Primitive recursive ordered fields and some applications

We establish primitive recursive (PR) versions of some known facts about computable ordered fields reals and reals, apply them to prove recursiveness several important problems in linear algebra analysis. One the central results this paper is a partial PR analogue Ershov–Madison’s theorem real closures fields. It allows us, particular, obtain root-finding algorithms algebraic with certain property (PR splitting). also relate corresponding as well introduce study notion metric space. enables us derive sufficient conditions for computing normal forms matrices solution operators symmetric hyperbolic systems PDEs. The methods represent mix symbolic approximate algorithms.