Generator complexity: Difference between revisions
Wikispaces>genewardsmith **Imported revision 515965268 - Original comment: ** |
Wikispaces>genewardsmith **Imported revision 515965338 - Original comment: ** |
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<h2>IMPORTED REVISION FROM WIKISPACES</h2> | <h2>IMPORTED REVISION FROM WIKISPACES</h2> | ||
This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br> | This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br> | ||
: This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2014-07-10 12: | : This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2014-07-10 12:58:26 UTC</tt>.<br> | ||
: The original revision id was <tt> | : The original revision id was <tt>515965338</tt>.<br> | ||
: The revision comment was: <tt></tt><br> | : The revision comment was: <tt></tt><br> | ||
The revision contents are below, presented both in the original Wikispaces Wikitext format, and in HTML exactly as Wikispaces rendered it.<br> | The revision contents are below, presented both in the original Wikispaces Wikitext format, and in HTML exactly as Wikispaces rendered it.<br> | ||
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=STD complexity= | =STD complexity= | ||
If B = <0 B₃ B₅ B₇ ... Bp| is the generator mapping val in weighted coordinates, and P is the period, then the //STD complexity// (a term due to Graham Breed) is P STD(B), where "STD" means the standard | If B = <0 B₃ B₅ B₇ ... Bp| is the generator mapping val in weighted coordinates, and P is the period, then the //STD complexity// (a term due to Graham Breed) is P STD(B), where "STD" means the standard deviation. If m is the mean of the coordinates of B (including the 0) and J is the [[JIP]] <1 1 1 ... 1|, STD(B) is √(C∙C/n) where C = B - mJ, n is the number of primes in the p-limit, and the dot denotes the dot product.</pre></div> | ||
<h4>Original HTML content:</h4> | <h4>Original HTML content:</h4> | ||
<div style="width:100%; max-height:400pt; overflow:auto; background-color:#f8f9fa; border: 1px solid #eaecf0; padding:0em"><pre style="margin:0px;border:none;background:none;word-wrap:break-word;width:200%;white-space: pre-wrap ! important" class="old-revision-html"><html><head><title>Generator complexity</title></head><body><!-- ws:start:WikiTextTocRule:6:&lt;img id=&quot;wikitext@@toc@@flat&quot; class=&quot;WikiMedia WikiMediaTocFlat&quot; title=&quot;Table of Contents&quot; src=&quot;/site/embedthumbnail/toc/flat?w=100&amp;h=16&quot;/&gt; --><!-- ws:end:WikiTextTocRule:6 --><!-- ws:start:WikiTextTocRule:7: --><a href="#Definition">Definition</a><!-- ws:end:WikiTextTocRule:7 --><!-- ws:start:WikiTextTocRule:8: --> | <a href="#Generator complexity and Kees expressibility">Generator complexity and Kees expressibility</a><!-- ws:end:WikiTextTocRule:8 --><!-- ws:start:WikiTextTocRule:9: --> | <a href="#STD complexity">STD complexity</a><!-- ws:end:WikiTextTocRule:9 --><!-- ws:start:WikiTextTocRule:10: --> | <div style="width:100%; max-height:400pt; overflow:auto; background-color:#f8f9fa; border: 1px solid #eaecf0; padding:0em"><pre style="margin:0px;border:none;background:none;word-wrap:break-word;width:200%;white-space: pre-wrap ! important" class="old-revision-html"><html><head><title>Generator complexity</title></head><body><!-- ws:start:WikiTextTocRule:6:&lt;img id=&quot;wikitext@@toc@@flat&quot; class=&quot;WikiMedia WikiMediaTocFlat&quot; title=&quot;Table of Contents&quot; src=&quot;/site/embedthumbnail/toc/flat?w=100&amp;h=16&quot;/&gt; --><!-- ws:end:WikiTextTocRule:6 --><!-- ws:start:WikiTextTocRule:7: --><a href="#Definition">Definition</a><!-- ws:end:WikiTextTocRule:7 --><!-- ws:start:WikiTextTocRule:8: --> | <a href="#Generator complexity and Kees expressibility">Generator complexity and Kees expressibility</a><!-- ws:end:WikiTextTocRule:8 --><!-- ws:start:WikiTextTocRule:9: --> | <a href="#STD complexity">STD complexity</a><!-- ws:end:WikiTextTocRule:9 --><!-- ws:start:WikiTextTocRule:10: --> | ||
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<!-- ws:start:WikiTextHeadingRule:4:&lt;h1&gt; --><h1 id="toc2"><a name="STD complexity"></a><!-- ws:end:WikiTextHeadingRule:4 -->STD complexity</h1> | <!-- ws:start:WikiTextHeadingRule:4:&lt;h1&gt; --><h1 id="toc2"><a name="STD complexity"></a><!-- ws:end:WikiTextHeadingRule:4 -->STD complexity</h1> | ||
If B = &lt;0 B₃ B₅ B₇ ... Bp| is the generator mapping val in weighted coordinates, and P is the period, then the <em>STD complexity</em> (a term due to Graham Breed) is P STD(B), where &quot;STD&quot; means the standard | If B = &lt;0 B₃ B₅ B₇ ... Bp| is the generator mapping val in weighted coordinates, and P is the period, then the <em>STD complexity</em> (a term due to Graham Breed) is P STD(B), where &quot;STD&quot; means the standard deviation. If m is the mean of the coordinates of B (including the 0) and J is the <a class="wiki_link" href="/JIP">JIP</a> &lt;1 1 1 ... 1|, STD(B) is √(C∙C/n) where C = B - mJ, n is the number of primes in the p-limit, and the dot denotes the dot product.</body></html></pre></div> | ||