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MyWikiBiz, Author Your Legacy — Wednesday November 27, 2024
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First, the enlargement map (or the secant transformation) E''G'' = ‹E''G''<sub>1</sub>,&nbsp;E''G''<sub>2</sub>›&nbsp;:&nbsp;E''U''<sup>&nbsp;&bull;</sup>&nbsp;&rarr;&nbsp;E''X''<sup>&nbsp;&bull;</sup> is defined by the following set of component equations:
 
First, the enlargement map (or the secant transformation) E''G'' = ‹E''G''<sub>1</sub>,&nbsp;E''G''<sub>2</sub>›&nbsp;:&nbsp;E''U''<sup>&nbsp;&bull;</sup>&nbsp;&rarr;&nbsp;E''X''<sup>&nbsp;&bull;</sup> is defined by the following set of component equations:
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<pre>
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{| align="center" border="1" cellpadding="12" cellspacing="0" style="background:lightcyan; font-weight:bold; text-align:left; width:96%"
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|   EG_i = G_i <u + du, v + dv>                |
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{| align="left" border="0" cellpadding="12" cellspacing="0" style="background:lightcyan; font-weight:bold; text-align:left; width:100%"
|                                                 |
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| width="8%"  | E''G''<sub>''i''</sub>
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| width="4%" | =
</pre>
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| width="88%" | ''G''<sub>''i''</sub>‹''u'' + d''u'', ''v'' + d''v''›
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</font><br>
    
Second, the difference map (or the chordal transformation) D''G'' = ‹D''G''<sub>1</sub>,&nbsp;D''G''<sub>2</sub>›&nbsp;:&nbsp;E''U''<sup>&nbsp;&bull;</sup>&nbsp;&rarr;&nbsp;E''X''<sup>&nbsp;&bull;</sup> is defined in component-wise fashion as the boolean sum of the initial proposition ''G''<sub>''i''</sub> and the enlarged proposition E''G''<sub>''i''</sub>, for ''i'' = 1, 2, according to the following set of equations:
 
Second, the difference map (or the chordal transformation) D''G'' = ‹D''G''<sub>1</sub>,&nbsp;D''G''<sub>2</sub>›&nbsp;:&nbsp;E''U''<sup>&nbsp;&bull;</sup>&nbsp;&rarr;&nbsp;E''X''<sup>&nbsp;&bull;</sup> is defined in component-wise fashion as the boolean sum of the initial proposition ''G''<sub>''i''</sub> and the enlarged proposition E''G''<sub>''i''</sub>, for ''i'' = 1, 2, according to the following set of equations:
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