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arXiv · 1710.06396

On the bit-size of non-radical triangular sets

Xavier Dahan
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Abstract

We present upper bounds on the bit-size of coefficients of non-radical lexicographical Groebner bases in purely triangular form (triangular sets) of dimension zero. This extends a previous work [Dahan-Schost, Issac'2004], constrained to radical triangular sets; it follows the same technical steps, based on interpolation. However, key notion of height of varieties is not available for points with multiplicities; therefore the bounds obtained are less universal and depend on some input data. We also introduce a related family of non- monic polynomials that have smaller coefficients, and smaller bounds. It is not obvious to compute them from the initial triangular set though.

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Xavier Dahan. 2017-10-17. On the bit-size of non-radical triangular sets. https://arxiv.org/abs/1710.06396

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