Hobbit: Difference between revisions
Wikispaces>genewardsmith **Imported revision 167499979 - Original comment: ** |
Wikispaces>genewardsmith **Imported revision 167500361 - 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>2010-10-04 03: | : This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2010-10-04 03:25:05 UTC</tt>.<br> | ||
: The original revision id was <tt> | : The original revision id was <tt>167500361</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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(6) Let P = I - Q, where I is the identity matrix. | (6) Let P = I - Q, where I is the identity matrix. | ||
(7) For a p-limit monzo or [[Fractional monzos|fractional monzo]] m we now define the seminorm | (7) For a p-limit monzo or [[Fractional monzos|fractional monzo]] m we now define the seminorm ||m||_s = ||mDP|| where the norm on the right is the ordinary Euclidean norm. | ||
|| m ||_s = || mDP || | |||
where the norm on the right is the ordinary Euclidean norm. | |||
(8) If v[1] is odd then for each integer j, 0 less than j less than or equal to v[1], we choose a corresponding monzo mj such that <v|m> = j, 0 less than <J|m> less than or equal to 1 where J is the JI mapping <log2(2) log2(3) ... log2(p)|, and ||m||_s is minimal. | (8) If v[1] is odd then for each integer j, 0 less than j less than or equal to v[1], we choose a corresponding monzo mj such that <v|m> = j, 0 less than <J|m> less than or equal to 1 where J is the JI mapping <log2(2) log2(3) ... log2(p)|, and ||m||_s is minimal. | ||
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(6) Let P = I - Q, where I is the identity matrix.<br /> | (6) Let P = I - Q, where I is the identity matrix.<br /> | ||
<br /> | <br /> | ||
(7) For a p-limit monzo or <a class="wiki_link" href="/Fractional%20monzos">fractional monzo</a> m we now define the seminorm | (7) For a p-limit monzo or <a class="wiki_link" href="/Fractional%20monzos">fractional monzo</a> m we now define the seminorm ||m||_s = ||mDP|| where the norm on the right is the ordinary Euclidean norm.<br /> | ||
where the norm on the right is the ordinary Euclidean norm.<br /> | |||
<br /> | <br /> | ||
(8) If v[1] is odd then for each integer j, 0 less than j less than or equal to v[1], we choose a corresponding monzo mj such that &lt;v|m&gt; = j, 0 less than &lt;J|m&gt; less than or equal to 1 where J is the JI mapping &lt;log2(2) log2(3) ... log2(p)|, and ||m||_s is minimal.<br /> | (8) If v[1] is odd then for each integer j, 0 less than j less than or equal to v[1], we choose a corresponding monzo mj such that &lt;v|m&gt; = j, 0 less than &lt;J|m&gt; less than or equal to 1 where J is the JI mapping &lt;log2(2) log2(3) ... log2(p)|, and ||m||_s is minimal.<br /> | ||