
alphaCertified
 Referenced in 29 articles
[sw07351]
 Algorithm 921: alphaCertified: Certifying solutions to polynomial systems. Smale’s αtheory uses estimates related ... convergence of Newton’s method to certify that Newton iterations will converge quadratically to solutions ... program alphaCertified implements algorithms based on αtheory to certify solutions of polynomial systems using ... floating point arithmetic. It also implements algorithms that certify whether a given point corresponds...

Mathemagix
 Referenced in 37 articles
[sw00553]
 scientific programming language for symbolic and certified numeric algorithms. This language can be compiled ... will illustrate possibilities offered for certified numeric computations with balls and intervals...

Berlekamp Zassenhaus
 Referenced in 4 articles
[sw28596]
 thus provide an efficient and certified factorization algorithm for arbitrary univariate polynomials. The algorithm first...

Axel
 Referenced in 21 articles
[sw06457]
 algorithms to compute intersection points or curves, singularities of algebraic curves or surfaces, certified topology...

CAQE
 Referenced in 6 articles
[sw25922]
 CAQE: a certifying QBF solver. We present a new CEGARbased algorithm ... algorithm builds on a decomposition of QBFs into a sequence of propositional formulas, which ... allowing us to certify the solver result. We implemented the algorithm in a solver called ... current QBF solvers and outperforms previous certifying solvers...

RationalFirstintegrals
 Referenced in 2 articles
[sw14472]
 planar polynomial vector fields. We present fast algorithms for computing rational first integrals with bounded ... transform their method into a certified algorithm computing rational first integrals via systems of linear...

HSPICE
 Referenced in 9 articles
[sw11821]
 foundrycertified MOS device models with stateoftheart simulation and analysis algorithms. With...

RookWalks
 Referenced in 2 articles
[sw11424]
 challenge to develop algorithms which can also certify the correctness of the equations we found...

NLCertify
 Referenced in 4 articles
[sw08786]
 Sollya environment, in which an iterative algorithm designed by Remez is implemented. Alternatively, the maxplus ... quadratic forms. In this way, NLCertify computes certified global estimators from approximations of primitive functions ... tree t. These various approximation and optimization algorithms are placed in a unified framework extending...

Synthia
 Referenced in 7 articles
[sw12933]
 partially implemented systems, in which case it certifies their realizability by synthesizing reference implementations ... arising infinite state space. Synthia’s analysis algorithm is based on a novel abstraction refinement...

IML  Integer Matrix Library
 Referenced in 14 articles
[sw00440]
 library of C source code which implements algorithms for computing exact solutions to dense systems ... right nullspace of an integer matrix. Certified linear system solving: compute a minimal denominator solution...

FoCaLiZe
 Referenced in 7 articles
[sw12384]
 providing a programming environment to develop certified programs. The environment is based on a functional ... noticeably efficient; for instance, the complex algorithms of the algebraic library provide runtime performances comparable...

RealCertify
 Referenced in 2 articles
[sw28191]
 RealCertify: a Maple package for certifying nonnegativity. Let Q (resp. R) be the field ... constraints in Q[X] is a classical algorithmic problem for symbolic computation. The Maple package...

3D spherical kernel
 Referenced in 5 articles
[sw11156]
 sphere. We present a CGAL kernel for algorithms manipulating 3D spheres, circles, and circular arcs ... sample molecular models), it is shown that certifying the result incurs a modest factor...

Real_Impl
 Referenced in 2 articles
[sw29247]
 this end, we also developed algorithms to precisely compute roots of a rational number ... factors. Our results have been used to certify termination proofs which involve polynomial interpretations over...

Slicing
 Referenced in 1 article
[sw29542]
 Archive of formal proofs: Towards Certified Slicing. Slicing is a widelyused technique with applications ... technology and software security. Thus verification of algorithms in these areas is often based...

Axl
 Referenced in 1 article
[sw25792]
 defined by polynomial equations. Moreover, Axl provides algorithms for processing these geometric representations, such ... models, singularities of algebraic curves or surfaces, certified topology of curves and surfaces...

Ball
 Referenced in 1 article
[sw26708]
 comparison and test of independence. The tailormade algorithms as well as engineering techniques are employed ... studies have been performed and the results certify the powerfulness of Ball package in analyzing...

ACETAF
 Referenced in 6 articles
[sw00014]
 ACETAF: A software package for computing validated bounds...

ACL2
 Referenced in 254 articles
[sw00060]
 ACL2 is both a programming language in which...