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Directory talk:Jon Awbrey/Papers/Differential Logic and Dynamic Systems 2.0 (view source)

Revision as of 21:22, 13 July 2008

276 bytes removed ,  21:22, 13 July 2008
→‎Table 9: HTML → TeX
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</font><br>
 
</font><br>
   −
<font face="courier new">
   
{| align="center" border="1" cellpadding="4" cellspacing="0" style="text-align:left; width:96%"
 
{| align="center" border="1" cellpadding="4" cellspacing="0" style="text-align:left; width:96%"
 
|+ '''Table 9.  Higher Order Differential Features'''
 
|+ '''Table 9.  Higher Order Differential Features'''
 
| width=50% |
 
| width=50% |
−
{| cellpadding="4"
+
<math>\begin{array}{ccccccl}
−
| <font face="lucida calligraphy">A</font>
+
\mathcal{A}
−
| =
+
& = &
−
| d<sup>0</sup><font face="lucida calligraphy">A</font>
+
\operatorname{d}^0 \mathcal{A}
−
| =
+
& = &
−
| {''a''<sub>1</sub>,
+
\{a_1, & \ldots, & a_n\} \\
−
| &hellip;,
+
\operatorname{d}\mathcal{A}
−
| ''a''<sub>''n''</sub>}
+
& = &
−
|-
+
\operatorname{d}^1 \mathcal{A}
−
| d<font face="lucida calligraphy">A</font>
+
& = &
−
| =
+
\{\operatorname{d}a_1, & \ldots, & \operatorname{d}a_n\} \\
−
| d<sup>1</sup><font face="lucida calligraphy">A</font>
+
&   &
−
| =
+
\operatorname{d}^k \mathcal{A}
−
| {d''a''<sub>1</sub>,
+
& = &
−
| &hellip;,
+
\{\operatorname{d}^k a_1,
−
| d''a''<sub>''n''</sub>}
+
& \ldots, &
−
|-
+
\operatorname{d}^k a_n\} \\
−
| &nbsp;
+
\operatorname{d}^* \mathcal{A}
−
| &nbsp;
+
& = &
−
| d<sup>''k''</sup><font face="lucida calligraphy">A</font>
+
\{\operatorname{d}^0 \mathcal{A},
−
| =
+
& \ldots, &
−
| {d<sup>''k''</sup>''a''<sub>''1''</sub>,
+
\operatorname{d}^k \mathcal{A},
−
| &hellip;,
+
& \ldots \}
−
| d<sup>''k''</sup>''a''<sub>''n''</sub>}
+
\end{array}</math>
−
|-
  −
| d<sup>*</sup><font face="lucida calligraphy">A</font>
  −
| =
  −
| {d<sup>0</sup><font face="lucida calligraphy">A</font>,
  −
| &hellip;,
  −
| d<sup>''k''</sup><font face="lucida calligraphy">A</font>,
  −
| &hellip;}
  −
|}
   
| width=50% |
 
| width=50% |
 
{| cellpadding="4"
 
{| cellpadding="4"
Jon Awbrey
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