<?xml version="1.0"?>
<div class="add">

<b>let </b><font color="Maroon">x</font> be    <a href="finseq_1.html#M2">FinSequence</a> of  <a href="numbers.html#K1">REAL</a> , <font color="Maroon">y</font> be    <a href="finseq_1.html#M2">FinSequence</a> of  <a href="numbers.html#K1">REAL</a> ;<br/><b>let </b><font color="Maroon">M</font> be   <a href="matrix_1.html#NM1">Matrix</a> of <a href="numbers.html#K1">REAL</a> ;<br/>



<b>assume </b><a NAME="E1:58"/><i><font color="Green">E43</font></i>: 
(  <a href="finseq_1.html#K3">len</a> <font color="Maroon">x</font> <a href="hidden.html#R1">=</a>  <a href="finseq_1.html#K3">len</a> <font color="Maroon">M</font> &amp;  <a href="finseq_1.html#K3">len</a> <font color="Maroon">y</font> <a href="hidden.html#R1">=</a>  <a href="matrix_1.html#K1">width</a> <font color="Maroon">M</font> &amp;  <a href="finseq_1.html#K3">len</a> <font color="Maroon">x</font> <a href="xxreal_0.html#NR4" target="_self">&gt;</a> 0 &amp;  <a href="finseq_1.html#K3">len</a> <font color="Maroon">y</font> <a href="xxreal_0.html#NR4" target="_self">&gt;</a> 0 )
 ;<br/>

<b>thus </b><span class="p1"><a href="euclid_2.html#K1">|(</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon">x</font> <a href="matrixr1.html#K12">*</a> <font color="Maroon">M</font></span>)</span>,<font color="Maroon">y</font></span><a href="euclid_2.html#K1">)|</a></span> = 
 <a href="matrprob.html#K5" target="_self">SumAll</a> <span class="p1">(<span class="default"><a href="matrprob.html#K6" target="_self">QuadraticForm</a> <font color="Maroon">x</font>,<font color="Maroon">M</font>,<font color="Maroon">y</font></span>)</span>
<b>by </b><i>, </i>
<br/>.= 
<span class="p1"><a href="euclid_2.html#K1">|(</a><span class="default"><font color="Maroon">x</font>,<span class="p2">(<span class="default"><font color="Maroon">M</font> <a href="matrixr1.html#K11">*</a> <font color="Maroon">y</font></span>)</span></span><a href="euclid_2.html#K1">)|</a></span>
<b>by </b><i>, </i>
;<br/>


</div>
