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Directory:Jon Awbrey/Papers/Cactus Language (view source)

Revision as of 03:56, 2 June 2009

490 bytes added ,  03:56, 2 June 2009
→‎Note 9: format table
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themselves, we may take the abstract view of the group's operational
 
themselves, we may take the abstract view of the group's operational
 
structure, say, in the form of the group operation table copied here:
 
structure, say, in the form of the group operation table copied here:
 +
</pre>
   −
o---------o---------o---------o---------o---------o
+
<br>
−
|        %        |        |        |        |
  −
|    ·    %    e    |    f    |    g    |    h    |
  −
|        %        |        |        |        |
  −
o=========o=========o=========o=========o=========o
  −
|        %        |        |        |        |
  −
|    e    %    e    |    f    |    g    |    h    |
  −
|        %        |        |        |        |
  −
o---------o---------o---------o---------o---------o
  −
|        %        |        |        |        |
  −
|    f    %    f    |    e    |    h    |    g    |
  −
|        %        |        |        |        |
  −
o---------o---------o---------o---------o---------o
  −
|        %        |        |        |        |
  −
|    g    %    g    |    h    |    e    |    f    |
  −
|        %        |        |        |        |
  −
o---------o---------o---------o---------o---------o
  −
|        %        |        |        |        |
  −
|    h    %    h    |    g    |    f    |    e    |
  −
|        %        |        |        |        |
  −
o---------o---------o---------o---------o---------o
      +
{| align="center" cellpadding="0" cellspacing="0" style="border-left:1px solid black; border-top:1px solid black; border-right:1px solid black; border-bottom:1px solid black; text-align:center; width:60%"
 +
|- style="height:50px"
 +
| width="12%" style="border-bottom:1px solid black; border-right:1px solid black" | <math>\cdot</math>
 +
| width="22%" style="border-bottom:1px solid black" |
 +
<math>\operatorname{e}</math>
 +
| width="22%" style="border-bottom:1px solid black" |
 +
<math>\operatorname{f}</math>
 +
| width="22%" style="border-bottom:1px solid black" |
 +
<math>\operatorname{g}</math>
 +
| width="22%" style="border-bottom:1px solid black" |
 +
<math>\operatorname{h}</math>
 +
|- style="height:50px"
 +
| style="border-right:1px solid black" | <math>\operatorname{e}</math>
 +
| <math>\operatorname{e}</math>
 +
| <math>\operatorname{f}</math>
 +
| <math>\operatorname{g}</math>
 +
| <math>\operatorname{h}</math>
 +
|- style="height:50px"
 +
| style="border-right:1px solid black" | <math>\operatorname{f}</math>
 +
| <math>\operatorname{f}</math>
 +
| <math>\operatorname{e}</math>
 +
| <math>\operatorname{h}</math>
 +
| <math>\operatorname{g}</math>
 +
|- style="height:50px"
 +
| style="border-right:1px solid black" | <math>\operatorname{g}</math>
 +
| <math>\operatorname{g}</math>
 +
| <math>\operatorname{h}</math>
 +
| <math>\operatorname{e}</math>
 +
| <math>\operatorname{f}</math>
 +
|- style="height:50px"
 +
| style="border-right:1px solid black" | <math>\operatorname{h}</math>
 +
| <math>\operatorname{h}</math>
 +
| <math>\operatorname{g}</math>
 +
| <math>\operatorname{f}</math>
 +
| <math>\operatorname{e}</math>
 +
|}
 +
 +
<br>
 +
 +
<pre>
 
This table is abstractly the same as, or isomorphic to, the versions with
 
This table is abstractly the same as, or isomorphic to, the versions with
 
the E_ij operators and the T_ij transformations that we discussed earlier.
 
the E_ij operators and the T_ij transformations that we discussed earlier.
Jon Awbrey
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