@inproceedings{86d76e5fd0d945599f407b5a8d34e6b4,

title = "Polynomial-time presentations of algebraic number fields",

abstract = "Using an extension of the notion of polynomial time presentable structure we show that some natural presentations of the ordered field ℝalg of algebraic reals and of the field ℂalg of algebraic complex numbers are polynomial-time equivalent to each other and are polynomial time. We also establish upper complexity bounds for the problem of rational polynomial evaluation in ℂalg and for the problem of root-finding for polynomials in ℂalg[x] which improve the previously known bound.",

keywords = "Algebraic number, Complexity bound, Ordered field, Polynomial, Polynomial-time presentable structure",

author = "Pavel Alaev and Victor Selivanov",

year = "2018",

month = jan,

day = "1",

doi = "10.1007/978-3-319-94418-0_2",

language = "English",

isbn = "9783319944173",

series = "Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)",

publisher = "Springer-Verlag GmbH and Co. KG",

pages = "20--29",

editor = "F Manea and RG Miller and D Nowotka",

booktitle = "Sailing Routes in the World of Computation - 14th Conference on Computability in Europe, CiE 2018, Proceedings",

address = "Germany",

note = "14th Conference on Computability in Europe, CiE 2018 ; Conference date: 30-07-2018 Through 03-08-2018",

}