
na20
 Referenced in 78 articles
[sw11505]
 roots of a polynomial with complex coefficients. The real and the imaginary parts ... designed to deal also with numerically hard polynomials like those arising from the symbolic preprocessing...

Polynomial Toolbox
 Referenced in 33 articles
[sw07237]
 Discretetime symmetric polynomial equations with complex coefficients. Discretetime symmetric polynomial equations with complex ... several algorithms are proposed and evaluated. Polynomial reduction algorithms are first described to study theoretical...

POLSYS_GLP
 Referenced in 9 articles
[sw07346]
 finding all the isolated solutions to polynomial systems of equations. After many years of development ... finding all isolated solutions of a complex coefficient polynomial system of equations. The package...

UBASIC
 Referenced in 30 articles
[sw06033]
 arithmetic of polynomials with complex, rational, or modulo p coefficients, as well as string handling...

QROOT
 Referenced in 16 articles
[sw07929]
 which may be of polynomial (with or without complex coefficients) or transcendental type. Although...

SqFreeEVAL
 Referenced in 11 articles
[sw07421]
 univariate polynomial with real coefficients, f∈ℝ[X]. Subdivision algorithms based on algebraic techniques ... purely numerical (e.g., function evaluation). The complexity of this algorithm is adaptive because the algorithm ... makes decisions based on local data. The complexity analysis of adaptive algorithms (and this algorithm ... integer polynomial f of degree d and whose coefficients can be written with at most...

na10
 Referenced in 51 articles
[sw11511]
 starting approximations we choosek i complex numbers lying on a suitable circle contained ... exact zeros of a “nearby” polynomial. This implies the backward stability of our algorithm ... deal with polynomials of any degree, not necessarily monic, whose zeros and coefficients are representable...

PolyBoRi
 Referenced in 49 articles
[sw00723]
 coefficients and degree per variable lying in {0,1}. The ring of Boolean polynomials ... polynomial ring, but rather the quotient ring of the polynomial ring over the field with ... each variable x. Therefore, the usual polynomial data structures seem not to be appropriate ... polynomials based on zerosuppressed binary decision diagrams, which are capable of handling these polynomials...

RMOP
 Referenced in 4 articles
[sw41350]
 coefficients in the threeterm recurrence relation of repeatedly modified orthogonal polynomials, the modifications involving ... linear function with real or complex coefficient. The respective Gaussian quadrature rules can be used...

Algebraic Numbers
 Referenced in 1 article
[sw28608]
 completely factorize real and complex polynomials, provided that all coefficients are rational numbers. Moreover...

lifting
 Referenced in 4 articles
[sw31749]
 intersection cut, then strengthen the cut coefficients corresponding to integral nonbasic variables using ... called trivial lifting procedure. Although of polynomialtime complexity in theory, this lifting procedure ... practical algorithm that computes trivial lifting coefficients in constant time, for arbitrary maximal latticefree...

MHS
 Referenced in 4 articles
[sw31594]
 complex number arising as the integral of a rational function with algebraic number coefficients over ... finitely many inequalities between polynomials with rational coefficients. Although periods are typically transcendental numbers, there...

polyzero
 Referenced in 0 articles
[sw05295]
 polynomial of one complex variable and has real coefficients(least squares method, interactive/file input, f77/C...

SNAKE
 Referenced in 2 articles
[sw21078]
 However, there was a problem that the complexity and the number of pairs of plaintexts ... finding the actual number of coefficients in the polynomial (or rational expression) used...

M4GB
 Referenced in 4 articles
[sw35027]
 reduces the time and data complexity `staircase’ related to the increasing degree of regularity ... operate only on tailreduced polynomials, i.e., polynomials of which all terms except the leading ... term polynomial multiplication, where all computations are done over coefficient vectors over the nonreducible...

Algorithm 954
 Referenced in 3 articles
[sw20214]
 polynomial coefficients. The key to the algorithm is a proper rescaling of both polynomials. This ... solver is based on dividing the cubic polynomial into six classes. By analyzing the root ... cubic. If the quartic has only complex roots, the present article shows that a stable...

fourier
 Referenced in 1 article
[sw20915]
 Selection for the number of desired Fourier coefficient pairs is made as well ... determine the roots of the Legendre polynomial, but finds the roots by looking ... matrix of the n’th degree Legendre polynomial. The companion matrix is constructed ... higher values of #numGauss#, leading to complex roots...

PoCET
 Referenced in 1 article
[sw33956]
 projection and collocationbased calculation of PCE coefficients, and the calculation of stochastic moments from ... paper we show how to perform a polynomial chaos expansion on a simple ordinary differential ... used to solve the more complex task of optimal experimental design...

ACETAF
 Referenced in 7 articles
[sw00014]
 ACETAF: A software package for computing validated bounds...

ADOLC
 Referenced in 257 articles
[sw00019]
 ADOLC: Automatic Differentiation of C/C++. We present...