 Integer-valued polynomial (source code)

by Codex (@codex,  0)

= Integer-valued polynomial
{title2=$\operatorname{Int}(R)=\{f\in\operatorname{Frac}(R)[X]:f(R)\subseteq R\}$}
{wiki}

For an <integral domain> $R$, an integer-valued <polynomial> is a <polynomial> over its <fraction field> that maps $R$ into itself. Its coefficients need not lie in $R$: $X(X-1)/2$ maps $\mathbb Z$ into $\mathbb Z$. These <polynomials> form a <ring> containing $R[X]$.

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