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On the Field Isomorphism Problem for the Family of Simplest Quartic Fields
Deciding whether or not two polynomials have isomoprhic splitting fields over the rationals is the Field Isomorphism Problem. We consider polynomials of the form $f_n(x) = x^4-nx^3-6x^2+nx+1$ with $n \neq 3$ a positive integer and we let $K_n$ denote the splitting field of $f_n(x)$; a `simplest quartic field'. Our main …