- Referenced in 409 articles
- systems of nonlinear equations (including unconstrained optimization) roots of univariate and multivariate nonlinear equations (simple ... clusters) quadrature for univariate functions univariate polynomial zeros (simple and clusters) interval arithmetic for real ... computations, fast) Gradients (to solve systems of nonlinear equations) Hessians (for global optimization) Taylor series ... simple) univariate functions univariate and multivariate (interval) polynomials rigorous real interval standard functions (fast, very...
- Referenced in 144 articles
- Laplace transforms, ordinary differential equations, systems of linear equations, polynomials, and sets, lists, vectors, matrices ... three dimensions. Computer algebra system...
- Referenced in 105 articles
- computer algebra system for solving systems of polynomial equations and inequations. It is a prototype...
- Referenced in 62 articles
- library for real solving polynomial systems of equations and inequalities. RAGlib is a Maple package ... study of real solutions of polynomial systems of equations and inequalities such as testing ... RAGlib Maple package allows to solve polynomial systems of equations/inequalities over the reals. Provided functionalities...
- Referenced in 70 articles
- facilities for symbolic computations with systems of polynomial equations. In particular, it allows to compute...
- Referenced in 72 articles
- from the symbolic preprocessing of systems of polynomial equations, where the degree and the size...
- Referenced in 738 articles
- mathematicians, scientists and engineers. Computer algebra system (CAS). It has been produced by a collaborative ... capabilities include: expansion and ordering of polynomials and rational functions; substitutions and pattern matching ... factorization of polynomials; facilities for the solution of a variety of algebraic equations; facilities...
- Referenced in 57 articles
- large bilinear algebraic systems is presented. The integrable polynomial vector evolution equations, quadratic Hamiltonians with ... structure and nonlocal 2+1-dimensional evolution equations are studied. An overview of the computer ... algorithm designed to length-reduce differential equations is presented. The program CRACK is a computer ... algebraic systems, ordinary, or partial differential equations with at most polynomial nonlinearity...
- Referenced in 39 articles
- over algebraic extension fields, solve systems of polynomial equations and inequations, and handle and prove...
- Referenced in 30 articles
- input data for a given system of polynomial equations $f(x)= 0$. The second module ... traces the solution curves of the homotopy equations to compute all isolated solutions ... performance of PHoM include some large polynomial systems that have not been solved previously...
- Referenced in 18 articles
- product homotopy code for solving polynomial systems of equations. The problem of solving large systems...
- Referenced in 145 articles
- vertices or a system of linear homogeneous Diophantine equations, inequalities and congruences or a binomial ... series and the Hilbert (or Ehrhart) (quasi) polynomial under a Z-grading (for example ... weighted) Ehrhart series and Lebesgue integrals of polynomials over rational polytopes via NmzIntegrate, a description ... lattice under consideration by a system of inequalities, equations and congruences...
- Referenced in 51 articles
- package to simplify overdetermined systems of nonlinear differential equations of polynomial type. The algorithms...
- Referenced in 15 articles
- space of several families of multivariate polynomial equation systems are given and we point...
- Referenced in 119 articles
- zeros or fixed points of nonlinear systems of equations that are globally convergent for almost ... tracking the homotopy zero curve: ordinary differential equation-based, normal flow, and augmented Jacobian matrix ... included for the special case of polynomial systems...
- Referenced in 60 articles
- differential equations (ODEs and PDEs). New algorithms are given to find exact polynomial solutions ... terms of Jacobi’s elliptic functions. For systems with parameters, the algorithms determine the conditions ... parameters so that the differential equations admit polynomial solutions in tanh, sech, combinations thereof, Jacobi...
- Referenced in 9 articles
- product homotopy code for solving polynomial systems of equations Globally convergent, probability-one homotopy methods ... isolated solutions to polynomial systems of equations. After many years of development, homotopy path trackers ... solutions of a complex coefficient polynomial system of equations. The package is intended ... support a general linear product (GLP) polynomial system structure. GLP structure is intermediate between...
- Referenced in 10 articles
- need to numerically solve systems of polynomial equations occurs frequently in various fields of mathematics ... class of numerical methods for solving these systems. Hom4PS ... software package for solving systems of polynomial equations that implements many different numerical homotopy methods ... range of hardware architectures including multi-core systems, computer clusters, distributed environments, and GPUs with...
- Referenced in 120 articles
- solution of a system of linear algebraic equations with a non-singular n×n matrix ... investigations of the BiCG part and the polynomial part. The second one is used...
- Referenced in 43 articles
- large system of linear ordinary differential equations (ODEs) with polynomial inhomogeneity. This is equivalent...