• SINGULAR

  • Referenced in 1330 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 1585 articles [sw00537]
  • quotient rings of graded or multi-graded polynomial rings with a monomial ordering. The core...
  • REDUCE

  • Referenced in 738 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 607 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...
  • OPQ

  • Referenced in 360 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...
  • INTLAB

  • Referenced in 409 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...
  • MersenneTwister

  • Referenced in 254 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...
  • GloptiPoly

  • Referenced in 287 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...
  • ISOLATE

  • Referenced in 206 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...
  • pchip

  • Referenced in 340 articles [sw10140]
  • pchip. Piecewise Cubic Hermite Interpolating Polynomial (PCHIP...
  • PHCpack

  • Referenced in 203 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...
  • eigs

  • Referenced in 314 articles [sw03702]
  • shifted QR-iteration, the author applies a polynomial filter to the Arnoldi (Lanczos) vector...
  • DDE-BIFTOOL

  • Referenced in 284 articles [sw02396]
  • connecting orbits are computed using piecewise polynomial collocation on adaptively refined meshes...
  • Octave

  • Referenced in 276 articles [sw00646]
  • nonlinear equations, integrating ordinary functions, manipulating polynomials, and integrating ordinary differential and differential-algebraic equations...
  • IRAM

  • Referenced in 192 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...
  • Sostools

  • Referenced in 264 articles [sw00891]
  • specify and solve sum of squares polynomial problems using a very simple, flexible, and intuitive...
  • FGb

  • Referenced in 235 articles [sw00286]
  • efficient program written in C for solving polynomial systems. The purpose of the FGb library...
  • NTRU

  • Referenced in 156 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...
  • Bertini

  • Referenced in 206 articles [sw06683]
  • Numerical Algebraic Geometry. Software for solving polynomial systems. Finds isolated solutions using total-degree start...