A copy of this work was available on the public web and has been preserved in the Wayback Machine. The capture dates from 2020; you can also visit <a rel="external noopener" href="https://arxiv.org/pdf/0911.1340v1.pdf">the original URL</a>. The file type is <code>application/pdf</code>.
Bounding the radii of balls meeting every connected component of semi-algebraic sets
[article]
<span title="2009-11-06">2009</span>
<i >
arXiv
</i>
<span class="release-stage" >pre-print</span>
Preserved Fulltext
We prove explicit bounds on the radius of a ball centered at the origin which is guaranteed to contain all bounded connected components of a semi-algebraic set S ⊂R^k defined by a quantifier-free formula involving s polynomials in Z[X_1, ..., X_k] having degrees at most d, and whose coefficients have bitsizes at most τ. Our bound is an explicit function of s, d, k and τ, and does not contain any undetermined constants. We also prove a similar bound on the radius of a ball guaranteed to
<span class="external-identifiers">
<a target="_blank" rel="external noopener" href="https://arxiv.org/abs/0911.1340v1">arXiv:0911.1340v1</a>
<a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/gievc3lrunfy5mi7bobe33kqte">fatcat:gievc3lrunfy5mi7bobe33kqte</a>
</span>
more »
... every connected component of S (including the unbounded components). While asymptotic bounds of the form 2^τ d^O (k) on these quantities were known before, some applications require bounds which are explicit and which hold for all values of s, d, k and τ. The bounds proved in this paper are of this nature.
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20200825120203/https://arxiv.org/pdf/0911.1340v1.pdf" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext">
<button class="ui simple right pointing dropdown compact black labeled icon button serp-button">
<i class="icon ia-icon"></i>
Web Archive
[PDF]
<div class="menu fulltext-thumbnail">
<img src="https://blobs.fatcat.wiki/thumbnail/pdf/cf/d2/cfd2276406dec2ab1f9dc9f26a2f4b71b42ccdf0.180px.jpg" alt="fulltext thumbnail" loading="lazy">
</div>
</button>
</a>
<a target="_blank" rel="external noopener" href="https://arxiv.org/abs/0911.1340v1" title="arxiv.org access">
<button class="ui compact blue labeled icon button serp-button">
<i class="file alternate outline icon"></i>
arxiv.org
</button>
</a>