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<div class="add">

<b>take </b>
<span class="p1"><a href="quaterni.html#K6" target="_self">[*</a><span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">x1</font> <a href="real_1.html#K4">*</a> <font color="Maroon">y1</font></span>)</span> <a href="real_1.html#K5">-</a> <span class="p5">(<span class="default"><font color="Maroon">x2</font> <a href="real_1.html#K4">*</a> <font color="Maroon">y2</font></span>)</span></span>)</span> <a href="real_1.html#K5">-</a> <span class="p4">(<span class="default"><font color="Maroon">x3</font> <a href="real_1.html#K4">*</a> <font color="Maroon">y3</font></span>)</span></span>)</span> <a href="real_1.html#K5">-</a> <span class="p3">(<span class="default"><font color="Maroon">x4</font> <a href="real_1.html#K4">*</a> <font color="Maroon">y4</font></span>)</span></span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">x1</font> <a href="real_1.html#K4">*</a> <font color="Maroon">y2</font></span>)</span> <a href="real_1.html#K3">+</a> <span class="p5">(<span class="default"><font color="Maroon">x2</font> <a href="real_1.html#K4">*</a> <font color="Maroon">y1</font></span>)</span></span>)</span> <a href="real_1.html#K3">+</a> <span class="p4">(<span class="default"><font color="Maroon">x3</font> <a href="real_1.html#K4">*</a> <font color="Maroon">y4</font></span>)</span></span>)</span> <a href="real_1.html#K5">-</a> <span class="p3">(<span class="default"><font color="Maroon">x4</font> <a href="real_1.html#K4">*</a> <font color="Maroon">y3</font></span>)</span></span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">x1</font> <a href="real_1.html#K4">*</a> <font color="Maroon">y3</font></span>)</span> <a href="real_1.html#K3">+</a> <span class="p5">(<span class="default"><font color="Maroon">y1</font> <a href="real_1.html#K4">*</a> <font color="Maroon">x3</font></span>)</span></span>)</span> <a href="real_1.html#K3">+</a> <span class="p4">(<span class="default"><font color="Maroon">y2</font> <a href="real_1.html#K4">*</a> <font color="Maroon">x4</font></span>)</span></span>)</span> <a href="real_1.html#K5">-</a> <span class="p3">(<span class="default"><font color="Maroon">y4</font> <a href="real_1.html#K4">*</a> <font color="Maroon">x2</font></span>)</span></span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">x1</font> <a href="real_1.html#K4">*</a> <font color="Maroon">y4</font></span>)</span> <a href="real_1.html#K3">+</a> <span class="p5">(<span class="default"><font color="Maroon">x4</font> <a href="real_1.html#K4">*</a> <font color="Maroon">y1</font></span>)</span></span>)</span> <a href="real_1.html#K3">+</a> <span class="p4">(<span class="default"><font color="Maroon">x2</font> <a href="real_1.html#K4">*</a> <font color="Maroon">y3</font></span>)</span></span>)</span> <a href="real_1.html#K5">-</a> <span class="p3">(<span class="default"><font color="Maroon">x3</font> <a href="real_1.html#K4">*</a> <font color="Maroon">y2</font></span>)</span></span>)</span></span><a href="quaterni.html#K6" target="_self">*]</a></span>
;<br/>

<b>thus </b><a NAME="E1:31_1_1"/>
 ex <font color="Olive">x1</font>, <font color="Olive">x2</font>, <font color="Olive">x3</font>, <font color="Olive">x4</font>, <font color="Olive">y1</font>, <font color="Olive">y2</font>, <font color="Olive">y3</font>, <font color="Olive">y4</font> being   <a href="subset_1.html#M1">Element</a> of  <a href="numbers.html#K1">REAL</a>  st <br/>( <font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="quaterni.html#K6" target="_self">[*</a><span class="default"><font color="Olive">x1</font>,<font color="Olive">x2</font>,<font color="Olive">x3</font>,<font color="Olive">x4</font></span><a href="quaterni.html#K6" target="_self">*]</a></span> &amp; <font color="Maroon">y</font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="quaterni.html#K6" target="_self">[*</a><span class="default"><font color="Olive">y1</font>,<font color="Olive">y2</font>,<font color="Olive">y3</font>,<font color="Olive">y4</font></span><a href="quaterni.html#K6" target="_self">*]</a></span> &amp; <span class="p1"><a href="quaterni.html#K6" target="_self">[*</a><span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">x1</font> <a href="real_1.html#K4">*</a> <font color="Maroon">y1</font></span>)</span> <a href="real_1.html#K5">-</a> <span class="p5">(<span class="default"><font color="Maroon">x2</font> <a href="real_1.html#K4">*</a> <font color="Maroon">y2</font></span>)</span></span>)</span> <a href="real_1.html#K5">-</a> <span class="p4">(<span class="default"><font color="Maroon">x3</font> <a href="real_1.html#K4">*</a> <font color="Maroon">y3</font></span>)</span></span>)</span> <a href="real_1.html#K5">-</a> <span class="p3">(<span class="default"><font color="Maroon">x4</font> <a href="real_1.html#K4">*</a> <font color="Maroon">y4</font></span>)</span></span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">x1</font> <a href="real_1.html#K4">*</a> <font color="Maroon">y2</font></span>)</span> <a href="real_1.html#K3">+</a> <span class="p5">(<span class="default"><font color="Maroon">x2</font> <a href="real_1.html#K4">*</a> <font color="Maroon">y1</font></span>)</span></span>)</span> <a href="real_1.html#K3">+</a> <span class="p4">(<span class="default"><font color="Maroon">x3</font> <a href="real_1.html#K4">*</a> <font color="Maroon">y4</font></span>)</span></span>)</span> <a href="real_1.html#K5">-</a> <span class="p3">(<span class="default"><font color="Maroon">x4</font> <a href="real_1.html#K4">*</a> <font color="Maroon">y3</font></span>)</span></span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">x1</font> <a href="real_1.html#K4">*</a> <font color="Maroon">y3</font></span>)</span> <a href="real_1.html#K3">+</a> <span class="p5">(<span class="default"><font color="Maroon">y1</font> <a href="real_1.html#K4">*</a> <font color="Maroon">x3</font></span>)</span></span>)</span> <a href="real_1.html#K3">+</a> <span class="p4">(<span class="default"><font color="Maroon">y2</font> <a href="real_1.html#K4">*</a> <font color="Maroon">x4</font></span>)</span></span>)</span> <a href="real_1.html#K5">-</a> <span class="p3">(<span class="default"><font color="Maroon">y4</font> <a href="real_1.html#K4">*</a> <font color="Maroon">x2</font></span>)</span></span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">x1</font> <a href="real_1.html#K4">*</a> <font color="Maroon">y4</font></span>)</span> <a href="real_1.html#K3">+</a> <span class="p5">(<span class="default"><font color="Maroon">x4</font> <a href="real_1.html#K4">*</a> <font color="Maroon">y1</font></span>)</span></span>)</span> <a href="real_1.html#K3">+</a> <span class="p4">(<span class="default"><font color="Maroon">x2</font> <a href="real_1.html#K4">*</a> <font color="Maroon">y3</font></span>)</span></span>)</span> <a href="real_1.html#K5">-</a> <span class="p3">(<span class="default"><font color="Maroon">x3</font> <a href="real_1.html#K4">*</a> <font color="Maroon">y2</font></span>)</span></span>)</span></span><a href="quaterni.html#K6" target="_self">*]</a></span> <a href="hidden.html#R1">=</a> <span class="p1"><a href="quaterni.html#K6" target="_self">[*</a><span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Olive">x1</font> <a href="real_1.html#K4">*</a> <font color="Olive">y1</font></span>)</span> <a href="real_1.html#K5">-</a> <span class="p5">(<span class="default"><font color="Olive">x2</font> <a href="real_1.html#K4">*</a> <font color="Olive">y2</font></span>)</span></span>)</span> <a href="real_1.html#K5">-</a> <span class="p4">(<span class="default"><font color="Olive">x3</font> <a href="real_1.html#K4">*</a> <font color="Olive">y3</font></span>)</span></span>)</span> <a href="real_1.html#K5">-</a> <span class="p3">(<span class="default"><font color="Olive">x4</font> <a href="real_1.html#K4">*</a> <font color="Olive">y4</font></span>)</span></span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Olive">x1</font> <a href="real_1.html#K4">*</a> <font color="Olive">y2</font></span>)</span> <a href="real_1.html#K3">+</a> <span class="p5">(<span class="default"><font color="Olive">x2</font> <a href="real_1.html#K4">*</a> <font color="Olive">y1</font></span>)</span></span>)</span> <a href="real_1.html#K3">+</a> <span class="p4">(<span class="default"><font color="Olive">x3</font> <a href="real_1.html#K4">*</a> <font color="Olive">y4</font></span>)</span></span>)</span> <a href="real_1.html#K5">-</a> <span class="p3">(<span class="default"><font color="Olive">x4</font> <a href="real_1.html#K4">*</a> <font color="Olive">y3</font></span>)</span></span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Olive">x1</font> <a href="real_1.html#K4">*</a> <font color="Olive">y3</font></span>)</span> <a href="real_1.html#K3">+</a> <span class="p5">(<span class="default"><font color="Olive">y1</font> <a href="real_1.html#K4">*</a> <font color="Olive">x3</font></span>)</span></span>)</span> <a href="real_1.html#K3">+</a> <span class="p4">(<span class="default"><font color="Olive">y2</font> <a href="real_1.html#K4">*</a> <font color="Olive">x4</font></span>)</span></span>)</span> <a href="real_1.html#K5">-</a> <span class="p3">(<span class="default"><font color="Olive">y4</font> <a href="real_1.html#K4">*</a> <font color="Olive">x2</font></span>)</span></span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Olive">x1</font> <a href="real_1.html#K4">*</a> <font color="Olive">y4</font></span>)</span> <a href="real_1.html#K3">+</a> <span class="p5">(<span class="default"><font color="Olive">x4</font> <a href="real_1.html#K4">*</a> <font color="Olive">y1</font></span>)</span></span>)</span> <a href="real_1.html#K3">+</a> <span class="p4">(<span class="default"><font color="Olive">x2</font> <a href="real_1.html#K4">*</a> <font color="Olive">y3</font></span>)</span></span>)</span> <a href="real_1.html#K5">-</a> <span class="p3">(<span class="default"><font color="Olive">x3</font> <a href="real_1.html#K4">*</a> <font color="Olive">y2</font></span>)</span></span>)</span></span><a href="quaterni.html#K6" target="_self">*]</a></span> )
 <b>by </b><i>, </i>;<br/>


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