Related papers: A Reduction Algorithm for Hilbert Modular Groups

Hilbert order is widely applied in many areas. However, most of the algorithms are confined to low dimensional cases. In this paper, algorithms for encoding and decoding arbitrary dimensional Hilbert order are presented. Eight algorithms…

This is a survey article on moduli of affine schemes equipped with an action of a reductive group. The emphasis is on examples and applications to the classification of spherical varieties.

We show how to efficiently compute Hilbert modular forms as orthogonal modular forms, generalizing and expanding upon the method of Birch.

These course notes are about computing modular forms and some of their arithmetic properties. Their aim is to explain and prove the modular symbols algorithm in as elementary and as explicit terms as possible, and to enable the devoted…

In this paper, we present a modular strategy which describes key properties of the absolute primary decomposition of an equidimensional polynomial ideal defined by polynomials with rational coefficients. The algorithm we design is based on…

The problem of reducing a Hidden Markov Model (HMM) to one of smaller dimension that exactly reproduces the same marginals is tackled by using a system-theoretic approach. Realization theory tools are extended to HMMs by leveraging suitable…

This article is the first in a series devoted to computing the class groups of real quadratic fields. We present a new relation between the class number and the index of unit groups. This relation generalizes Hilbert class field theory for…

Group theory is a particularly fertile field for the design of practical algorithms. Algorithms have been developed across the various branches of the subject and they find wide application. Because of its relative maturity, computational…

In this presentation we shall deal with some aspects of the theory of Hilbert functions of modules over local rings, and we intend to guide the reader along one of the possible routes through the last three decades of progress in this area…

We describe algorithms for computing geometric invariants for Hilbert modular surfaces, and we report on their implementation.

This note presents the Hilbert series technique to a wider audience in the context of constructing group-invariant Lagrangians. This technique provides a fast way to calculate the number of operators of a specified mass dimension for a…

In this paper we give an algorithm to determine all finite matrix groups over a number field. Our algorithm is based on the representation theory of finite groups.

We propose a new quantifier elimination algorithm for the theory of linear real arithmetic. This algorithm uses as subroutine satisfiability modulo this theory, a problem for which there are several implementations available. The quantifier…

Many complex engineering systems consist of multiple subsystems that are developed by different teams of engineers. To analyse, simulate and control such complex systems, accurate yet computationally efficient models are required. Modular…

In this paper, we examine the general algorithm for class group computations, when we do not have a small defining polynomial for the number field. Based on a result of Biasse and Fieker, we simplify their algorithm, improve the complexity…

An algorithm for irreducible decomposition of representations of finite groups over fields of characteristic zero is described. The algorithm uses the fact that the decomposition induces a partition of the invariant inner product into a…

The reduction algorithm is used to compute reduced ideals of a number field. However, there are reduced ideals that can never be obtained from this algorithm. In this paper, we will show that these ideals have inverses of larger norms among…

We present an exposition of our ongoing project in a new area of applicable mathematics: practical computation with finitely generated linear groups over infinite fields. Methodology and algorithms available for practical computation in…

In this paper, a practicable simulation-free model order reduction method by nonlinear moment matching is developed. Based on the steady-state interpretation of linear moment matching, we comprehensively explain the extension of this…

We present a uniform methodology for computing with finitely generated matrix groups over any infinite field. As one application, we completely solve the problem of deciding finiteness in this class of groups. We also present an algorithm…