Colton Pauderis

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The asymptotically fastest algorithms for many linear algebra problems on integer matrices, including solving a system of linear equations and computing the determinant, use high-order lifting. Currently, high-order lifting requires the use of a randomized shifted number system to detect and avoid error-producing carries. By interleaving quadratic and(More)
We present a new heuristic algorithm for computing the determinant of a nonsingular <i>n</i> x <i>n</i> integer matrix. Extensive empirical results from a highly optimized implementation show the running time grows approximately as <i>n</i><sup>3</sup> log <i>n</i>, even for input matrices with a highly nontrivial Smith invariant structure. We extend the(More)
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