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  "path": "/abs/2605.07784v1",
  "publishedAt": "2026-05-11T00:00:00.000Z",
  "site": "https://arxiv.org",
  "tags": [
    "George Labahn",
    "Arne Storjohann"
  ],
  "textContent": "**Authors:** George Labahn, Arne Storjohann\n\nGiven a full column rank $M \\in \\Z^{\\ell \\times m}$ and an $F \\in \\Z^{n \\times m}$ we present an algorithm to compute the $n \\times n$ basis in Hermite form of the integer lattice comprised of all rows $p \\in \\Z^{1 \\times n}$ such that $pF \\in \\Z^{1 \\times m}$ is in the integer lattice generated by the rows of $M$. The algorithm is randomized of the Las Vegas type, that is, it can fail with probability at most $1/2$, but if fail is not returned it guarantees to produce the correct result. When $M$ is square and $F=I_m$, then the computed basis is the Hermite normal form of $M$, and the algorithm uses about the same number of bit operations as required to multiply together two matrices of the same dimension and size of entries as $M$.",
  "title": "Computing bases in Hermite normal form of lattices of integer relations"
}