In algebraic geometry, one studies the solutions to polynomial equations, or, equivalently, to
linear partial differential equations with constant coefficients. These lecture notes address …

We showcase applications of nonlinear algebra in the sciences and engineering. Our review
is organized into eight themes: polynomial optimization, partial differential equations …

We develop algebraic tools for statistical inference from samples of rotation matrices. This
rests on the theory of D-modules in algebraic analysis. Noncommutative Gröbner bases are …

The authors prove that for arbitrarily given b∈(0,∞), r∈(0, 1) and n∈ N 0, and for λ∈ R, the
functions a↦ F (a, b; a+ b; r) a λ and a↦ F (a, b; a+ b; r)-∑ k= 0 n (a, k)(b, k)(a+ b, k) k! rka λ …

These are the lecture notes of the graduate level course “D-Modules and Holonomic
Functions” taught by the author in the fall term 2023 at KTH and Stockholm University, and …

Theses are the lecture notes of the graduate level course “D-Modules and Holonomic
Functions” at KTH and Stockholm University taught by the author in the fall term 2023. The …

The Weyl algebra D= C [x1,..., xn]〈∂ 1,...,∂ n〉 is the free algebra over C generated by
x1,..., xn,∂ 1,...,∂ n, modulo the following relations. All generators commute except of xi …

▶ 1F1 related to distribution of largest eigenvalue of Wishart matrices▶ stated in Muirhead's
book [8]▶ holonomic gradient method in [4]▶ 0F1 related to the Fisher distribution▶ …