
SINGULAR
 Referenced in 1314 articles
[sw00866]
 SINGULAR is a Computer Algebra system (CAS) for polynomial computations in commutative algebra, algebraic geometry...

PHCpack
 Referenced in 203 articles
[sw00705]
 PHCpack: A generalpurpose solver for polynomial systems by homotopy continuation. Polynomial systems occur ... accomplished on exploiting structure in a polynomial system, in particular its sparsity. In this paper...

FGb
 Referenced in 234 articles
[sw00286]
 program written in C for solving polynomial systems. The purpose of the FGb library...

Bertini
 Referenced in 204 articles
[sw06683]
 Numerical Algebraic Geometry. Software for solving polynomial systems. Finds isolated solutions using totaldegree start...

NTRU
 Referenced in 153 articles
[sw11761]
 decryption use a mixing system suggested by polynomial algebra combined with a clustering principle based ... comes from the interaction of the polynomial mixing system with the independence of reduction modulo...

HOMPACK
 Referenced in 119 articles
[sw05324]
 finding zeros or fixed points of nonlinear systems of equations that are globally convergent ... included for the special case of polynomial systems...

HOM4PS
 Referenced in 70 articles
[sw00410]
 software package for solving polynomial systems by the polyhedral homotopy continuation method. HOM4PS ... polyhedral homotopy continuation method for solving polynomial systems. It updates its original version HOM4PS...

RAGlib
 Referenced in 60 articles
[sw00774]
 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...

CoCoA
 Referenced in 605 articles
[sw00143]
 CoCoA is a system for Computations in Commutative Algebra. It is able to perform simple ... sophisticated operations on multivaraiate polynomials and on various data related to them (ideals, modules, matrices ... Poincare’ series and Hilbert functions, factorization of polynomials, toric ideals. The capabilities of CoCoA ... highlevel programming language. For convenience, the system offers a textual interface, an Emacs mode...

Macaulay2
 Referenced in 1576 articles
[sw00537]
 Macaulay2 is a software system devoted to supporting research in algebraic geometry and commutative algebra ... quotient rings of graded or multigraded polynomial rings with a monomial ordering. The core ... closure of rings, and more. Computer algebra system...

REDUCE
 Referenced in 737 articles
[sw00789]
 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...

Kronecker
 Referenced in 105 articles
[sw00495]
 Magma computer algebra system for solving systems of polynomial equations and inequations...

INTLAB
 Referenced in 407 articles
[sw04004]
 structured matrices) sparse s.p.d. linear systems systems of nonlinear equations (including unconstrained optimization) roots ... clusters) quadrature for univariate functions univariate polynomial zeros (simple and clusters) interval arithmetic for real ... mode, vectorized computations, fast) Gradients (to solve systems of nonlinear equations) Hessians (for global optimization ... simple) univariate functions univariate and multivariate (interval) polynomials rigorous real interval standard functions (fast, very...

alphaCertified
 Referenced in 37 articles
[sw07351]
 Algorithm 921: alphaCertified: Certifying solutions to polynomial systems. Smale’s αtheory uses estimates related ... quadratically to solutions to a square polynomial system. The program alphaCertified implements algorithms based ... theory to certify solutions of polynomial systems using both exact rational arithmetic and arbitrary precision...

Maxima
 Referenced in 144 articles
[sw00560]
 Laplace transforms, ordinary differential equations, systems of linear equations, polynomials, and sets, lists, vectors, matrices ... three dimensions. Computer algebra system...

Epsilon
 Referenced in 39 articles
[sw00244]
 functions implemented in Maple and Java for polynomial elimination and decomposition with (geometric) applications ... systems of multivariate (differential) polynomials, decompose polynomial systems into triangular systems of various kinds (regular ... varieties into irreducible or unmixed subvarieties, decompose polynomial ideals into primary components, factorize ... polynomials over algebraic extension fields, solve systems of polynomial equations and inequations, and handle...

na20
 Referenced in 71 articles
[sw11505]
 arising from the symbolic preprocessing of systems of polynomial equations, where the degree...

PHoM
 Referenced in 30 articles
[sw04645]
 polyhedral homotopy continuation method for polynomial systems. PHoM is a software package ... finding all isolated solutions of polynomial systems using a polyhedral homotopy continuation method. Among three ... from input data for a given system of polynomial equations $f(x)= 0$. The second ... performance of PHoM include some large polynomial systems that have not been solved previously...

RegularChains
 Referenced in 69 articles
[sw00796]
 provides facilities for symbolic computations with systems of polynomial equations. In particular, it allows...

HOMPACK90
 Referenced in 45 articles
[sw00412]
 finding zeros or fixed points of nonlinear systems using globally convergent probabilityone homotopy algorithms ... driver for the special case of polynomial systems is also provided. Changes to HOMPACK include...