counts for
9 papers · 1 filter
A SageMath Package for Elementary and Sign Vectors with Applications to Chemical Reaction Networks
Marcus S. Aichmayr, Stefan Müller, Georg Regensburger
We present our SageMath package elementary_vectors for computing elementary and sign vectors of real subspaces. In this setting, elementary vectors are support-minimal vectors that…
How to automatise proofs of operator statements: Moore-Penrose inverse -- a case study
Klara Bernauer, Clemens Hofstadler, Georg Regensburger
We describe a recently developed algebraic framework for proving first-order statements about linear operators by computations with noncommutative polynomials. Furthermore, we pres…
Computing elements of certain form in ideals to prove properties of operators
Clemens Hofstadler, Clemens G. Raab, Georg Regensburger
Proving statements about linear operators expressed in terms of identities often leads to finding elements of certain form in noncommutative polynomial ideals. We illustrate this b…
Compatible rewriting of noncommutative polynomials for proving operator identities
Cyrille Chenavier, Clemens Hofstadler, Clemens G. Raab +1
The goal of this paper is to prove operator identities using equalities between noncommutative polynomials. In general, a polynomial expression is not valid in terms of operators,…
Symbolic Derivation of Mean-Field PDEs from Lattice-Based Models
Christoph Koutschan, Helene Ranetbauer, Georg Regensburger +1
Transportation processes, which play a prominent role in the life and social sciences, are typically described by discrete models on lattices. For studying their dynamics a continu…
Planar Linkages Following a Prescribed Motion
Matteo Gallet, Christoph Koutschan, Zijia Li +3
Designing mechanical devices, called linkages, that draw a given plane curve has been a topic that interested engineers and mathematicians for hundreds of years, and recently also…
Composing and Factoring Generalized Green's Operators and Ordinary Boundary Problems
Anja Korporal, Georg Regensburger
We consider solution operators of linear ordinary boundary problems with "too many" boundary conditions, which are not always solvable. These generalized Green's operators are a ce…
Regular and Singular Boundary Problems in Maple
Anja Korporal, Georg Regensburger, Markus Rosenkranz
We describe a new Maple package for treating boundary problems for linear ordinary differential equations, allowing two-/multipoint as well as Stieltjes boundary conditions. For ex…
Symbolic Analysis for Boundary Problems: From Rewriting to Parametrized Gröbner Bases
Markus Rosenkranz, Georg Regensburger, Loredana Tec +1
We review our algebraic framework for linear boundary problems (concentrating on ordinary differential equations). Its starting point is an appropriate algebraization of the domain…