Результаты исследований: Публикации в книгах, отчётах, сборниках, трудах конференций › статья в сборнике материалов конференции › научная › Рецензирование
Polynomial-time presentations of algebraic number fields. / Alaev, Pavel; Selivanov, Victor.
Sailing Routes in the World of Computation - 14th Conference on Computability in Europe, CiE 2018, Proceedings. ред. / F Manea; RG Miller; D Nowotka. Springer, 2018. стр. 20-29 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Том 10936 LNCS).Результаты исследований: Публикации в книгах, отчётах, сборниках, трудах конференций › статья в сборнике материалов конференции › научная › Рецензирование
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TY - GEN
T1 - Polynomial-time presentations of algebraic number fields
AU - Alaev, Pavel
AU - Selivanov, Victor
PY - 2018/1/1
Y1 - 2018/1/1
N2 - 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.
AB - 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.
KW - Algebraic number
KW - Complexity bound
KW - Ordered field
KW - Polynomial
KW - Polynomial-time presentable structure
UR - http://www.scopus.com/inward/record.url?scp=85051111244&partnerID=8YFLogxK
U2 - 10.1007/978-3-319-94418-0_2
DO - 10.1007/978-3-319-94418-0_2
M3 - Conference contribution
AN - SCOPUS:85051111244
SN - 9783319944173
T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
SP - 20
EP - 29
BT - Sailing Routes in the World of Computation - 14th Conference on Computability in Europe, CiE 2018, Proceedings
A2 - Manea, F
A2 - Miller, RG
A2 - Nowotka, D
PB - Springer
T2 - 14th Conference on Computability in Europe, CiE 2018
Y2 - 30 July 2018 through 3 August 2018
ER -
ID: 16113332