Related papers: Equivariant Perturbation in Gomory and Johnson's I…
We present software for investigations with cut generating functions in the Gomory-Johnson model and extensions, implemented in the computer algebra system SageMath.
We construct a two-sided discontinuous piecewise linear minimal valid function for the 1-row Gomory--Johnson model which is not extreme, but which is not a convex combination of other piecewise linear minimal valid functions. The new…
We study an abstract setting for cutting planes for integer programming called the infinite group problem. In this abstraction, cutting planes are computed via cut generating function that act on the simplex tableau. In this function space,…
In this note we announce the availability of an electronic compendium of extreme functions for Gomory--Johnson's infinite group problem. These functions serve as the strongest cut-generating functions for integer linear optimization…
Using a metaprogramming technique and semialgebraic computations, we provide computer-based proofs for old and new cutting-plane theorems in Gomory--Johnson's model of cut generating functions.
In this self-contained paper, we present a theory of the piecewise linear minimal valid functions for the 1-row Gomory-Johnson infinite group problem. The non-extreme minimal valid functions are those that admit effective perturbations. We…
We give an algorithm for testing the extremality of minimal valid functions for Gomory and Johnson's infinite group problem that are piecewise linear (possibly discontinuous) with rational breakpoints. This is the first set of necessary and…
This is a survey on the infinite group problem, an infinite-dimensional relaxation of integer linear optimization problems introduced by Ralph Gomory and Ellis Johnson in their groundbreaking papers titled "Some continuous functions related…
We describe new computer-based search strategies for extreme functions for the Gomory--Johnson infinite group problem. They lead to the discovery of new extreme functions, whose existence settles several open questions.
We give an algorithm for testing the extremality of a large class of minimal valid functions for the two-dimensional infinite group problem.
The Gauss-Jordan elimination algorithm is extended to reduce a row-finite $\omega\times\omega$ matrix to lower row-reduced form, founded on a strategy of rightmost pivot elements. Such reduced matrix form preserves row equivalence, unlike…
We introduce QuiverTools, a new software package, available in both a SageMath and Julia version, to study quivers and their moduli spaces of representations. Its key features are the computation of general subdimension vectors, leading to…
The construction of the general solution sequence of row-finite linear systems is accomplished by implementing -ad infinitum- the Gauss-Jordan algorithm under a rightmost pivot elimination strategy. The algorithm generates a basis (finite…
For the purposes of electric circuit simulation, we consider an iterative simulation model based on solving systems of linear equations by Gauss-Jordan elimination (GJE) for individual moments in time. To accelerate the simulation, we…
We present a new open source implementation in the SageMath computer algebra system of algorithms for the numerical solution of linear ODEs with polynomial coefficients. Our code supports regular singular connection problems and provides…
Computer algebra systems are complex software systems that cover a wide range of scientific and practical problems. However, the absolute coverage cannot be achieved. Often, it is required to create a user extension for an existing computer…
In this paper we present \texttt{SymOrb.jl}, a software which combines group representation theory and variational methods to provide numerical solutions of singular dynamical systems of paramount relevance in Celestial Mechanics and other…
This note summarizes the talk by the author at the workshop "Geometry and Computer Science" held in Pescara in February 2017. We present how SageMath can help in research in Complex and Differential Geometry, with two simple applications,…
We describe a recently developed algebraic framework for proving first-order statements about linear operators by computations with noncommutative polynomials. Furthermore, we present our new SageMath package operator_gb, which offers…
Several continued fraction expansions for $e$ have been produced by an automated conjecture generator (ACG) called \emph{The Ramanujan Machine}. Some of these were already known, some have recently been proved and some remain unproven.…