Constructive Algebra

Harold M. Edwards

Chapter Chapter 6 in Essays in Constructive Mathematics, 2022, pp 205-212 from Springer

Abstract: Abstract The first essay of this chapter introduces c-fields, which are built from the rational numbers $$\mathbf {Q}$$ Q by a finite sequence of algebraic or transcendental adjunctions. One knows how to represent quantities in c-fields, how to determine if two representations are equal, and how to perform the four field operations of rational computation, i.e., rational arithmetic. The definitions and constructions of c-fields provide a lan guage in which the theorems and proofs of the subsequent chapters can be stated and proved constructively. The second essay describes an algorithm for irreducible factorization of univariate polynomials with coefficients in a c-field based on methods introduced in earlier essays. The final essay discusses the role of algorithms.

Date: 2022
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DOI: 10.1007/978-3-030-98558-5_6

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