Related papers: GAPS: Generator for Automatic Polynomial Solvers
Over the past decade, the Gr\"obner basis theory and automatic solver generation have lead to a large number of solutions to geometric vision problems. In practically all cases, the derived solvers apply a fixed elimination template to…
In computer vision applications, the following problem often arises: Given a family of (Laurent) polynomial systems with the same monomial structure but varying coefficients, find a solver that computes solutions for any family member as…
Polynomial system solving is a classical problem in mathematics with a wide range of applications. This makes its complexity a fundamental problem in computer science. Depending on the context, solving has different meanings. In order to…
An algorithm to generate a minimal comprehensive Gr\"obner\, basis of a parametric polynomial system from an arbitrary faithful comprehensive Gr\"obner\, system is presented. A basis of a parametric polynomial ideal is a comprehensive…
Solving systems of polynomial equations is a central problem in nonlinear and computational algebra. Since Buchberger's algorithm for computing Gr\"obner bases in the 60s, there has been a lot of progress in this domain. Moreover, these…
Many computer vision applications require robust and efficient estimation of camera geometry from a minimal number of input data measurements, i.e., solving minimal problems in a RANSAC framework. Minimal problems are usually formulated as…
Many computer vision applications require robust and efficient estimation of camera geometry. The robust estimation is usually based on solving camera geometry problems from a minimal number of input data measurements, i.e. solving minimal…
Solving a polynomial system, or computing an associated Gr\"obner basis, has been a fundamental task in computational algebra. However, it is also known for its notorious doubly exponential time complexity in the number of variables in the…
Many computer vision applications require robust estimation of the underlying geometry, in terms of camera motion and 3D structure of the scene. These robust methods often rely on running minimal solvers in a RANSAC framework. In this paper…
Gr{\"o}bner bases is one the most powerful tools in algorithmic non-linear algebra. Their computation is an intrinsically hard problem with a complexity at least single exponential in the number of variables. However, in most of the cases,…
This paper is concerned with linear algebra based methods for solving exactly polynomial systems through so-called Gr\"obner bases, which allow one to compute modulo the polynomial ideal generated by the input equations. This is a topical…
Geometry problem solving presents a formidable challenge within the NLP community. Existing approaches often rely on models designed for solving math word problems, neglecting the unique characteristics of geometry math problems.…
Analyzing and reasoning about safety properties of software systems becomes an especially challenging task for programs with complex flow and, in particular, with loops or recursion. For such programs one needs additional information, for…
The main idea in this paper is merging two techniques that have been recently developed. On the one hand, we consider MCCGS, standing for Minimal Canonical Comprehensive Groebner Systems, a recently introduced computational tool yielding…
The intersection of deep learning and symbolic mathematics has seen rapid progress in recent years, exemplified by the work of Lample and Charton. They demonstrated that effective training of machine learning models for solving mathematical…
We present a new open source C library \texttt{msolve} dedicated to solving multivariate polynomial systems of dimension zero through computer algebra methods. The core algorithmic framework of \texttt{msolve} relies on Gr\''obner bases and…
Consider a subfield of the field of rational functions in several indeterminates. We present an algorithm that, given a set of generators of such a subfield, finds a simple generating set. We provide an implementation of the algorithm and…
We present a polynomial preconditioner for solving large systems of linear equations. The polynomial is derived from the minimum residual polynomial (the GMRES polynomial) and is more straightforward to compute and implement than many…
Many computer vision applications require robust and efficient estimation of camera geometry. The robust estimation is usually based on solving camera geometry problems from a minimal number of input data measurements, i.e., solving minimal…
We are concerned with the problem of decomposing the parameter space of a parametric system of polynomial equations, and possibly some polynomial inequality constraints, with respect to the number of real solutions that the system attains.…