_fmpz_poly_factor_inflation_is_irreducible_capelli

By Capelli's theorem, for prime $p$ the polynomial $T(x^p)$ is irreducible over $\mathbb{Q}$ if and only if $\theta$, the image of $x$ in $K = \mathbb{Q}[x]/(T)$, is not a $p$-th power in $K$. For $\deg T = 1$, and for $\deg T = 2$ with $p = 2$, this is decided exactly (the return value is 1 precisely when $T(x^p)$ is irreducible). Otherwise the function searches for a rational prime $q$, with $T$ squarefree modulo $q$ and $q$ dividing neither the leading nor the constant coefficient of $T$, such that $\theta$ reduces to a non-$p$-th power in some residue field of $K$ above $q$, which is detected with Euler's criterion $\theta^{(q^f - 1)/p} \ne 1$ in a residue field of degree $f$; any such witness proves $\theta \notin K^p$. The search budget is linear in $\deg T$ (for inputs with abelian splitting fields of exponent $p$, such as deflations of Swinnerton-Dyer polynomials, witnesses have density only $1/(p \deg T)$ among the primes and occur only in degree-1 residue fields), and the search stops early when the accumulated local evidence makes irreducibility unlikely.