%This macro provides the typesetting of the math of the second horizontal area
%of the column 1of page 8.
%
%The macro has one parameter
%       1) The width usable for typeseting the math.
\newcommand\TEightFactTwo[1]{
   \parbox[t]{#1}{%
      \def\LineOfArrayA##1##2##3{##1&=&##2&=##3\\}%
      \def\LineOfArrayB##1##2##3##4{##1&=&##2&##3=##4\\}%
      %This macro should add a negative spave in the last column
      %of a line of the array. For a strange reason when a line is alone the
      %value is much too far at right. This a pure visual layout, like one
      %is accustomized to do in Word.
      \def\LastColPosition{\hspace{-32.6ex}}
      \TEightSeriesFactAFontSize
         \noindent
         $\begin{array}{lllll}
         %x^1
            \LineOfArrayA{x^1}{x^{\underline 1}}{x^{\overline 1}}
         %x^2
            \LineOfArrayA{x^2}{x^{\underline 2} + x^{\underline 1}}{x^{\overline 2} - x^{\overline 1}}
         %x^3
            \LineOfArrayA{x^3}{x^{\underline 3} + 3 x^{\underline 2} + x^{\underline 1}}
                        {x^{\overline 3}- 3 x^{\overline 2} + x^{\overline 1}}
         %x^4
            \LineOfArrayA{x^4}{x^{\underline 4} + 6 x^{\underline 3}+ 7 x^{\underline 2} + x^{\underline 1}}
                        {x^{\overline 4} - 6 x^{\overline 3}+ 7 x^{\overline 2} - x^{\overline 1}}
         %x^5
            \LineOfArrayA{x^5}{x^{\underline 5} + 15x^{\underline 4} + 25 x^{\underline 3}+ 10 x^{\underline 2} + x^{\underline 1}}
                        {x^{\underline 5} - 15 x^{\overline 4} + 25 x^{\overline 3}- 10 x^{\overline 2} + x^{\overline 1}}
         \end{array}$

         \par\vspace{1ex plus .2ex minus .5ex}
         \centerline{\rule{5cm}{.5pt}}
         \par\vspace{1ex plus .2ex minus .5ex}

         \noindent
         $\begin{array}{llllll}
         %Line 1
            \LineOfArrayB{x^{\overline 1}}{x^1}{x^{\underline 1}}{x^1}
         %Line 2
            \LineOfArrayB{x^{\overline 2}}{x^2 + x^1}{x^{\underline 2}}{x^2 - x^1}
         %Line 3
            \LineOfArrayB{x^{\overline 3}}{x^3 + 3x^2 + 2x^1}{x^{\underline 3}}{x^3 - 3x^2 + 2x^1}
         %Line 4
            \LineOfArrayB{x^{\overline 4}}{x^4 + 6x^3 + 11x^2 + 6x^1}
                        {x^{\underline 4}}{x^4 - 6x^3 + 11x^2 - 6x^1}
         %Line 5
            \LineOfArrayB{x^{\overline 5}}{x^5 + 10 x^4 + 35 x^3 + 50 x^2 + 24 x^1}
                        {x^{\underline 5}}{x^5 - 10 x^4 + 35 x^3 - 50 x^2 +}
           & & & & & \LastColPosition 24 x^1\\
         \end{array}$
   }
}
