Factoring polynomials over function fields Article Swipe

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José Felipe Voloch ·

YOU? · · 2021 · Open Access · · DOI: https://doi.org/10.48550/arxiv.2107.09865 · OA: W4309794152

If K/k is a function field in one variable of positive characteristic, we describe a general algorithm to factor one-variable polynomials with coefficients in K. The algorithm is flexible enough to find factors subject to additional restrictions, e.g., to find all roots that belong to a given finite dimensional k-subspace of K more efficiently. It also provides a deterministic polynomial time irreducibility test in small characteristic. We also discuss some applications.