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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>2011-06-25 16:39:27 UTC</tt>.<br>

: This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2011-06-25 16:44:54 UTC</tt>.<br>

: The original revision id was <tt>~~238731837~~</tt>.<br>

: The original revision id was <tt>238732299</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>

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* Take the transpose of the pseudoinverse of V, call that U

* Find a basis for the commas of V

* For each row of U, clear denominators and append the monzos of the comma basis for V

* For each row U[i] of U, clear denominators and append the monzos of the comma basis for V

* Saturate the result to a list of monzos, call that S

* Apply ~~each~~ val of V (dot product) to S

* Apply the ith val V[i] (dot product) to each element of S

* Insert V.S[i] in front of S[i] as the first element, obtaining a modified list T

* Insert V[i].S[j] in front of the elements of S[j] as the first element, obtaining a modified list T

* Hermite reduce the modified list T, take the first row, and remove the first element (which should be a 1.)

* Consider the rest to be a monzo, which may be converted to a rational number if you prefer

* This is the corresponding transveral generator to the ith val of V; it may be reduced to an equivalent generator of minimal Tenney height by multiplying by the commas of V

* This is the corresponding transveral generator to the ith val V[i] of V; it may be reduced to an equivalent generator of minimal Tenney height by multiplying by the commas of V

*</pre></div>

</pre></div>

<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>Transversal generators</title></head><body><a href="#Definition">Definition</a> | <a href="#Examples">Examples</a> | <a href="#Finding the transversal generators">Finding the transversal generators</a>

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We can find transveral generators for V by the following procedure:<br />

<br />

<ul><li>Take the transpose of the pseudoinverse of V, call that U</li><li>Find a basis for the commas of V</li><li>For each row of U, clear denominators and append the monzos of the comma basis for V</li><li>Saturate the result to a list of monzos, call that S</li><li>Apply ~~each~~ val of V (dot product) to S</li><li>Insert V.S[i] in front of S[i] as the first element, obtaining a modified list T</li><li>Hermite reduce the modified list T, take the first row, and remove the first element (which should be a 1.)</li><li>Consider the rest to be a monzo, which may be converted to a rational number if you prefer</li><li>This is the corresponding transveral generator to the ith val of V; it may be reduced to an equivalent generator of minimal Tenney height by multiplying by the commas of V</li></ul>*</body></html></pre></div>

<ul><li>Take the transpose of the pseudoinverse of V, call that U</li><li>Find a basis for the commas of V</li><li>For each row U[i] of U, clear denominators and append the monzos of the comma basis for V</li><li>Saturate the result to a list of monzos, call that S</li><li>Apply the ith val V[i] (dot product) to each element of S</li><li>Insert V[i].S[j] in front of the elements of S[j] as the first element, obtaining a modified list T</li><li>Hermite reduce the modified list T, take the first row, and remove the first element (which should be a 1.)</li><li>Consider the rest to be a monzo, which may be converted to a rational number if you prefer</li><li>This is the corresponding transveral generator to the ith val V[i] of V; it may be reduced to an equivalent generator of minimal Tenney height by multiplying by the commas of V</li></ul></body></html></pre></div>

@@ 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>2011-06-25 16:39:27 UTC</tt>.<br>
+: This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2011-06-25 16:44:54 UTC</tt>.<br>
-: The original revision id was <tt>238731837</tt>.<br>
+: The original revision id was <tt>238732299</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>
@@ Line 33: / Line 33: @@
 * Take the transpose of the pseudoinverse of V, call that U
 * Find a basis for the commas of V
-* For each row of U, clear denominators and append the monzos of the comma basis for V
+* For each row U[i] of U, clear denominators and append the monzos of the comma basis for V
 * Saturate the result to a list of monzos, call that S
-* Apply each val of V (dot product) to S
+* Apply the ith val V[i] (dot product) to each element of S
-* Insert V.S[i] in front of S[i] as the first element, obtaining a modified list T
+* Insert V[i].S[j] in front of the elements of S[j] as the first element, obtaining a modified list T
 * Hermite reduce the modified list T, take the first row, and remove the first element (which should be a 1.)
 * Consider the rest to be a monzo, which may be converted to a rational number if you prefer
-* This is the corresponding transveral generator to the ith val of V; it may be reduced to an equivalent generator of minimal Tenney height by multiplying by the commas of V
+* This is the corresponding transveral generator to the ith val V[i] of V; it may be reduced to an equivalent generator of minimal Tenney height by multiplying by the commas of V
-*</pre></div>
+</pre></div>
 <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">&lt;html&gt;&lt;head&gt;&lt;title&gt;Transversal generators&lt;/title&gt;&lt;/head&gt;&lt;body&gt;&lt;!-- ws:start:WikiTextTocRule:6:&amp;lt;img id=&amp;quot;wikitext@@toc@@flat&amp;quot; class=&amp;quot;WikiMedia WikiMediaTocFlat&amp;quot; title=&amp;quot;Table of Contents&amp;quot; src=&amp;quot;/site/embedthumbnail/toc/flat?w=100&amp;amp;h=16&amp;quot;/&amp;gt; --&gt;&lt;!-- ws:end:WikiTextTocRule:6 --&gt;&lt;!-- ws:start:WikiTextTocRule:7: --&gt;&lt;a href="#Definition"&gt;Definition&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:7 --&gt;&lt;!-- ws:start:WikiTextTocRule:8: --&gt; | &lt;a href="#Examples"&gt;Examples&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:8 --&gt;&lt;!-- ws:start:WikiTextTocRule:9: --&gt; | &lt;a href="#Finding the transversal generators"&gt;Finding the transversal generators&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:9 --&gt;&lt;!-- ws:start:WikiTextTocRule:10: --&gt;
@@ Line 67: / Line 67: @@
 We can find transveral generators for V by the following procedure:&lt;br /&gt;
 &lt;br /&gt;
-&lt;ul&gt;&lt;li&gt;Take the transpose of the pseudoinverse of V, call that U&lt;/li&gt;&lt;li&gt;Find a basis for the commas of V&lt;/li&gt;&lt;li&gt;For each row of U, clear denominators and append the monzos of the comma basis for V&lt;/li&gt;&lt;li&gt;Saturate the result to a list of monzos, call that S&lt;/li&gt;&lt;li&gt;Apply each val of V (dot product) to S&lt;/li&gt;&lt;li&gt;Insert V.S[i] in front of S[i] as the first element, obtaining a modified list T&lt;/li&gt;&lt;li&gt;Hermite reduce the modified list T, take the first row, and remove the first element (which should be a 1.)&lt;/li&gt;&lt;li&gt;Consider the rest to be a monzo, which may be converted to a rational number if you prefer&lt;/li&gt;&lt;li&gt;This is the corresponding transveral generator to the ith val of V; it may be reduced to an equivalent generator of minimal Tenney height by multiplying by the commas of V&lt;/li&gt;&lt;/ul&gt;*&lt;/body&gt;&lt;/html&gt;</pre></div>
+&lt;ul&gt;&lt;li&gt;Take the transpose of the pseudoinverse of V, call that U&lt;/li&gt;&lt;li&gt;Find a basis for the commas of V&lt;/li&gt;&lt;li&gt;For each row U[i] of U, clear denominators and append the monzos of the comma basis for V&lt;/li&gt;&lt;li&gt;Saturate the result to a list of monzos, call that S&lt;/li&gt;&lt;li&gt;Apply the ith val V[i] (dot product) to each element of S&lt;/li&gt;&lt;li&gt;Insert V[i].S[j] in front of the elements of S[j] as the first element, obtaining a modified list T&lt;/li&gt;&lt;li&gt;Hermite reduce the modified list T, take the first row, and remove the first element (which should be a 1.)&lt;/li&gt;&lt;li&gt;Consider the rest to be a monzo, which may be converted to a rational number if you prefer&lt;/li&gt;&lt;li&gt;This is the corresponding transveral generator to the ith val V[i] of V; it may be reduced to an equivalent generator of minimal Tenney height by multiplying by the commas of V&lt;/li&gt;&lt;/ul&gt;&lt;/body&gt;&lt;/html&gt;</pre></div>