We give an introduction to the OSCAR Computer Algebra System (see https://oscar.computeralgebra.de) for computations in algebra, geometry, and number theory.
It is important that results published in papers are understandable and verifiable by other mathematicians. Even if they read them a hundred years from now. If a paper is highly dependent on a software component this may often be difficult. The software could be out of date, very difficult to install or contain bugs that were never checked for. Computed results might not be available anymore...
Given a first order autonomous algebraic ordinary differential equation, i.e. an equation of the form
F(y, y')=0 with F ∈ K[y, y'],
where K is an computable field such as the rational numbers, we present a method to compute all formal Puiseux series solutions. In fact, all of the solutions are convergent Puiseux series.
By considering y and y' as independent variables, F implicitly defines...
Wir zeigen die wichtigsten Neuerungen in Maple 2022 aus dem Bereich symbolische Mathematik, darüber hinaus einiges aus den Themen Numerik, Programmierung und Performance, Benutzeroberfläche und Grafik sowie Connectivity.
In group theory, we have a certain type of groups, i.e. algebraic groups. Thanks to an additional underlying structure, we have certain rules for the action of the groups on themselves and their associated Lie algebras.
We are interested in solving several problems concerning algebraic groups (for example linked to representation theory) in small characteristic. These complex problems often...
We present a novel, practical method to determine the Frattini subgroup of a polycyclic group. This method is based on new theoretical investigations about complements and module strucure of elementary abelian sections in polycyclic groups. We have implemented our method in GAP and include a discussion of this implementation.
Homomorphisms of modules are fundamental objects in algebra and applied mathematics. Recent developments in symbolic computation allow a formal verification and exploration of identities between homomorphisms. Systems of those identities define varieties similar as in classical algebraic geometry. For constant-free systems one has a Galois connection to free algebras, and morphisms of...
Conditional independence is a ternary relation from probability theory between subcollections of jointly distributed random variables. Among normally distributed (i.e., "Gaussian") variables, these relations are characterized by the vanishing of specific subdeterminants of the distribution's positive definite covariance matrix.
The combinatorial structures realizable as conditional...
In this talk we shed light on varieties of moments arising from graphical models. A directed graph corresponds to a statistical model where the nodes represent random variables and arrows encode relations between them. The polynomial relations between entries of the covariance matrices have been previously studied from an algebraic and combinatorial point of view. Dropping Gaussianity makes...
