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Lengths of developments in K((G))
Mourgues and Ressayre (J Symb Logic 58:641–647,
1993 ) showed that every real closed field F has an integer part, where this is an ordered subring... -
Black-Box Identity Testing of Depth-4 Multilinear Circuits
We study the problem of identity testing for multilinear ΣΠΣΠ ( k ) circuits, i.e., multilinear depth-4 circuits with fan-in k at the top + gate. We...
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On the Convergence of Chebyshev’s Method for Multiple Polynomial Zeros
In this paper we investigate the local convergence of Chebyshev’s iterative method for the computation of a multiple polynomial zero. We establish...
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On the degree of univariate polynomials over the integers
We study the following problem raised by von zur Gathen and Roche [6]:
What is the minimal degree of a nonconstant polynomial f : {0,..., n } → {0,..., m ...
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Reaching fixed points as limits in subspaces
A strictly contracting map** of a spherically complete ultrametric space has a unique fixed point. In general, the fixed point can be approached by...
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Convergence of the two-point Weierstrass root-finding method
In this paper we present new local and semilocal convergence theorems for the two-point Weierstrass method for the simultaneous computation of...
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On the Convergence of Halley’s Method for Multiple Polynomial Zeros
In this paper, we investigate the local convergence of Halley’s method for the computation of a multiple polynomial zero with known multiplicity. We...
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Sparse bivariate polynomial factorization
Motivated by Sasaki’s work on the extended Hensel construction for solving multivariate algebraic equations, we present a generalized Hensel lifting,...
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An efficient algorithm for factoring polynomials over algebraic extension field
An efficient algorithm is proposed for factoring polynomials over an algebraic extension field defined by a polynomial ring modulo a maximal ideal....
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Computing polynomial univariate representations of zero-dimensional ideals by Gröbner basis
Rational Univariate Representation (RUR) of zero-dimensional ideals is used to describe the zeros of zero-dimensional ideals and RUR has been studied...
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Efficient Arithmetic in Successive Algebraic Extension Fields Using Symmetries
In this article, we present new results for efficient arithmetic operations in a number field K represented by successive extensions. These results...
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Multiplication Matrices and Ideals of Projective Dimension Zero
We introduce the concept of multiplication matrices for ideals of projective dimension zero. We discuss various applications and, in particular, we...
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Tight bounds for rational sums of squares over totally real fields
Let K be a totally real Galois number field. Hillar proved that if f ∈ ℚ[ x 1 , ..., x n ] is a sum of m squares in K [ x 1 , ..., x ...
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Border bases and kernels of homomorphisms and of derivations
Border bases are an alternative to Gröbner bases. The former have several more desirable properties. In this paper some constructions and operations...
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Quasi-permutation polynomials
A quasi-permutation polynomial is a polynomial which is a bijection from one subset of a finite field onto another with the same number of elements....
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Applications of Cogalois Theory to Elementary Field Arithmetic
The aim of this expository paper is to present those basic concepts and facts of Cogalois theory which will be used for obtaining in a natural and...