Geodesic
Fields of algebraic numbers computable in polynomial time. I
Algebra i logika, Tome 58 (2019) no. 6, pp. 673-705

Voir la notice de l'article provenant de la source Math-Net.Ru

It is proved that the field of complex algebraic numbers has an isomorphic presentation computable in polynomial time. A similar fact is proved for the ordered field of real algebraic numbers. The constructed polynomially computable presentations are based on a natural presentation of algebraic numbers via rational polynomials. Also new algorithms for computing values of polynomials on algebraic numbers and for solving equations in one variable with algebraic coefficients are presented.
Keywords: field of complex algebraic numbers, ordered field of real algebraic numbers, polynomially computable presentation. 
@article{AL_2019_58_6_a0,
     author = {P. E. Alaev and V. L. Selivanov},
     title = {Fields of algebraic numbers computable in polynomial time. {I}},
     journal = {Algebra i logika},
     pages = {673--705},
     publisher = {mathdoc},
     volume = {58},
     number = {6},
     year = {2019},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/AL_2019_58_6_a0/}
}
TY  - JOUR
AU  - P. E. Alaev
AU  - V. L. Selivanov
TI  - Fields of algebraic numbers computable in polynomial time. I
JO  - Algebra i logika
PY  - 2019
SP  - 673
EP  - 705
VL  - 58
IS  - 6
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/AL_2019_58_6_a0/
LA  - ru
ID  - AL_2019_58_6_a0
ER  - 
%0 Journal Article
%A P. E. Alaev
%A V. L. Selivanov
%T Fields of algebraic numbers computable in polynomial time. I
%J Algebra i logika
%D 2019
%P 673-705
%V 58
%N 6
%I mathdoc
%U http://geodesic.mathdoc.fr/item/AL_2019_58_6_a0/
%G ru
%F AL_2019_58_6_a0
P. E. Alaev; V. L. Selivanov. Fields of algebraic numbers computable in polynomial time. I. Algebra i logika, Tome 58 (2019) no. 6, pp. 673-705. http://geodesic.mathdoc.fr/item/AL_2019_58_6_a0/