Hahn distance: Difference between revisions
Wikispaces>genewardsmith **Imported revision 357266516 - Original comment: ** |
Wikispaces>genewardsmith **Imported revision 357266856 - 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>2012-08-10 22: | : This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2012-08-10 22:11:18 UTC</tt>.<br> | ||
: The original revision id was <tt> | : The original revision id was <tt>357266856</tt>.<br> | ||
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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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In the 13-limit the formula for Hahn distance can be given as | In the 13-limit the formula for Hahn distance can be given as | ||
[[math]] | [[math]] | ||
|| | | || |x_1\ x_2\ x_3\ x_4\ x_5\ x_6> ||_{hahn} = (|y|+|x_3|+|x_4|+|x_5|+|x_6|+|y+x_3+x_4+x_5+x_6|)/2 | ||
[[math]] | [[math]] | ||
where y = signum(x2)ceil(|x2/2|); here "signum" is +1 or -1 depending on the sign of x2 and "ceil" is the ceiling function. Hahn distance for the 5, 7, 9 or 11 limit can all be found from this formula also. </pre></div> | where y = signum(x2)ceil(|x2/2|); here "signum" is +1 or -1 depending on the sign of x2 and "ceil" is the ceiling function. Hahn distance for the 5, 7, 9 or 11 limit can all be found from this formula also. </pre></div> | ||
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<!-- ws:start:WikiTextMathRule:3: | <!-- ws:start:WikiTextMathRule:3: | ||
[[math]]&lt;br/&gt; | [[math]]&lt;br/&gt; | ||
|| | | || |x_1\ x_2\ x_3\ x_4\ x_5\ x_6&gt; ||_{hahn} = (|y|+|x_3|+|x_4|+|x_5|+|x_6|+|y+x_3+x_4+x_5+x_6|)/2&lt;br/&gt;[[math]] | ||
--><script type="math/tex">|| | | --><script type="math/tex">|| |x_1\ x_2\ x_3\ x_4\ x_5\ x_6> ||_{hahn} = (|y|+|x_3|+|x_4|+|x_5|+|x_6|+|y+x_3+x_4+x_5+x_6|)/2</script><!-- ws:end:WikiTextMathRule:3 --><br /> | ||
where y = signum(x2)ceil(|x2/2|); here &quot;signum&quot; is +1 or -1 depending on the sign of x2 and &quot;ceil&quot; is the ceiling function. Hahn distance for the 5, 7, 9 or 11 limit can all be found from this formula also.</body></html></pre></div> | where y = signum(x2)ceil(|x2/2|); here &quot;signum&quot; is +1 or -1 depending on the sign of x2 and &quot;ceil&quot; is the ceiling function. Hahn distance for the 5, 7, 9 or 11 limit can all be found from this formula also.</body></html></pre></div> | ||