Derivatives and Integrals: An Annotated Discourse

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    <title>Pre-Formatted Text</title>
    <p>
      In Sage, if you wanted to build a matrix,
          <idx>matrix</idx>
      then you would use the <c>matrix()</c> constructor.
      Here is the matrix of second partials of <m>f(x,y)=x^3+8x^2y^3 + y^4</m>,
      as you would enter it in Sage.
      Notice that <c>SR</c> is the ring of symbolic expressions,
      <c>Symbolic Ring</c>.
    </p>
<pre>
var('x', 'y')
J = matrix(SR, [
[6*x + 16*y^3, 48*x*y^2],
[48*x*y^2, 48*x^2*y + 12*y^2]
])
</pre>
    <p>
      That accomplished, Sage will easily and naturally provide a <latex /> representation of the matrix with the command <c>latex(J)</c>.
    </p>
<pre>
\left(\begin{array}{rr}
16 \, y^{3} + 6 \, x &amp; -48 \, x y^{2} \\
48 \, x y^{2} &amp; 48 \, x^{2} y + 12 \, y^{2}
\end{array}\right)
</pre>
    <p>
      The <c>pre</c> element surrounds text that should be preserved verbatim.
      It is like a special kind of paragraph,
      and can be used almost everywhere that a paragraph can be used.
      The realization of preformatted text should be robust enough that it can be cut from documents and pasted without any substitutions of
      <q>fancier</q>
      Unicode characters for generic ASCII characters.
      Try the
      <q>minus</q>
      sign on the <m>48</m> above to see if it does not become a dash,
      or the single quotes on the Sage variables.
    </p>
    <p>
      For Sage input code,
      the first non-whitespace character sets the left margin,
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      see Section<nbsp /><xref ref="section-programs" />.
      Examine the source of the following example to help understand this paragraph.
    </p>
<pre>
A normal line
An indented line
An outdented line
</pre>
    <p>
      Snippets should also be robust for cut/paste operations.
      For example, you should not get
      <q>curly</q>
      <q>smart</q>
      quote marks in verbatim text:
      <c>this should have "dumb" quote marks</c>.
      Here are a few characters that should migrate through <latex /> to a PDF unmolested:
      <c>'"----"'</c>
    </p>
    <p>
      <c>If you write a very long snippet of inline code (i.e. within a &lt;c&gt;
      element) it can impinge on the right margin,
      since very long words will not hypenate,
      unless you have a dash/hypen.
      Such as when you use words like pneumonoultramicroscopicsilicovolcanoconiosis,
      parastratiosphecomyia stratiosphecomyioides,
      floccinaucinihilipilification, or subdermatoglyphic.
      For output in LaTeX we get line-breaking, and perhaps word-spacing,
      but we do not get hyphenation and the font is fixed-width.
      So not always perfect.
      Consider other options like &lt;cd&gt; or &lt;pre&gt;
      below.</c>
    </p>
    <p>
      An intermediate type of verbatim text can be accomplished with the <tag>cd</tag> tag,
      short for
      <q>code display.</q>
      It allows for larger chunks of verbatim text to show up in the middle of a paragraph,
      but with some vertical space above and below,
      and centered between the margins.
      It can be
      <cd>authored as a single line</cd>
      or if you wish to have multiple lines
      <cd>
        <cline>there is the &lt;cline&gt; tag</cline>
        <cline>meant to model the line tag</cline>
        <cline>and short for "code line"</cline>
      </cd>
      and you may even
      <cd>
        <cline>use a single cline</cline>
      </cd>
      if you like to have your source closely model the visual look of the output.
    </p>
    <p>
      With the <attr>showspaces</attr> attribute of <tag>cd</tag> set to <c>all</c> there will be a visual indication of every space character,
      which is nice if indentation is critical.
      For example,
      <cd showspaces="all">
        <cline>there is the &lt;cline&gt; tag</cline>
        <cline>meant to model the line tag</cline>
        <cline>and short for "code line"</cline>
      </cd>
      and as single line
      <cd showspaces="all">authored as a single line</cd>
      that is not structured with <tag>cline</tag> elements.
    </p>
    <p>
      The <tag>pre</tag> tag is meant for use outside of paragraphs,
      but is otherwise very similar.
      The source may also be structured as a sequence of <tag>cline</tag> as in the next example,
      recycling content from above.
    </p>
<pre>
<cline>If you write a very long snippet of inline code (i.e. within</cline>
<cline>a &lt;c&gt; element) it can impinge on the right margin, since</cline>
<cline>very long words will not hypenate, unless you have a dash/hypen.</cline>
<cline>Such as when you use words like</cline>
<cline>pneumonoultramicroscopicsilicovolcanoconiosis,</cline>
<cline>parastratiosphecomyia stratiosphecomyioides,</cline>
<cline>floccinaucinihilipilification, or subdermatoglyphic. For output</cline>
<cline>in LaTeX we get line-breaking, and perhaps word-spacing, but we</cline>
<cline>do not get hyphenation and the font is fixed-width. So not always</cline>
<cline>perfect. Consider other options like &lt;cd&gt; or &lt;pre&gt; below.</cline>
</pre>
    <p>
      We use a Unicode right arrow (Unicode Character 'RIGHTWARDS ARROW', U+2192) to sometimes indicate the truncation of long lines in a text file.
      It is available in our usual monospace font for <latex />/PDF, but we include a use here in order to make certain that is always the case.
      Here: <c>→</c>.
    </p>
  </section>