Intersection number

Discrete mathematics

Vector space

Aerospace engineering

Differential algebraic equation

Pure mathematics

Mathematics

Intersection (aeronautics)

Algorithm

Algebra over a field

Algebraic number field

Engineering

Mathematical analysis

Geometry

Computation

Algebraic geometry

Intersection theory

Differential equation

Point (geometry)

Field (mathematics)

Ordinary differential equation

Scalar (mathematics)

Algebraic number

Journal of Mathematical Physics

Intersection numbers of twisted cocycles arise in mathematics in the field of algebraic geometry. Quite recently, they appeared in physics: Intersection numbers of twisted cocycles define a scalar product on the vector space of Feynman integrals. With this application, the practical and efficient computation of intersection numbers of twisted cocycles becomes a topic of interest. An existing algorithm for the computation of intersection numbers of twisted cocycles requires in intermediate steps the introduction of algebraic extensions (for example, square roots) although the final result may be expressed without algebraic extensions. In this article, I present an improvement of this algorithm, which avoids algebraic extensions.

On the computation of intersection numbers for twisted cocycles