A Fundamental Theorem

Harold M. Edwards

Chapter Chapter 1 in Essays in Constructive Mathematics, 2022, pp 13-45 from Springer

Abstract: Abstract The fundamental theorem of this chapter constructs a splitting field for a given polynomial. Stated differently, for polynomials whose coefficients are integer polynomials in finitely many indeterminates, computation is extended in such a way that the given polynomial can be written as a product of linear factors. The construction begins with the notion of a root field of an irreducible polynomial and requires an algorithmic solution of the factorization problem. The end result is a theorem that deserves the name Fundamental Theorem of Algebra more than the usual version stated over the complex numbers.

Date: 2022
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DOI: 10.1007/978-3-030-98558-5_1

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