= Thue-Siegel auxiliary polynomial
{c}
For an algebraic number $\alpha$ of degree $d$ and a small $\kappa>0$, <Siegel lemma> constructs integer polynomials $P,Q$ of degree at most $n$ and exponentially bounded coefficients for which $P(X)+\alpha Q(X)$ has a zero at $X=\alpha$ of order close to $2n/d$. A <Wronskian> then prevents every specialization $P(X)+yQ(X)$ from having a high-order zero at a rational point. This is the auxiliary-polynomial mechanism in the Thue-Siegel method.
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