Fields of algebraic numbers computable in polynomial time. I

DOI10.1007/s10469-020-09565-0zbMath1484.03058OpenAlexW3009523158WikidataQ114691257 ScholiaQ114691257MaRDI QIDQ784464

P. E. Alaev, Victor L. Selivanov

Publication date: 3 August 2020

Published in: Algebra and Logic (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s10469-020-09565-0

zbMATH Keywords

field of complex algebraic numbersordered field of real algebraic numberspolynomially computable presentation

Mathematics Subject Classification ID

Number-theoretic algorithms; complexity (11Y16) Algebraic numbers; rings of algebraic integers (11R04) Model theory (number-theoretic aspects) (11U09) Computable structure theory, computable model theory (03C57) Theory of numerations, effectively presented structures (03D45)

Related Items (10)

Fields of algebraic numbers computable in polynomial time. II ⋮ Generalization of the subset sum problem and cubic forms ⋮ A criterion for P-computability of structures ⋮ The complexity of inversion in groups ⋮ Polynomially computable structures with finitely many generators ⋮ Primitive recursive ordered fields and some applications ⋮ Heuristic algorithms for recognition of some cubic hypersurfaces ⋮ Finitely generated structures computable in polynomial time ⋮ Quotient structures and groups computable in polynomial time ⋮ Searching for applicable versions of computable structures

Cites Work

• Existence and uniqueness of structures computable in polynomial time
• Factoring polynomials with rational coefficients
• Polynomial algorithms in computer algebra
• Structures computable in polynomial time. I
• On the degree of extensions generated by finitely many algebraic numbers
• Theorie Der Numerierungen III
• Computable Algebra, General Theory and Theory of Computable Fields
• The Calculation of Multivariate Polynomial Resultants
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