Cartesian scale: Difference between revisions
Wikispaces>genewardsmith **Imported revision 479904292 - Original comment: ** |
Wikispaces>genewardsmith **Imported revision 479904396 - Original comment: ** |
||
| Line 1: | Line 1: | ||
<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>2013-12-30 16: | : This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2013-12-30 16:09:21 UTC</tt>.<br> | ||
: The original revision id was <tt> | : The original revision id was <tt>479904396</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> | ||
| Line 10: | Line 10: | ||
\{{ℇ^n {g_1}^{i_1} {g_2}^{i_2} \ldots {g_k}^{i_k}| 0 \leq i_1 \leq m_1, 0 \leq i_2 \leq m_2, \ldots, 0 \leq i_k \leq m_k}\}. | \{{ℇ^n {g_1}^{i_1} {g_2}^{i_2} \ldots {g_k}^{i_k}| 0 \leq i_1 \leq m_1, 0 \leq i_2 \leq m_2, \ldots, 0 \leq i_k \leq m_k}\}. | ||
[[math]] | [[math]] | ||
Here the multiplicities are fixed positive integers, and n ranges over all integers, with the scale sorted | Here the multiplicities are fixed positive integers, and n ranges over all integers, with the scale sorted by ascending size and with all duplicates removed. If intervals are written additively as cents, then Descartes(ℇ, g, m) is | ||
[[math]] | [[math]] | ||
\{{nℇ + i_1g_1 + \ldots + i_kg_k| 0 \leq i_1 \leq m_1 \ldots 0 \leq i_k \leq m_k}\}. | \{{nℇ + i_1g_1 + \ldots + i_kg_k| 0 \leq i_1 \leq m_1 \ldots 0 \leq i_k \leq m_k}\}. | ||
| Line 28: | Line 28: | ||
\{{ℇ^n {g_1}^{i_1} {g_2}^{i_2} \ldots {g_k}^{i_k}| 0 \leq i_1 \leq m_1, 0 \leq i_2 \leq m_2, \ldots, 0 \leq i_k \leq m_k}\}.&lt;br/&gt;[[math]] | \{{ℇ^n {g_1}^{i_1} {g_2}^{i_2} \ldots {g_k}^{i_k}| 0 \leq i_1 \leq m_1, 0 \leq i_2 \leq m_2, \ldots, 0 \leq i_k \leq m_k}\}.&lt;br/&gt;[[math]] | ||
--><script type="math/tex">\{{ℇ^n {g_1}^{i_1} {g_2}^{i_2} \ldots {g_k}^{i_k}| 0 \leq i_1 \leq m_1, 0 \leq i_2 \leq m_2, \ldots, 0 \leq i_k \leq m_k}\}.</script><!-- ws:end:WikiTextMathRule:0 --><br /> | --><script type="math/tex">\{{ℇ^n {g_1}^{i_1} {g_2}^{i_2} \ldots {g_k}^{i_k}| 0 \leq i_1 \leq m_1, 0 \leq i_2 \leq m_2, \ldots, 0 \leq i_k \leq m_k}\}.</script><!-- ws:end:WikiTextMathRule:0 --><br /> | ||
Here the multiplicities are fixed positive integers, and n ranges over all integers, with the scale sorted | Here the multiplicities are fixed positive integers, and n ranges over all integers, with the scale sorted by ascending size and with all duplicates removed. If intervals are written additively as cents, then Descartes(ℇ, g, m) is <br /> | ||
<!-- ws:start:WikiTextMathRule:1: | <!-- ws:start:WikiTextMathRule:1: | ||
[[math]]&lt;br/&gt; | [[math]]&lt;br/&gt; | ||