Mathematics for computer algebra
Mathematics for computer algebra
Polynomial and matrix computations (vol. 1): fundamental algorithms
Polynomial and matrix computations (vol. 1): fundamental algorithms
Simultaneous elimination by using several tools from real algebraic geometry
Journal of Symbolic Computation - Special issue on polynomial elimination—algorithms and applications
Polynomials and Linear Control Systems
Polynomials and Linear Control Systems
On computing polynomial GCDs in alternate bases
Proceedings of the 2006 international symposium on Symbolic and algebraic computation
Numerical optimization in hybrid symbolic-numeric computation
Proceedings of the 2007 international workshop on Symbolic-numeric computation
Block LU factorization of Hankel and Bezout matrices and Euclidean algorithm
International Journal of Computer Mathematics
Computing polynomial LCM and GCD in lagrange basis
ACM Communications in Computer Algebra
Computing multivariate approximate GCD based on Barnett's theorem
Proceedings of the 2009 conference on Symbolic numeric computation
Blind image deconvolution via fast approximate GCD
Proceedings of the 2010 International Symposium on Symbolic and Algebraic Computation
Multivariate resultants in Bernstein basis
ADG'08 Proceedings of the 7th international conference on Automated deduction in geometry
Root-finding by expansion with independent constraints
Computers & Mathematics with Applications
Recursive polynomial remainder sequence and the nested subresultants
CASC'05 Proceedings of the 8th international conference on Computer Algebra in Scientific Computing
Using Smith normal forms and µ-bases to compute all the singularities of rational planar curves
Computer Aided Geometric Design
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This article provides a new presentation of Barnett's theorems giving the degree (resp. coefficients) of the greatest common divisor of several univariate polynomials with coefficients in an integral domain by means of the rank (resp. linear dependencies of the columns) of several Bezout-like matrices. This new presentation uses Bezout or hybrid Bezout matrices instead of polynomials evaluated in a companion matrix as in the original Barnett's presentation. Moreover, this presentation also allows us to compute the coefficients of the considered greatest common divisor in an easier way than in the original Barnett's theorems.