Convex scale: Difference between revisions

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<h2>IMPORTED REVISION FROM WIKISPACES</h2>

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>2011-10-19 15:46:56 UTC</tt>.<br>

: This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2011-10-19 15:48:45 UTC</tt>.<br>

: The original revision id was <tt>~~266530210~~</tt>.<br>

: The original revision id was <tt>266530940</tt>.<br>

: The revision comment was: <tt></tt><br>

: The revision comment was: <tt>Reverted to Oct 19, 2011 12:27 pm</tt><br>

The revision contents are below, presented both in the original Wikispaces Wikitext format, and in HTML exactly as Wikispaces rendered it.<br>

<h4>Original Wikitext content:</h4>

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$b = d_1 a_1 + d_2 a_2 + \dots + d_k a_k$

[[math]]

where $d_i = c_i/c$. Note that while the coefficients $d_i$ are allowed to be positive rational numbers (now summing to 1), b is still an integral vector, ie an n-tuple of integers.

where d_i = c_i/c. Note that while the coefficients d_i are allowed to be positive rational numbers (now summing to 1), b is still an integral vector, ie an n-tuple of integers.

===Convex set===

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$b = d_1 a_1 + d_2 a_2 + \dots + d_k a_k$&lt;br/&gt;[[math]]

--><script type="math/tex">$b = d_1 a_1 + d_2 a_2 + \dots + d_k a_k$</script><br />

where $d_i = c_i/c$. Note that while the coefficients $d_i$ are allowed to be positive rational numbers (now summing to 1), b is still an integral vector, ie an n-tuple of integers.<br />

where d_i = c_i/c. Note that while the coefficients d_i are allowed to be positive rational numbers (now summing to 1), b is still an integral vector, ie an n-tuple of integers.<br />

<br />

<h3 id="toc2"><a name="x-Formal definition-Convex set"></a>Convex set</h3>

@@ Line 1: / Line 1: @@
 <h2>IMPORTED REVISION FROM WIKISPACES</h2>
 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>2011-10-19 15:46:56 UTC</tt>.<br>
+: This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2011-10-19 15:48:45 UTC</tt>.<br>
-: The original revision id was <tt>266530210</tt>.<br>
+: The original revision id was <tt>266530940</tt>.<br>
-: The revision comment was: <tt></tt><br>
+: The revision comment was: <tt>Reverted to Oct 19, 2011 12:27 pm</tt><br>
 The revision contents are below, presented both in the original Wikispaces Wikitext format, and in HTML exactly as Wikispaces rendered it.<br>
 <h4>Original Wikitext content:</h4>
@@ Line 29: / Line 29: @@
 $b = d_1 a_1 + d_2 a_2 + \dots + d_k a_k$
 [[math]]
-where $d_i = c_i/c$. Note that while the coefficients $d_i$ are allowed to be positive rational numbers (now summing to 1), b is still an integral vector, ie an n-tuple of integers.
+where d_i = c_i/c. Note that while the coefficients d_i are allowed to be positive rational numbers (now summing to 1), b is still an integral vector, ie an n-tuple of integers.
 ===Convex set===
@@ Line 67: / Line 67: @@
 $b = d_1 a_1 + d_2 a_2 + \dots + d_k a_k$&amp;lt;br/&amp;gt;[[math]]
   --&gt;&lt;script type="math/tex"&gt;$b = d_1 a_1 + d_2 a_2 + \dots + d_k a_k$&lt;/script&gt;&lt;!-- ws:end:WikiTextMathRule:2 --&gt;&lt;br /&gt;
-where $d_i = c_i/c$. Note that while the coefficients $d_i$ are allowed to be positive rational numbers (now summing to 1), b is still an integral vector, ie an n-tuple of integers.&lt;br /&gt;
+where d_i = c_i/c. Note that while the coefficients d_i are allowed to be positive rational numbers (now summing to 1), b is still an integral vector, ie an n-tuple of integers.&lt;br /&gt;
 &lt;br /&gt;
 &lt;!-- ws:start:WikiTextHeadingRule:7:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc2"&gt;&lt;a name="x-Formal definition-Convex set"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:7 --&gt;Convex set&lt;/h3&gt;