PreTeXt Sample Book Abstract Algebra (SAMPLE ONLY)

      <section xml:id="doenet">

        <title>DoenetML</title>

        <p>
          This preliminary DoenetML example is for testing use on a Runestone server, where it will use the SPLICE protocol to report out events.
          To the reader, it should <em>behave</em> identically when not on a Runestone server.
        </p>

        <!-- 2024-04-25: This exact interactive appears in the sample article, within a figure. -->

        <interactive label="interactive-doenetml-example" platform="doenetml" width="100%" aspect="3:2">

        <slate surface="doenetml">
  &lt;p&gt;
  Adjust the vectors &lt;m&gt;\vec u&lt;/m&gt;, &lt;m&gt;\vec v&lt;/m&gt;, and &lt;m&gt;\vec w&lt;/m&gt; in the
  left graph to visualize the areas calculated by
  &lt;m&gt;\det[\vec u\hspace{0.5em}\vec w]&lt;/m&gt;, &lt;m&gt;\det[\vec v\hspace{0.5em}\vec w]&lt;/m&gt;,
  and
  &lt;m&gt;\det[\vec u+\vec v\hspace{0.5em}\vec w]&lt;/m&gt;.
&lt;/p&gt;
&lt;setup&gt;&lt;line through="(0,0) $v" name="vLine"/&gt;&lt;math simplify  name="c"&gt;$cv.x/$v.x&lt;/math&gt;&lt;/setup&gt;
&lt;sideBySide&gt;
  &lt;graph xmin="-4" ymin="-4" xmax="16" ymax="16"&gt;
    &lt;m draggable="false" anchor="(10,14)"&gt;
      \det[\vec u\hspace{0.5em}\vec w],
      \det[\vec v\hspace{0.5em}\vec w]
    &lt;/m&gt;
    &lt;point name="u" styleNumber="3"&gt;
      (6,2)
      &lt;label&gt;&lt;m&gt;\vec u&lt;/m&gt;&lt;/label&gt;
    &lt;/point&gt;
    &lt;point name="w" styleNumber="3"&gt;
      (3,7)
      &lt;label&gt;&lt;m&gt;\vec w&lt;/m&gt;&lt;/label&gt;
    &lt;/point&gt;
    &lt;point name="uPlusV" styleNumber="4"&gt;
      (9,5)
      &lt;label&gt;&lt;m&gt;\vec v&lt;/m&gt;&lt;/label&gt;
    &lt;/point&gt;
    &lt;polygon vertices="(0,0) $u $u+$w $w" filled draggable="false" styleNumber="3"/&gt;
    &lt;polygon vertices="$u $uPlusV $uPlusV+$w $u+$w" filled draggable="false" styleNumber="4"/&gt;
    &lt;lineSegment endpoints="(0,0) $uPlusV" styleNumber="6"/&gt;
    &lt;lineSegment endpoints="$w $uPlusV+$w" styleNumber="6"/&gt;
  &lt;/graph&gt;
  &lt;graph xmin="-4" ymin="-4" xmax="16" ymax="16"&gt;
    &lt;m draggable="false" anchor="(12,14)"&gt;
      \det[\vec u+\vec v\hspace{0.5em}\vec w]
    &lt;/m&gt;
    &lt;polygon vertices="(0,0) $uPlusV $uPlusV+$w $w" filled draggable="false" styleNumber="2"/&gt;
    &lt;point draggable="false" styleNumber="3"&gt;
      $w
      &lt;label&gt;&lt;m&gt;\vec w&lt;/m&gt;&lt;/label&gt;
    &lt;/point&gt;
    &lt;point draggable="false" styleNumber="4"&gt;
      $uPlusV
      &lt;label&gt;&lt;m&gt;\vec u+\vec v&lt;/m&gt;&lt;/label&gt;
    &lt;/point&gt;
    &lt;lineSegment endpoints="(0,0) $u" styleNumber="6"/&gt;
    &lt;lineSegment endpoints="$u $uPlusV" styleNumber="6"/&gt;
    &lt;lineSegment endpoints="$w $w+$u" styleNumber="6"/&gt;
    &lt;lineSegment endpoints="$w+$u $w+$uPlusV" styleNumber="6"/&gt;
  &lt;/graph&gt;
&lt;/sideBySide&gt;
        </slate> </interactive>

      </section>