Computing minimal nullspace bases

  title={Computing minimal nullspace bases},
  author={Wei Zhou and George Labahn and Arne Storjohann},
In this paper we present a deterministic algorithm for the computation of a minimal nullspace basis of an <i>m</i> x <i>n</i> input matrix of univariate polynomials over a field K with <i>m</i> ≤ <i>n</i>. This algorithm computes a minimal nullspace basis of a degree <i>d</i> input matrix with a cost of <i>O</i>~ (<i>n</i><sub>ω</sub> ⌈<i>md</i>/<i>n</i>⌉) field operations in K. Here the soft-<i>O</i> notation is Big-<i>O</i> with log factors removed while ω is the exponent of matrix… 
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