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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 Functions</title>
    <para xml:id="S1.p1">
      <equation xml:id="S1.Ex1">
        <Math mode="display" tex="g(a)=g(b)" xml:id="S1.Ex1.m1" text="g@(a) = g@(b)">
          <XMath>
            <XMApp>
              <XMTok meaning="equals" role="RELOP">=</XMTok>
              <XMApp>
                <XMTok role="FUNCTION" argclose=")" argopen="(" font="italic">g</XMTok>
                <XMTok role="ID" font="italic">a</XMTok>
              </XMApp>
              <XMApp>
                <XMTok role="FUNCTION" argclose=")" argopen="(" font="italic">g</XMTok>
                <XMTok role="ID" font="italic">b</XMTok>
              </XMApp>
            </XMApp>
          </XMath>
        </Math>
      </equation>
      <equation xml:id="S1.Ex2">
        <Math mode="display" tex="f(a)=g(h(c))" xml:id="S1.Ex2.m1" text="f@(a) = g@(h@(c))">
          <XMath>
            <XMApp>
              <XMTok meaning="equals" role="RELOP">=</XMTok>
              <XMApp>
                <XMTok role="FUNCTION" argclose=")" argopen="(" font="italic">f</XMTok>
                <XMTok role="ID" font="italic">a</XMTok>
              </XMApp>
              <XMApp>
                <XMTok role="FUNCTION" argclose=")" argopen="(" font="italic">g</XMTok>
                <XMApp>
                  <XMTok role="FUNCTION" argclose=")" argopen="(" font="italic">h</XMTok>
                  <XMTok role="ID" font="italic">c</XMTok>
                </XMApp>
              </XMApp>
            </XMApp>
          </XMath>
        </Math>
      </equation>
      <equation xml:id="S1.Ex3">
        <Math mode="display" tex="h(c)=\sin a^{2}" xml:id="S1.Ex3.m1" text="h@(c) = sine@(a ^ 2)">
          <XMath>
            <XMApp>
              <XMTok meaning="equals" role="RELOP">=</XMTok>
              <XMApp>
                <XMTok role="FUNCTION" argclose=")" argopen="(" font="italic">h</XMTok>
                <XMTok role="ID" font="italic">c</XMTok>
              </XMApp>
              <XMApp>
                <XMTok meaning="sine" role="TRIGFUNCTION">sin</XMTok>
                <XMApp>
                  <XMTok role="SUPERSCRIPTOP" scriptpos="post2"/>
                  <XMTok role="ID" font="italic">a</XMTok>
                  <XMTok meaning="2" role="NUMBER">2</XMTok>
                </XMApp>
              </XMApp>
            </XMApp>
          </XMath>
        </Math>
      </equation>
      <equation xml:id="S1.Ex4">
        <Math mode="display" tex="\sin f(a)" xml:id="S1.Ex4.m1" text="sine@(f@(a))">
          <XMath>
            <XMApp>
              <XMTok meaning="sine" role="TRIGFUNCTION">sin</XMTok>
              <XMApp>
                <XMTok role="FUNCTION" argclose=")" argopen="(" font="italic">f</XMTok>
                <XMTok role="ID" font="italic">a</XMTok>
              </XMApp>
            </XMApp>
          </XMath>
        </Math>
      </equation>
    </para>
  </section>
  <section refnum="2" xml:id="S2">
    <title>Trigonometric functions</title>
    <para xml:id="S2.p1">
      <equation xml:id="S2.Ex5">
        <Math mode="display" tex="\sin a+\tan b" xml:id="S2.Ex5.m1" text="sine@(a) + tangent@(b)">
          <XMath>
            <XMApp>
              <XMTok meaning="plus" role="ADDOP">+</XMTok>
              <XMApp>
                <XMTok meaning="sine" role="TRIGFUNCTION">sin</XMTok>
                <XMTok role="ID" font="italic">a</XMTok>
              </XMApp>
              <XMApp>
                <XMTok meaning="tangent" role="TRIGFUNCTION">tan</XMTok>
                <XMTok role="ID" font="italic">b</XMTok>
              </XMApp>
            </XMApp>
          </XMath>
        </Math>
      </equation>
      <equation xml:id="S2.Ex6">
        <Math mode="display" tex="\sin a\cos b\neq\sin(a\cos b)" xml:id="S2.Ex6.m1" text="sine@(a) * cosine@(b) not-equals sine@(a * cosine@(b))">
          <XMath>
            <XMApp>
              <XMTok meaning="not-equals" name="neq" role="RELOP">≠</XMTok>
              <XMApp>
                <XMTok meaning="times" role="MULOP">⁢</XMTok>
                <XMApp>
                  <XMTok meaning="sine" role="TRIGFUNCTION">sin</XMTok>
                  <XMTok role="ID" font="italic">a</XMTok>
                </XMApp>
                <XMApp>
                  <XMTok meaning="cosine" role="TRIGFUNCTION">cos</XMTok>
                  <XMTok role="ID" font="italic">b</XMTok>
                </XMApp>
              </XMApp>
              <XMApp>
                <XMTok meaning="sine" role="TRIGFUNCTION" argclose=")" argopen="(">sin</XMTok>
                <XMApp>
                  <XMTok meaning="times" role="MULOP">⁢</XMTok>
                  <XMTok role="ID" font="italic">a</XMTok>
                  <XMApp>
                    <XMTok meaning="cosine" role="TRIGFUNCTION">cos</XMTok>
                    <XMTok role="ID" font="italic">b</XMTok>
                  </XMApp>
                </XMApp>
              </XMApp>
            </XMApp>
          </XMath>
        </Math>
      </equation>
      <equation xml:id="S2.Ex7">
        <Math mode="display" tex="\sin 2\pi\neq\log 2x^{2}" xml:id="S2.Ex7.m1" text="sine@(2 * pi) not-equals logarithm@(2 * x ^ 2)">
          <XMath>
            <XMApp>
              <XMTok meaning="not-equals" name="neq" role="RELOP">≠</XMTok>
              <XMApp>
                <XMTok meaning="sine" role="TRIGFUNCTION">sin</XMTok>
                <XMApp>
                  <XMTok meaning="times" role="MULOP">⁢</XMTok>
                  <XMTok meaning="2" role="NUMBER">2</XMTok>
                  <XMTok name="pi" role="UNKNOWN" font="italic">π</XMTok>
                </XMApp>
              </XMApp>
              <XMApp>
                <XMTok meaning="logarithm" role="OPFUNCTION">log</XMTok>
                <XMApp>
                  <XMTok meaning="times" role="MULOP">⁢</XMTok>
                  <XMTok meaning="2" role="NUMBER">2</XMTok>
                  <XMApp>
                    <XMTok role="SUPERSCRIPTOP" scriptpos="post2"/>
                    <XMTok role="UNKNOWN" font="italic">x</XMTok>
                    <XMTok meaning="2" role="NUMBER">2</XMTok>
                  </XMApp>
                </XMApp>
              </XMApp>
            </XMApp>
          </XMath>
        </Math>
      </equation>
    </para>
  </section>
  <section refnum="3" xml:id="S3">
    <title>Missing arguments</title>
    <para xml:id="S3.p1">
      <equation xml:id="S3.Ex8">
        <Math mode="display" tex="fgh" xml:id="S3.Ex8.m1" text="f * g * h">
          <XMath>
            <XMApp>
              <XMTok meaning="times" role="MULOP">⁢</XMTok>
              <XMTok role="FUNCTION" font="italic">f</XMTok>
              <XMTok role="FUNCTION" font="italic">g</XMTok>
              <XMTok role="FUNCTION" font="italic">h</XMTok>
            </XMApp>
          </XMath>
        </Math>
      </equation>
      <equation xml:id="S3.Ex9">
        <Math mode="display" tex="fgha" xml:id="S3.Ex9.m1" text="f * g * h * a">
          <XMath>
            <XMApp>
              <XMTok meaning="times" role="MULOP">⁢</XMTok>
              <XMTok role="FUNCTION" font="italic">f</XMTok>
              <XMTok role="FUNCTION" font="italic">g</XMTok>
              <XMTok role="FUNCTION" font="italic">h</XMTok>
              <XMTok role="ID" font="italic">a</XMTok>
            </XMApp>
          </XMath>
        </Math>
      </equation>
    </para>
  </section>
  <section refnum="4" xml:id="S4">
    <title>Operator-like functions</title>
    <para xml:id="S4.p1">
      <equation xml:id="S4.Ex10">
        <Math mode="display" tex="FGH" xml:id="S4.Ex10.m1" text="F@(G@(H))">
          <XMath>
            <XMApp>
              <XMTok role="OPFUNCTION" font="italic">F</XMTok>
              <XMApp>
                <XMTok role="OPFUNCTION" font="italic">G</XMTok>
                <XMTok role="OPFUNCTION" font="italic">H</XMTok>
              </XMApp>
            </XMApp>
          </XMath>
        </Math>
      </equation>
      <equation xml:id="S4.Ex11">
        <Math mode="display" tex="FGHa" xml:id="S4.Ex11.m1" text="F@(G@(H@(a)))">
          <XMath>
            <XMApp>
              <XMTok role="OPFUNCTION" font="italic">F</XMTok>
              <XMApp>
                <XMTok role="OPFUNCTION" font="italic">G</XMTok>
                <XMApp>
                  <XMTok role="OPFUNCTION" font="italic">H</XMTok>
                  <XMTok role="ID" font="italic">a</XMTok>
                </XMApp>
              </XMApp>
            </XMApp>
          </XMath>
        </Math>
      </equation>
    </para>
    <para xml:id="S4.p2">
      <equation xml:id="S4.Ex12">
        <Math mode="display" tex="f^{{\prime}}(a)=a^{2}" xml:id="S4.Ex12.m1" text="(f ^ prime)@(a) = a ^ 2">
          <XMath>
            <XMApp>
              <XMTok meaning="equals" role="RELOP">=</XMTok>
              <XMApp>
                <XMApp argclose=")" argopen="(">
                  <XMTok role="SUPERSCRIPTOP" scriptpos="post2"/>
                  <XMTok role="FUNCTION" font="italic">f</XMTok>
                  <XMTok name="prime" role="SUPOP">′</XMTok>
                </XMApp>
                <XMTok role="ID" font="italic">a</XMTok>
              </XMApp>
              <XMApp>
                <XMTok role="SUPERSCRIPTOP" scriptpos="post2"/>
                <XMTok role="ID" font="italic">a</XMTok>
                <XMTok meaning="2" role="NUMBER">2</XMTok>
              </XMApp>
            </XMApp>
          </XMath>
        </Math>
      </equation>
      <equation xml:id="S4.Ex13">
        <Math mode="display" tex="f^{2}(a)=g^{b}(2)" xml:id="S4.Ex13.m1" text="(f ^ 2)@(a) = (g ^ b)@(2)">
          <XMath>
            <XMApp>
              <XMTok meaning="equals" role="RELOP">=</XMTok>
              <XMApp>
                <XMApp argclose=")" argopen="(">
                  <XMTok role="SUPERSCRIPTOP" scriptpos="post2"/>
                  <XMTok role="FUNCTION" font="italic">f</XMTok>
                  <XMTok meaning="2" role="NUMBER">2</XMTok>
                </XMApp>
                <XMTok role="ID" font="italic">a</XMTok>
              </XMApp>
              <XMApp>
                <XMApp argclose=")" argopen="(">
                  <XMTok role="SUPERSCRIPTOP" scriptpos="post2"/>
                  <XMTok role="FUNCTION" font="italic">g</XMTok>
                  <XMTok role="ID" font="italic">b</XMTok>
                </XMApp>
                <XMTok meaning="2" role="NUMBER">2</XMTok>
              </XMApp>
            </XMApp>
          </XMath>
        </Math>
      </equation>
    </para>
  </section>
  <section refnum="5" xml:id="S5">
    <title>Scripts</title>
    <para xml:id="S5.p1">
      <equation xml:id="S5.Ex14">
        <Math mode="display" tex="\ln a=\log _{e}a=\ln _{{+}}b" xml:id="S5.Ex14.m1" text="natural-logarithm@(a) = (logarithm _ e)@(a) = (natural-logarithm _ +)@(b)">
          <XMath>
            <XMApp>
              <XMTok meaning="multirelation"/>
              <XMApp>
                <XMTok meaning="natural-logarithm" role="OPFUNCTION">ln</XMTok>
                <XMTok role="ID" font="italic">a</XMTok>
              </XMApp>
              <XMTok meaning="equals" role="RELOP">=</XMTok>
              <XMApp>
                <XMApp>
                  <XMTok role="SUBSCRIPTOP" scriptpos="post2"/>
                  <XMTok meaning="logarithm" role="OPFUNCTION">log</XMTok>
                  <XMTok role="ID" font="italic">e</XMTok>
                </XMApp>
                <XMTok role="ID" font="italic">a</XMTok>
              </XMApp>
              <XMTok meaning="equals" role="RELOP">=</XMTok>
              <XMApp>
                <XMApp>
                  <XMTok role="SUBSCRIPTOP" scriptpos="post2"/>
                  <XMTok meaning="natural-logarithm" role="OPFUNCTION">ln</XMTok>
                  <XMTok meaning="plus" role="ADDOP">+</XMTok>
                </XMApp>
                <XMTok role="ID" font="italic">b</XMTok>
              </XMApp>
            </XMApp>
          </XMath>
        </Math>
      </equation>
    </para>
  </section>
</document>
