Towards faster real algebraic numbers

Authors:
Renaud Rioboo
Affiliations:
Laboratoire d'Informatique de Paris 6 (LIP6) Université Pierre et Marie Curie (Paris 6) 8, rue du, Capitaine Scott F-75015 Paris, France
Venue:
Proceedings of the 2002 international symposium on Symbolic and algebraic computation
Year:
2002

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Abstract

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 algorithms. This allows us to work in the ring of real algebraic integers instead of the field of real algebraic numbers avoiding many denominators.