• # PHCpack

• Referenced in 168 articles [sw00705]
• PHCpack: A general-purpose 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...
• # NTRU

• Referenced in 133 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 115 articles [sw05324]
• finding zeros or fixed points of nonlinear systems of equations that are globally convergent ... included for the special case of polynomial systems...
• # CoCoA

• Referenced in 541 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 ... high-level programming language. For convenience, the system offers a textual interface, an Emacs mode...
• # RAGlib

• Referenced in 53 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...
• # HOM4PS

• Referenced in 55 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...
• # Macaulay2

• Referenced in 1192 articles [sw00537]
• Macaulay2 is a software system devoted to supporting research in algebraic geometry and commutative algebra ... quotient rings of graded or multi-graded polynomial rings with a monomial ordering. The core ... closure of rings, and more. Computer algebra system...
• # REDUCE

• Referenced in 693 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...
• # Epsilon

• Referenced in 35 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...
• # INTLAB

• Referenced in 316 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...
• # PHoM

• Referenced in 27 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...
• # Maxima

• Referenced in 111 articles [sw00560]
• Laplace transforms, ordinary differential equations, systems of linear equations, polynomials, and sets, lists, vectors, matrices ... three dimensions. Computer algebra system...
• # HOMPACK90

• Referenced in 42 articles [sw00412]
• finding zeros or fixed points of nonlinear systems using globally convergent probability-one homotopy algorithms ... driver for the special case of polynomial systems is also provided. Changes to HOMPACK include...
• # alphaCertified

• Referenced in 22 articles [sw07351]
• Algorithm 921: alphaCertified: Certifying solutions to polynomial systems. Smale’s α-theory 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...