 Hilbert subset (source code)

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= Hilbert subset
{c}
{title2=$H_K(f_1,\ldots,f_r;h)$}

= Hilbert set
{c}
{synonym}

For a finite family of irreducible separable <polynomials> $f_i(T,X)$ and a nonzero exclusion <polynomial> $h(T)$, this is the set of parameters $a\in K$ with $h(a)\ne0$ for which every specialization remains irreducible of its original degree. A <Hilbertian field> has infinitely many points in each such set. Denominators, leading coefficients and discriminants can be included in $h$.

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