Before being mortally wounded in a duel at age 20, Évariste Galois discovered the hidden structure of polynomial equations. By studying the relationships between their solutions — rather than the ...
For a computable field F, the splitting set S is the set of polynomials p(X) ∈ F[X] which factor over F, and the root set R is the set of polynomials with roots in F. Work by Frohlich and Shepherdson ...
The basic facts about separable extensions of discrete fields and factoring polynomials are developed in the constructive spirit of Errett Bishop. The ability to factor polynomials is shown to be ...
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