Computer algebra: symbolic and algebraic computation (2nd ed.)
Journal of Symbolic Computation
On the combinatorial and algebraic complexity of quantifier elimination
Journal of the ACM (JACM)
Generic computation of the real closure of an ordered field
Selected papers presented at the international IMACS symposium on Symbolic computation, new trends and developments
Dynamic evaluation and real closure
Selected papers presented at the international IMACS symposium on Symbolic computation, new trends and developments
Computing in the field of complex algebraic numbers
Journal of Symbolic Computation - Special issue: validated numerical methods and computer algebra
New structure theorem for subresultants
Journal of Symbolic Computation - Special issue on symbolic computation in algebra, analysis and geometry
Sylvester—Habicht sequences and fast Cauchy index computation
Journal of Symbolic Computation
Polynomial Gcd Computations over Towers of Algebraic Extensions
AAECC-11 Proceedings of the 11th International Symposium on Applied Algebra, Algebraic Algorithms and Error-Correcting Codes
About a New Method for Computing in Algebraic Number Fields
EUROCAL '85 Research Contributions from the European Conference on Computer Algebra-Volume 2
Univariate real root isolation in an extension field
Proceedings of the 36th international symposium on Symbolic and algebraic computation
The diamond operator: implementation of exact real algebraic numbers
CASC'05 Proceedings of the 8th international conference on Computer Algebra in Scientific Computing
Univariate real root isolation in multiple extension fields
Proceedings of the 37th International Symposium on Symbolic and Algebraic Computation
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This paper presents a new encoding scheme for real algebraic number manipulations which enhances current Axiom's real closure. Algebraic manipulations are performed using different instantiations of sub-resultant-like algorithms instead of Euclidean-like algorithms. We use these algorithms to compute polynomial gcds and Bezout relations, to compute the roots and the signs of algebraic numbers. This allows us to work in the ring of real algebraic integers instead of the field of real algebraic numbers avoiding many denominators.