• SINGULAR

  • Referenced in 951 articles [sw00866]
  • Computer Algebra system (CAS) for polynomial computations in commutative algebra, algebraic geometry, and singularity theory ... large variety of baserings. The baserings are polynomial rings over a field (e.g., finite fields ... Tangent Cone algorithm. Furthermore, it provides polynomial factorizations, resultant, characteristic set and gcd computations, syzygy...
  • Macaulay2

  • Referenced in 1005 articles [sw00537]
  • quotient rings of graded or multi-graded polynomial rings with a monomial ordering. The core...
  • REDUCE

  • Referenced in 641 articles [sw00789]
  • capabilities include: expansion and ordering of polynomials and rational functions; substitutions and pattern matching ... syntax; analytic differentiation and integration; factorization of polynomials; facilities for the solution of a variety...
  • CoCoA

  • Referenced in 484 articles [sw00143]
  • perform simple and sophisticated operations on multivaraiate polynomials and on various data related to them ... Poincare’ series and Hilbert functions, factorization of polynomials, toric ideals. The capabilities of CoCoA...
  • INTLAB

  • Referenced in 279 articles [sw04004]
  • clusters) quadrature for univariate functions univariate polynomial zeros (simple and clusters) interval arithmetic for real ... simple) univariate functions univariate and multivariate (interval) polynomials rigorous real interval standard functions (fast, very...
  • OPQ

  • Referenced in 197 articles [sw11881]
  • Orthogonal polynomials. Computation and approximation. Orthogonal polynomials are a widely used class of mathematical functions ... downloadable from the Internet, to generate orthogonal polynomials of a great variety: OPQ: A MATLAB ... SUITE OF PROGRAMS FOR GENERATING ORTHOGONAL POLYNOMIALS AND RELATED QUADRATURE RULES...
  • MersenneTwister

  • Referenced in 178 articles [sw05367]
  • admit a Mersenne-prime period. The characteristic polynomial has many terms. The distribution ... that checks the primitivity of the characteristic polynomial of MT with computational complexity ... where p is the degree of the polynomial. We implemented this generator in portable ... efficient algorithms that are unique to polynomial calculations over the two-element field...
  • ISOLATE

  • Referenced in 167 articles [sw07741]
  • Efficient isolation of polynomial’s real roots. This paper revisits an algorithm isolating the real ... roots of a univariate polynomial using Descartes’ rule of signs. It follows work of Vincent ... Krandick’s variant, independently of the input polynomial. From this new algorithm, we derive ... algorithm still works with huge polynomials, including orthogonal polynomials of degree 1000 and more, which...
  • eigs

  • Referenced in 273 articles [sw03702]
  • shifted QR-iteration, the author applies a polynomial filter to the Arnoldi (Lanczos) vector...
  • pchip

  • Referenced in 268 articles [sw10140]
  • pchip. Piecewise Cubic Hermite Interpolating Polynomial (PCHIP...
  • GloptiPoly

  • Referenced in 187 articles [sw04343]
  • GloptiPoly 3 can handle moment problems with polynomial data. Many important applications in e.g. optimization ... after some transformation) of the GPM with polynomial data.The approach is similar to that used...
  • PHCpack

  • Referenced in 144 articles [sw00705]
  • PHCpack: A general-purpose solver for polynomial systems by homotopy continuation Polynomial systems occur ... been accomplished on exploiting structure in a polynomial system, in particular its sparsity. In this...
  • FGb

  • Referenced in 216 articles [sw00286]
  • efficient program written in C for solving polynomial systems. The purpose of the FGb library...
  • IRAM

  • Referenced in 138 articles [sw08795]
  • Implicit application of polynomial filters in a k-step Arnoldi method. The author describes ... shifted QR-iteration, the author applies a polynomial filter to the Arnoldi (Lanczos) vector...
  • DDE-BIFTOOL

  • Referenced in 184 articles [sw02396]
  • connecting orbits are computed using piecewise polynomial collocation on adaptively refined meshes...
  • Octave

  • Referenced in 175 articles [sw00646]
  • nonlinear equations, integrating ordinary functions, manipulating polynomials, and integrating ordinary differential and differential-algebraic equations...
  • Sostools

  • Referenced in 166 articles [sw00891]
  • specify and solve sum of squares polynomial problems using a very simple, flexible, and intuitive...
  • NTRU

  • Referenced in 110 articles [sw11761]
  • decryption use a mixing system suggested by polynomial algebra combined with a clustering principle based ... cryptosystem comes from the interaction of the polynomial mixing system with the independence of reduction...
  • MultRoot

  • Referenced in 82 articles [sw00604]
  • MultRoot - -a Matlab package for computing polynomial roots and multiplicities MultRoot is a collection ... Matlab modules for accurate computation of polynomial roots, especially roots with non-trivial multiplicities ... blackbox-type software, MultRoot requires the polynomial coefficients as the only input, and outputs ... without using multiprecision arithmetic, even if the polynomial coefficients are inexact. A comprehensive test suite...