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Two Variants of Bézout Subresultants for Several Univariate Polynomials
In this paper, we develop two variants of Bézout subresultant formulas for several polynomials, i.e., hybrid Bézout subresultant polynomial and...
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Subresultant Chains Using Bézout Matrices
Subresultant chains over rings of multivariate polynomials are calculated using a speculative approach based on the Bézout matrix. Our experimental...
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On Calculating Partial Sums of Multiple Numerical Series by Methods of Computer Algebra
AbstractA method to calculate partial sums of some multiple numerical series arising when searching for the resultant of a polynomial and an entire...
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On the Distance to the Nearest Defective Matrix
The problem of finding the Frobenius distance in the \(\mathbb C^{n\times n} \)...
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A Modular Algorithm for Computing the Intersection of a One-Dimensional Quasi-Component and a Hypersurface
Computing triangular decompositions of polynomial systems can be performed incrementally with a procedure named Intersect. This procedure computes...
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Efficient computation of Riemann–Roch spaces for plane curves with ordinary singularities
We revisit the seminal Brill–Noether algorithm for plane curves with ordinary singularities. Our new approach takes advantage of fast algorithms for...
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Factorization of Polynomials Given by Arithmetic Branching Programs
Given a multivariate polynomial computed by an arithmetic branching program (ABP) of size s , we show that all its factors can be computed by...
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A General Method of Finding New Symplectic Schemes for Hamiltonian Mechanics
The explicit symplectic difference schemes are considered for the numerical solution of molecular dynamics problems described by systems with...
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Computational Schemes for Subresultant Chains
Subresultants are one of the most fundamental tools in computer algebra. They are at the core of numerous algorithms including, but not limited to,...
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Approximate GCD in a Bernstein Basis
We adapt Victor Y. Pan’s root-based algorithm for finding approximate GCD to the case where the polynomials are expressed in Bernstein bases. We use...
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More Efficient Algorithms for the NTRU Key Generation Using the Field Norm
NTRU lattices [13] are a class of polynomial rings which allow for compact and efficient representations of the lattice basis, thereby offering very...
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Jacobi’s Bound: Jacobi’s results translated in Kőnig’s, Egerváry’s and Ritt’s mathematical languages
Jacobi’s results on the computation of the order and of the normal forms of a differential system are translated in the formalism of differential...
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The Sylvester Resultant Matrix and Image Deblurring
This paper describes the application of the Sylvester resultant matrix to image deblurring. In particular, an image is represented as a bivariate...
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Parameterization of the discriminant set of a polynomial
The discriminant set of a real polynomial is studied. It is shown that this set has a complex hierarchical structure and consists of algebraic...
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On the zeta Mahler measure function of the Jacobian determinant, condition numbers and the height of the generic discriminant
In Cassaigne and Maillot (J Number Theory 83:226–255,
2000 ) and, later on, in Akatsuka (J Number Theory 129:2713–2734,2009 ) the authors introduced... -
Distance Evaluation Between an Ellipse and an Ellipsoid
We solve in ℝ n the problem of distance evaluation between a quadric and a manifold obtained as the intersection...