Resolvent computations by resultants without extraneous powers
ISSAC '97 Proceedings of the 1997 international symposium on Symbolic and algebraic computation
Deformation techniques for efficient polynomial equation solving
Journal of Complexity
Using Galois ideals for computing relative resolvents
Journal of Symbolic Computation - Algorithmic methods in Galois Theory
A Gröbner free alternative for polynomial system solving
Journal of Complexity
Proceedings of the 2001 international symposium on Symbolic and algebraic computation
Modern Computer Algebra
Fast arithmetic for triangular sets: From theory to practice
Journal of Symbolic Computation
Fast arithmetics in artin-schreier towers over finite fields
Proceedings of the 2009 international symposium on Symbolic and algebraic computation
Computations modulo regular chains
Proceedings of the 2009 international symposium on Symbolic and algebraic computation
Polynomial evaluation and interpolation on special sets of points
Journal of Complexity - Festschrift for the 70th birthday of Arnold Schönhage
Fast computation of special resultants
Journal of Symbolic Computation
Proceedings of the 36th international symposium on Symbolic and algebraic computation
Algebraic computation of resolvents without extraneous powers
European Journal of Combinatorics
Fast algorithms for l-adic towers over finite fields
Proceedings of the 38th international symposium on International symposium on symbolic and algebraic computation
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Let k be a field and let f ∈ k [T] be a polynomial of degree n. The universal decomposition algebra A is the quotient of k [X1,...,Xn] by the ideal of symmetric relations (those polynomials that vanish on all permutations of the roots of f). We show how to obtain efficient algorithms to compute in A. We use a univariate representation of A, i.e. an isomorphism of the form A k[T]/Q(T), since in this representation, arithmetic operations in A are known to be quasi-optimal. We give details for two related algorithms, to find the isomorphism above, and to compute the characteristic polynomial of any element of A.