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

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

T2 - computability in europe, 2018

Y2 - 30 July 2018

ER -