Related papers: Truth Table Invariant Cylindrical Algebraic Decomp…

Canonical quantisation of constrained systems with first class constraints via Dirac's operator constraint method proceeds by the thory of Rigged Hilbert spaces, sometimes also called Refined Algebraic Quantisation (RAQ). This method can…

Tensor decompositions have become essential tools for feature extraction and compression of multiway data. Recent advances in tensor operators have enabled desirable properties of standard matrix algebra to be retained for multilinear…

Due to the rapid development of quantum computing, the compact representation of quantum operations based on decision diagrams has been received more and more attraction. Since variable orders have a significant impact on the size of the…

The cylindrical algebraic covering method was originally proposed to decide the satisfiability of a set of non-linear real arithmetic constraints. We reformulate and extend the cylindrical algebraic covering method to allow for checking the…

Computed Tomography (CT) has been widely adopted in medicine and it is increasingly being used in scientific and industrial applications. Parallelly, research in different mathematical areas concerning discrete inverse problems has led to…

Matrix operations such as matrix inversion, eigenvalue decomposition, singular value decomposition are ubiquitous in real-world applications. Unfortunately, many of these matrix operations so time and memory expensive that they are…

Topological data analysis leverages topological features to analyze datasets, with applications in diverse fields like medical sciences and biology. A key tool of this theory is the persistence diagram, which encodes topological information…

We present two new algorithms for the computation of the q-integer linear decomposition of a multivariate polynomial. Such a decomposition is essential for the treatment of q-hypergeometric symbolic summation via creative telescoping and…

We consider natural algebraic differential operations acting on geometric quantities over smooth manifolds. We introduce a method of study and classification of such operations, called IT-reduction. It reduces the study of natural…

This paper studies binary quadratic programs in which the objective is defined by a Euclidean distance matrix, subject to a general polyhedral constraint set. This class of nonconcave maximisation problems includes the capacitated,…

A practical approach is presented which allows the use of a non-invariant regularization scheme for the computation of quantum corrections in perturbative quantum field theory. The theoretical control of algebraic renormalization over…

We present an exact and complete algorithm to isolate the real solutions of a zero-dimensional bivariate polynomial system. The proposed algorithm constitutes an elimination method which improves upon existing approaches in a number of…

Cylindrical algebraic decomposition is a classical construction in real algebraic geometry. Although there are many algorithms to compute a cylindrical algebraic decomposition, their practical performance is still very limited. In this…

We introduce an algebraic methodology for designing exactly-solvable Lie model Hamiltonians. The idea consists in looking at the algebra generated by bond operators. We illustrate how this method can be applied to solve numerous problems of…

We provide first the functional analysis background required for reduced order modeling and present the underlying concepts of reduced basis model reduction. The projection-based model reduction framework under affinity assumptions,…

Elimination theory has many applications, in particular, it describes explicitly an image of a complex line under rational transformation and determines the number of common zeroes of two polynomials in one variable. We generalize classical…

Complexity bounds for many problems on matrices with univariate polynomial entries have been improved in the last few years. Still, for most related algorithms, efficient implementations are not available, which leaves open the question of…

Hidden symmetries in a covariant Hamiltonian formulation are investigated involving gauge covariant equations of motion. The special role of the Stackel-Killing tensors is pointed out. A reduction procedure is used to reduce the original…

In this paper we propose, implement, and test the first practical decomposition algorithms for the width parameters treecut width and treedepth. These two parameters have recently gained a lot of attention in the theoretical research…

Transforming a matrix over a field to echelon form, or decomposing the matrix as a product of structured matrices that reveal the rank profile, is a fundamental building block of computational exact linear algebra. This paper surveys the…