Absolutely irreducible

In mathematics, a multivariate polynomial defined over the rational numbers is absolutely irreducible if it is irreducible over the complex field. For example, ${\displaystyle x^{2}+y^{2}-1}$ is absolutely irreducible, but while ${\displaystyle x^{2}+y^{2}}$ is irreducible over the integers and the reals, it is reducible over the complex numbers as ${\displaystyle x^{2}+y^{2}=(x+iy)(x-iy),}$ and thus not absolutely irreducible.

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