• SINGULAR

  • Referenced in 1471 articles [sw00866]
  • Tangent Cone algorithm. Furthermore, it provides polynomial factorizations, resultant, characteristic set and gcd computations, syzygy...
  • REDUCE

  • Referenced in 743 articles [sw00789]
  • capabilities include: expansion and ordering of polynomials and rational functions; substitutions and pattern matching ... program syntax; analytic differentiation and integration; factorization of polynomials; facilities for the solution...
  • CoCoA

  • Referenced in 649 articles [sw00143]
  • perform simple and sophisticated operations on multivaraiate polynomials and on various data related to them ... schemes, Poincare’ series and Hilbert functions, factorization of polynomials, toric ideals. The capabilities of CoCoA...
  • Epsilon

  • Referenced in 41 articles [sw00244]
  • decompose polynomial ideals into primary components, factorize polynomials over algebraic extension fields, solve systems...
  • FOXBOX

  • Referenced in 16 articles [sw00307]
  • compute the greatest common divisor and factorize polynomials in black box representation, producing as output ... black box polynomial, for example, one which was computed for an irreducible factor. We establish ... underlying field and polynomial arithmetic. Multiple arithmetic plugins can be used in the same computation...
  • ILUM

  • Referenced in 63 articles [sw07244]
  • preconditioning techniques based on incomplete LU (ILU) factorizations offer a limited degree of parallelism ... some form of polynomial precoditioning or applying the usual ILU factorization to a matrix obtained...
  • JAS

  • Referenced in 15 articles [sw05877]
  • solvable polynomials, power-series, multivariate polynomial factorization, Grobner bases, and applications...
  • Berlekamp Zassenhaus

  • Referenced in 9 articles [sw28596]
  • Berlekamp-Zassenhaus algorithm for factoring square-free integer polynomials in Isabelle/HOL. We further adapt ... square-free factorization algorithm to integer polynomials, and thus provide an efficient and certified factorization ... algorithm for arbitrary univariate polynomials. The algorithm first performs a factorization in the prime field ... experiments we verify that our algorithm factors polynomials of degree 100 within seconds...
  • MPSolve

  • Referenced in 14 articles [sw05298]
  • polynomial and power series factorizations, spectral factorizations, matrix polynomials and matrix power series, interpolation problems...
  • FAST16

  • Referenced in 5 articles [sw00262]
  • FAST16: A software program for factorizing polynomials over large GF(p) [For the entire collection ... authors consider the problem of factorizing square-free polynomials over large, finite, prime fields. They ... square-free polynomial. The algorithm first searches for a factorization of the f into ... find a factorization of $fsb{(r)}$ into products of polynomials, such that each of them...
  • pqTelescope

  • Referenced in 7 articles [sw14276]
  • Paule’s concept of greatest factorial factorization of polynomials can be extended to the bibasic...
  • LLL Factorization

  • Referenced in 2 articles [sw28660]
  • verified factorization algorithm for integer polynomials with polynomial complexity ... Short vectors in lattices and factors of integer polynomials are related. Each factor ... belongs to a certain lattice. When factoring polynomials, the condition that we are looking ... reduction algorithm: an algorithm to factor square-free integer polynomials which runs in polynomial time...
  • Lacunaryx

  • Referenced in 4 articles [sw20573]
  • Lacunaryx: computing bounded-degree factors of lacunary polynomials. In this paper, we report ... factorization algorithms, distributed as a library called Lacunaryx. These algorithms take as input a polynomial ... irreducible degree-≤d factors. The complexity of these algorithms is polynomial in the sparse size...
  • CharSets

  • Referenced in 3 articles [sw13623]
  • solving systems of polynomial equations, and factorizing multivariate polynomials over algebraic extension fields...
  • Verified LLL

  • Referenced in 2 articles [sw28661]
  • first polynomial-time algorithm to factor polynomials. In this work we present the first mechanized...
  • Tensorlab

  • Referenced in 62 articles [sw14255]
  • coupled) matrix and tensor factorizations with structured factors and support for dense, sparse and incomplete ... numerical complex differentiation, global minimization of bivariate polynomials and rational functions: both real and complex...
  • CREP

  • Referenced in 5 articles [sw30215]
  • groups or the finite-dimensional factor algebras of polynomial algebras. If one wants to approach...
  • PHClab

  • Referenced in 15 articles [sw09668]
  • Octave to solve a list of polynomial systems. PHClab also interfaces to the numerical irreducible ... giving access to the tools to represent, factor, and intersect positive dimensional solution sets...
  • Rings

  • Referenced in 2 articles [sw22196]
  • coefficient rings. Basic algebra, GCDs and factorization of polynomials are implemented with...