相关论文: Software for cut-generating functions in the Gomor…
We present software for investigations with cut-generating functions in the Gomory--Johnson model and extensions, implemented in the computer algebra system SageMath.
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 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…
We study continuous (strongly) minimal cut generating functions for the model where all variables are integer. We consider both the original Gomory-Johnson setting as well as a recent extension by Cornu\'ejols and Y{\i}ld{\i}z. We show that…
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,…
We assume some standard choices for the branch cuts of a group of functions and consider the problem of then calculating the branch cuts of expressions involving those functions. Typical examples include the addition formulae for inverse…
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.
The SageManifolds project aims at extending the mathematics software system Sage towards differential geometry and tensor calculus. Like Sage, SageManifolds is free, open-source and is based on the Python programming language. We discuss…
We report on implementations for algorithms treating algebraic and arithmetic properties of hypergeometric functions in the computer algebra system SageMath. We treat hypergeometric series over the rational numbers, over finite fields, and…
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 mathematical software system polymake provides a wide range of functions for convex polytopes, simplicial complexes, and other objects. A large part of this paper is dedicated to a tutorial which exemplifies the usage. Later sections…
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…
The new finite state machine package in the mathematics software system SageMath is presented and illustrated by many examples. Several combinatorial problems, in particular digit problems, are introduced, modeled by automata and…
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,…
A new method to derive Multivariate Quadratic equation systems (MQ) for the input and output bit variables of a cryptographic S-box from its algebraic expressions with the aid of the computer mathematics software system SageMath is…
Mathematical educational soft explore, investigating in a dynamical way, some algebraically, geometrically problems, the expected results being used to involve a lot of mathematical results. One such software soft is GeoGebra. The software…
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 investigate new methods for generating Lagrangian cuts to solve two-stage stochastic integer programs. Lagrangian cuts can be added to a Benders reformulation, and are derived from solving single scenario integer programming subproblems…
Many algorithms for determining properties of real algebraic or semi-algebraic sets rely upon the ability to compute smooth points. Existing methods to compute smooth points on semi-algebraic sets use symbolic quantifier elimination tools.…
Sequential sampling models (SSMs) are a widely used framework describing decision-making as a stochastic, dynamic process of evidence accumulation. SSMs popularity across cognitive science has driven the development of various software…