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<?latexml class="article"?>
<?latexml package="latexml"?>
<?latexml RelaxNGSchema="LaTeXML"?>
<document xmlns="http://dlmf.nist.gov/LaTeXML">
  <section refnum="1" xml:id="S1">
    <title>Basic math</title>
    <para xml:id="S1.p1">
      <equation xml:id="S1.Ex1">
        <Math mode="display" tex="a+b+c-d+e" xml:id="S1.Ex1.m1" text="((a + b + c) - d) + e">
          <XMath>
            <XMApp>
              <XMTok meaning="plus" role="ADDOP">+</XMTok>
              <XMApp>
                <XMTok meaning="minus" role="ADDOP">-</XMTok>
                <XMApp>
                  <XMTok meaning="plus" role="ADDOP">+</XMTok>
                  <XMTok role="ID" font="italic">a</XMTok>
                  <XMTok role="ID" font="italic">b</XMTok>
                  <XMTok role="ID" font="italic">c</XMTok>
                </XMApp>
                <XMTok role="ID" font="italic">d</XMTok>
              </XMApp>
              <XMTok role="ID" font="italic">e</XMTok>
            </XMApp>
          </XMath>
        </Math>
      </equation>
      <equation xml:id="S1.Ex2">
        <Math mode="display" tex="a+bc-de" xml:id="S1.Ex2.m1" text="(a + b * c) - d * e">
          <XMath>
            <XMApp>
              <XMTok meaning="minus" role="ADDOP">-</XMTok>
              <XMApp>
                <XMTok meaning="plus" role="ADDOP">+</XMTok>
                <XMTok role="ID" font="italic">a</XMTok>
                <XMApp>
                  <XMTok meaning="times" role="MULOP">⁢</XMTok>
                  <XMTok role="ID" font="italic">b</XMTok>
                  <XMTok role="ID" font="italic">c</XMTok>
                </XMApp>
              </XMApp>
              <XMApp>
                <XMTok meaning="times" role="MULOP">⁢</XMTok>
                <XMTok role="ID" font="italic">d</XMTok>
                <XMTok role="ID" font="italic">e</XMTok>
              </XMApp>
            </XMApp>
          </XMath>
        </Math>
      </equation>
      <equation xml:id="S1.Ex3">
        <Math mode="display" tex="abc/de" xml:id="S1.Ex3.m1" text="((a * b * c) / d) * e">
          <XMath>
            <XMApp>
              <XMTok meaning="times" role="MULOP">⁢</XMTok>
              <XMApp>
                <XMTok meaning="divide" role="MULOP" style="inline">/</XMTok>
                <XMApp>
                  <XMTok meaning="times" role="MULOP">⁢</XMTok>
                  <XMTok role="ID" font="italic">a</XMTok>
                  <XMTok role="ID" font="italic">b</XMTok>
                  <XMTok role="ID" font="italic">c</XMTok>
                </XMApp>
                <XMTok role="ID" font="italic">d</XMTok>
              </XMApp>
              <XMTok role="ID" font="italic">e</XMTok>
            </XMApp>
          </XMath>
        </Math>
      </equation>
      <equation xml:id="S1.Ex4">
        <Math mode="display" tex="a\times b\times c/d\times e" xml:id="S1.Ex4.m1" text="((a * b * c) / d) * e">
          <XMath>
            <XMApp>
              <XMTok meaning="times" role="MULOP">×</XMTok>
              <XMApp>
                <XMTok meaning="divide" role="MULOP" style="inline">/</XMTok>
                <XMApp>
                  <XMTok meaning="times" role="MULOP">×</XMTok>
                  <XMTok role="ID" font="italic">a</XMTok>
                  <XMTok role="ID" font="italic">b</XMTok>
                  <XMTok role="ID" font="italic">c</XMTok>
                </XMApp>
                <XMTok role="ID" font="italic">d</XMTok>
              </XMApp>
              <XMTok role="ID" font="italic">e</XMTok>
            </XMApp>
          </XMath>
        </Math>
      </equation>
    </para>
  </section>
  <section refnum="2" xml:id="S2">
    <title>Evaluate At</title>
    <para xml:id="S2.p1">
      <equation xml:id="S2.Ex5">
        <Math mode="display" tex="a|_{\infty}" xml:id="S2.Ex5.m1" text="evaluated-at@(a, infinity)">
          <XMath>
            <XMApp>
              <XMTok meaning="evaluated-at"/>
              <XMTok role="ID" font="italic">a</XMTok>
              <XMTok meaning="infinity" name="infty" role="ID">∞</XMTok>
            </XMApp>
          </XMath>
        </Math>
      </equation>
      <equation xml:id="S2.Ex6">
        <Math mode="display" tex="ab|_{{a=0}}cd|_{{c=0}}e" xml:id="S2.Ex6.m1" text="evaluated-at@(evaluated-at@(a * b, a = 0) * c * d, c = 0) * e">
          <XMath>
            <XMApp>
              <XMTok meaning="times" role="MULOP">⁢</XMTok>
              <XMApp>
                <XMTok meaning="evaluated-at"/>
                <XMApp>
                  <XMTok meaning="times" role="MULOP">⁢</XMTok>
                  <XMApp>
                    <XMTok meaning="evaluated-at"/>
                    <XMApp>
                      <XMTok meaning="times" role="MULOP">⁢</XMTok>
                      <XMTok role="ID" font="italic">a</XMTok>
                      <XMTok role="ID" font="italic">b</XMTok>
                    </XMApp>
                    <XMApp>
                      <XMTok meaning="equals" role="RELOP">=</XMTok>
                      <XMTok role="ID" font="italic">a</XMTok>
                      <XMTok meaning="0" role="NUMBER">0</XMTok>
                    </XMApp>
                  </XMApp>
                  <XMTok role="ID" font="italic">c</XMTok>
                  <XMTok role="ID" font="italic">d</XMTok>
                </XMApp>
                <XMApp>
                  <XMTok meaning="equals" role="RELOP">=</XMTok>
                  <XMTok role="ID" font="italic">c</XMTok>
                  <XMTok meaning="0" role="NUMBER">0</XMTok>
                </XMApp>
              </XMApp>
              <XMTok role="ID" font="italic">e</XMTok>
            </XMApp>
          </XMath>
        </Math>
      </equation>
    </para>
  </section>
  <section refnum="3" xml:id="S3">
    <title>Absolute values</title>
    <para xml:id="S3.p1">
      <equation xml:id="S3.Ex7">
        <Math mode="display" tex="|a|" xml:id="S3.Ex7.m1" text="absolute-value@(a)">
          <XMath>
            <XMApp>
              <XMTok meaning="absolute-value" role="FENCED" argclose="|" argopen="|"/>
              <XMTok role="ID" font="italic">a</XMTok>
            </XMApp>
          </XMath>
        </Math>
      </equation>
      <equation xml:id="S3.Ex8">
        <Math mode="display" tex="||a||" xml:id="S3.Ex8.m1" text="norm@(a)">
          <XMath>
            <XMApp>
              <XMTok meaning="norm" role="FENCED" argclose="||" argopen="||"/>
              <XMTok role="ID" font="italic">a</XMTok>
            </XMApp>
          </XMath>
        </Math>
      </equation>
      <equation xml:id="S3.Ex9">
        <Math mode="display" tex="|a|_{\infty}" xml:id="S3.Ex9.m1" text="(absolute-value@(a)) _ infinity">
          <XMath>
            <XMApp>
              <XMTok role="SUBSCRIPTOP" scriptpos="post2"/>
              <XMApp>
                <XMTok meaning="absolute-value" role="FENCED" argclose="|" argopen="|"/>
                <XMTok role="ID" font="italic">a</XMTok>
              </XMApp>
              <XMTok meaning="infinity" name="infty" role="ID">∞</XMTok>
            </XMApp>
          </XMath>
        </Math>
      </equation>
      <equation xml:id="S3.Ex10">
        <Math mode="display" tex="|a+b|" xml:id="S3.Ex10.m1" text="absolute-value@(a + b)">
          <XMath>
            <XMApp>
              <XMTok meaning="absolute-value" role="FENCED" argclose="|" argopen="|"/>
              <XMApp>
                <XMTok meaning="plus" role="ADDOP">+</XMTok>
                <XMTok role="ID" font="italic">a</XMTok>
                <XMTok role="ID" font="italic">b</XMTok>
              </XMApp>
            </XMApp>
          </XMath>
        </Math>
      </equation>
      <equation xml:id="S3.Ex11">
        <Math mode="display" tex="|a-|b||" xml:id="S3.Ex11.m1" text="absolute-value@(a - absolute-value@(b))">
          <XMath>
            <XMApp>
              <XMTok meaning="absolute-value" role="FENCED" argclose="|" argopen="|"/>
              <XMApp>
                <XMTok meaning="minus" role="ADDOP">-</XMTok>
                <XMTok role="ID" font="italic">a</XMTok>
                <XMApp>
                  <XMTok meaning="absolute-value" role="FENCED" argclose="|" argopen="|"/>
                  <XMTok role="ID" font="italic">b</XMTok>
                </XMApp>
              </XMApp>
            </XMApp>
          </XMath>
        </Math>
      </equation>
    </para>
  </section>
  <section refnum="4" xml:id="S4">
    <title>Failures w/o Backtracking</title>
    <para xml:id="S4.p1">
      <equation xml:id="S4.Ex12">
        <Math mode="display" tex="||a|-|b||" xml:id="S4.Ex12.m1" text="absolute-value@(absolute-value@(a) - absolute-value@(b))">
          <XMath>
            <XMApp>
              <XMTok meaning="absolute-value" role="FENCED" argclose="|" argopen="|"/>
              <XMApp>
                <XMTok meaning="minus" role="ADDOP">-</XMTok>
                <XMApp>
                  <XMTok meaning="absolute-value" role="FENCED" argclose="|" argopen="|"/>
                  <XMTok role="ID" font="italic">a</XMTok>
                </XMApp>
                <XMApp>
                  <XMTok meaning="absolute-value" role="FENCED" argclose="|" argopen="|"/>
                  <XMTok role="ID" font="italic">b</XMTok>
                </XMApp>
              </XMApp>
            </XMApp>
          </XMath>
        </Math>
      </equation>
      <equation xml:id="S4.Ex13">
        <Math mode="display" tex="||a|-b|" xml:id="S4.Ex13.m1" text="absolute-value@(absolute-value@(a) - b)">
          <XMath>
            <XMApp>
              <XMTok meaning="absolute-value" role="FENCED" argclose="|" argopen="|"/>
              <XMApp>
                <XMTok meaning="minus" role="ADDOP">-</XMTok>
                <XMApp>
                  <XMTok meaning="absolute-value" role="FENCED" argclose="|" argopen="|"/>
                  <XMTok role="ID" font="italic">a</XMTok>
                </XMApp>
                <XMTok role="ID" font="italic">b</XMTok>
              </XMApp>
            </XMApp>
          </XMath>
        </Math>
      </equation>
      <equation xml:id="S4.Ex14">
        <Math mode="display" tex="|a|b|_{\infty}" xml:id="S4.Ex14.m1" text="evaluated-at@(absolute-value@(a) * b, infinity)">
          <XMath>
            <XMApp>
              <XMTok meaning="evaluated-at"/>
              <XMApp>
                <XMTok meaning="times" role="MULOP">⁢</XMTok>
                <XMApp>
                  <XMTok meaning="absolute-value" role="FENCED" argclose="|" argopen="|"/>
                  <XMTok role="ID" font="italic">a</XMTok>
                </XMApp>
                <XMTok role="ID" font="italic">b</XMTok>
              </XMApp>
              <XMTok meaning="infinity" name="infty" role="ID">∞</XMTok>
            </XMApp>
          </XMath>
        </Math>
      </equation>
    </para>
  </section>
</document>
