Computability in Europe 2006
Logical Approaches to Computational Barriers 

Regular Talk:

Speaker:  Peter Peshev 
Author(s):  Peter Peshev and Dimiter Skordev 
Presentation:  FTA20MIN.pdf 
Slot:  Tue, 15:1015:30, Faraday D (col. 4) 
A proof by P. C. Rosenbloom of the fundamental theorem of algebra is used in the paper for obtaining a subrecursive refinement of the theorem. Arbitrary complex numbers are supposed to be represented as limits of such sequences of rational ones that the distance between the nth term of the sequence and its limit is not greater than the reciprocal of n+1. In the case when polynomials of a fixed degree are considered, we show the existence of computable operators that belong to the second Grzegorczyk class and transform any representations of the coefficients of any monic polynomial into representations of its roots.