Factoring Polynomials over Algebraic Number Fields

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  • Affiliations:

  • Venue:
  • SIAM Journal on Computing
  • Year:
  • 2011

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Abstract

We show that if $f(x)$ is a polynomial in $Z [ \alpha ][ x ]$, where $\alpha $ satisfies a monic irreducible polynomial over $Z$, then $f(x)$ can be factored over $Q(\alpha )[ x ]$ in polynomial time. We also show that the splitting field of $f(x)$ can be determined in time polynomial in ([Splitting field of $f(x): Q $], $\log | (x) |$).