101 citations · 629 across the 59 of their papers we have counts for
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Advanced Computer Algebra for Determinants
Christoph Koutschan, Thotsaporn "Aek" Thanatipanonda
We prove three conjectures concerning the evaluation of determinants, which are related to the counting of plane partitions and rhombus tilings. One of them was posed by George And…
Third order integrability conditions for homogeneous potentials of degree -1
Thierry Combot, Christoph Koutschan
We prove an integrability criterion of order 3 for a homogeneous potential of degree -1 in the plane. Still, this criterion depends on some integer and it is impossible to apply it…
On Kahan's Rules for Determining Branch Cuts
Frédéric Chyzak, James Davenport, Christoph Koutschan +1
In computer algebra there are different ways of approaching the mathematical concept of functions, one of which is by defining them as solutions of differential equations. We compa…
On Two-generated Non-commutative Algebras Subject to the Affine Relation
Christoph Koutschan, Viktor Levandovskyy, Oleksandr Motsak
We consider algebras over a field K, generated by two variables x and y subject to the single relation yx = qxy + ax + by + c for q in K^* and a, b, c in K. We prove, that among su…
Lattice Green's Functions of the Higher-Dimensional Face-Centered Cubic Lattices
Christoph Koutschan
We study the face-centered cubic lattice (fcc) in up to six dimensions. In particular, we are concerned with lattice Green's functions (LGF) and return probabilities. Computer alge…
Computer Algebra meets Finite Elements: an Efficient Implementation for Maxwell's Equations
Christoph Koutschan, Christoph Lehrenfeld, Joachim Schoeberl
We consider the numerical discretization of the time-domain Maxwell's equations with an energy-conserving discontinuous Galerkin finite element formulation. This particular formula…