Decreasing the nesting depth of expressions involving square roots
Journal of Symbolic Computation
Simplification of expressions involving radicals
Journal of Symbolic Computation
Detecting algebraic dependencies between unnested radicals (extended abstract)
ISSAC '90 Proceedings of the international symposium on Symbolic and algebraic computation
Simplification of nested radicals
SIAM Journal on Computing
A course in computational algebraic number theory
A course in computational algebraic number theory
Lattices and Factorization of Polynomials over Algebraic Number Fields
EUROCAM '82 Proceedings of the European Computer Algebra Conference on Computer Algebra
Factoring polynominals over algebraic number fields
EUROCAL '83 Proceedings of the European Computer Algebra Conference on Computer Algebra
Algebraic factoring and rational function integration
SYMSAC '76 Proceedings of the third ACM symposium on Symbolic and algebraic computation
Simplification of radical expressions
SYMSAC '76 Proceedings of the third ACM symposium on Symbolic and algebraic computation
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Based on a criterion due to Kneser, we present new results for the degree of field extensions generated by finitely many radicals. We also improve an algorithm given by Zippel for computing a basis for such an extension field. This algorithm may be effectively used by computer algebra systems to normalize expressions involving radicals.