Derivatives and Integrals: An Annotated Discourse

<section xml:id="advanced-numbering" label="section-advanced-numbering">
  <title>Advanced Numbering</title>
  <introduction>
    <p>
      This section demonstrates the numbering
          <idx>numbering</idx>
      patterns used throughout <pretext />.
      There are five subsections.
      Two intermediate subsections each have two subsubsections.
      This creates a total of seven divisions that are leaves of the document tree.
      In each leaf we have placed two numbered theorems, for a total of fourteen.
      There is no real content, this is just a demonstration.
    </p>
    <p>
      Use values of <c>0</c> through <c>3</c> for the <c>numbering.theorems.level</c> parameter to see how these numbers change accordingly.
      It is easiest to compare if you use <c>chunk.level &lt; 2</c> so the theorems all land on the same page if you are previewing in HTML.
    </p>
  </introduction>
  <subsection>
    <title>One</title>
    <p>
      A document leaf.
    </p>
    <theorem xml:id="theorem-number-01">
      <title>First Theorem</title>
      <creator>Cauchy</creator>
      <statement>
        <p>
          No statement.
        </p>
      </statement>
    </theorem>


    <theorem xml:id="theorem-number-02">
      <title>Second Theorem</title>
      <creator>Bunyakovsky</creator>
      <statement>
        <p>
          No statement.
        </p>
      </statement>
    </theorem>
  </subsection>
  <subsection>
    <title>Two</title>
    <introduction>
      <p>
        Further subdivided.
      </p>
    </introduction>
    <subsubsection>
      <title>Uno</title>
      <p>
        A document leaf.
      </p>
      <theorem xml:id="theorem-number-03">
        <title>First Theorem!</title>
        <creator>Schwarz</creator>
        <statement>
          <p>
            No statement.
          </p>
        </statement>
      </theorem>
      <theorem xml:id="theorem-number-04">
        <title>Second Theorem?</title>
        <creator>Inequality</creator>
        <statement>
          <p>
            No statement.
          </p>
        </statement>
      </theorem>
    </subsubsection>
    <subsubsection>
      <title>Dos</title>
      <p>
        A document leaf.
      </p>
      <theorem xml:id="theorem-number-05">
        <title>First Theorem?</title>
        <statement>
          <p>
            No statement.
          </p>
        </statement>
      </theorem>
      <theorem xml:id="theorem-number-06">
        <title>Second Theorem!</title>
        <statement>
          <p>
            No statement.
          </p>
        </statement>
      </theorem>
    </subsubsection>
  </subsection>
  <subsection>
    <title>Three</title>
    <p>
      A document leaf.
    </p>
    <theorem xml:id="theorem-number-07">
      <title>First Theorem</title>
      <statement>
        <p>
          No statement.
        </p>
      </statement>
    </theorem>
    <theorem xml:id="theorem-number-08">
      <title>Second Theorem</title>
      <statement>
        <p>
          No statement.
        </p>
      </statement>
    </theorem>
  </subsection>
  <subsection>
    <title>Four</title>
    <introduction>
      <p>
        Further subdivided.
        We include two theorems as numbered items in the introduction to test their numbers,
        which should always be logical.
      </p>
      <theorem xml:id="theorem-good-one">
        <title>Good Numbered Theorem One</title>
        <statement>
          <p>
            No statement.
          </p>
        </statement>
      </theorem>
      <theorem xml:id="theorem-good-two">
        <title>Good Numbered Theorem Two</title>
        <statement>
          <p>
            No statement.
          </p>
        </statement>
      </theorem>
    </introduction>
    <subsubsection>
      <title>Uno</title>
      <p>
        A document leaf.
      </p>
      <theorem xml:id="theorem-number-09">
        <title>First Theorem</title>
        <statement>
          <p>
            No statement.
          </p>
        </statement>
      </theorem>
      <theorem xml:id="theorem-number-10">
        <title>Second Theorem</title>
        <statement>
          <p>
            No statement.
          </p>
        </statement>
      </theorem>
    </subsubsection>
    <subsubsection>
      <title>Dos</title>
      <p>
        A document leaf.
      </p>
      <theorem xml:id="theorem-number-11">
        <title>First Theorem</title>
        <statement>
          <p>
            No statement.
          </p>
        </statement>
      </theorem>
      <theorem xml:id="theorem-number-12">
        <title>Second Theorem</title>
        <statement>
          <p>
            No statement.
          </p>
        </statement>
      </theorem>
    </subsubsection>
    <conclusion>
      <p>
        Conclusion now.
        We include two theorems as numbered items in the conclusion to test their numbers,
        which are sometimes totally illogical and are inconsistent across output formats.
        To see the effect,
        set the level for numbering theorems to <c>3</c>.
        See this GitHub
        <url href="https://github.com/PreTeXtBook/pretext/issues/139" visual="github.com/PreTeXtBook/pretext/issues/139">Issue #139</url>
        for details.
      </p>
      <theorem xml:id="theorem-bad-one">
        <title>Bad Numbered Theorem One</title>
        <statement>
          <p>
            No statement.
          </p>
        </statement>
      </theorem>
      <theorem xml:id="theorem-bad-two">
        <title>Bad Numbered Theorem Two</title>
        <statement>
          <p>
            No statement.
          </p>
        </statement>
      </theorem>
    </conclusion>
  </subsection>
  <subsection>
    <title>Five</title>
    <p>
      A document leaf.
    </p>
    <theorem xml:id="theorem-number-13">
      <title>First Theorem</title>
      <statement>
        <p>
          No statement.
        </p>
      </statement>
    </theorem>
    <theorem xml:id="theorem-number-14">
      <title>Second Theorem</title>
      <statement>
        <p>
          No statement.
        </p>
      </statement>
    </theorem>
  </subsection>
  <subsection xml:id="subsection-local-theorems">
    <title>Theorems in This Section</title>
    <p>
      We have a lot of theorems in this section,
      so we illustrate including an automatic list of these here.
      We use the <c>elements</c> attribute to limit the list to <c>theorem</c> elements,
      and we use the <c>scope</c> attribute to limit the list to this <c>section</c>.
      You can use an introductory <c>p</c> like this one, or not.
      The list gets no title or visual separation,
      so use the usual subdivision elements to make that happen.
      The <c>elements</c> attribute can be a space-delimited list of many different elements.
      This list should not include the Fundamental Theorem of Calculus, Theorem<nbsp /><xref ref="theorem-FTC" />.
      See a slightly different example in <xref ref="appendix-results" text="type-global" />.
    </p>
    <list-of elements="theorem" scope="section" />
  </subsection>
  <subsection xml:id="subsection-with-an-exercise">
    <title>A Title with ] a Right Bracket</title>
    <p>
      <latex /> has trouble with brackets that end up inside optional arguments,
      so this subsection title is only a check on the defense against that.
      And now an <tag>exercise</tag> with a title that could really be a problem.
    </p>
    <exercise xml:id="exercise-difficult-title">
      <title>A Right Brace } and a Right Bracket]</title>
      <statement>
        <p>
          The right brace is is used as a grouping character in <latex /> so this is just a test of its behavior in titles.
        </p>
      </statement>
      <hint>
        <p>
          A faux hint to get this exercise to migrate into a <tag>solutions</tag>.
        </p>
      </hint>
    </exercise>
  </subsection>
  <subsection>
    <title>A Title with } a Right Brace</title>
    <p>
      And now a right brace in a division title.
    </p>
  </subsection>
  <subsection>
    <title>A Title with <m>a]b</m> a Math Right Bracket</title>
    <p>
      And now a right bracket within math in a division title.
    </p>
    <p>
      We do not test a right brace within math,
      since it should be escaped, as is normal <latex /> practice.
    </p>
  </subsection>
  <subsection>
    <title>Just an Exercise</title>
    <exercise>
      <title>An Extraneous Exercise</title>
      <statement>
        <p>
          This exercise is here just as a test of the <tag>solutions</tag> division coming next.
          So it is serving a purpose, even if it is not apparent.
        </p>
      </statement>
      <hint>
        <p>
          A hint, so this exercise looks identical in structure to the one in the previous subsection.
        </p>
      </hint>
    </exercise>
  </subsection>
  <solutions inline="hint" scope="subsection-with-an-exercise">
    <introduction>
      <p>
        This is a <tag>solutions</tag> division,
        which will be a peer of the other <tag>subsection</tag> in this <tag>section</tag>.
        The default behavior is to look to the parent division (a <tag>section</tag> here) and collect all the hints,
        answers, and solutions from every <tag>exercise</tag>
        (and friends)
        inside this containing division.
        (There are just two, similar inline <tag>exercise</tag>.)
      </p>
      <p>
        But instead of the default,
        we employ a <attr>scope</attr> attribute to <em>define</em>
        the parent division of the exercises whose solutions will be shown.
        In this example we specify the <tag>subsection</tag> that is two back,
        the one which tests brackets in titles.
      </p>
    </introduction>
  </solutions>
</section>