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  <section inlist="toc" xml:id="S1">
    <tags>
      <tag>1</tag>
      <tag role="refnum">1</tag>
      <tag role="typerefnum">§1</tag>
    </tags>
    <title><tag close=" ">1</tag>Basic math</title>
    <para xml:id="S1.p1">
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        </Math>
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    </para>
  </section>
  <section inlist="toc" xml:id="S2">
    <tags>
      <tag>2</tag>
      <tag role="refnum">2</tag>
      <tag role="typerefnum">§2</tag>
    </tags>
    <title><tag close=" ">2</tag>Intervals</title>
    <para xml:id="S2.p1">
      <equation xml:id="S2.Ex3">
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                <XMTok meaning="open-interval"/>
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                <XMRef idref="S2.Ex3.m1.2"/>
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          </XMath>
        </Math>
      </equation>
      <equation xml:id="S2.Ex4">
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        </Math>
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        </Math>
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      <equation xml:id="S2.Ex6">
        <Math mode="display" tex="[a,b]" text="closed-interval@(a, b)" xml:id="S2.Ex6.m1">
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    </para>
  </section>
  <section inlist="toc" xml:id="S3">
    <tags>
      <tag>3</tag>
      <tag role="refnum">3</tag>
      <tag role="typerefnum">§3</tag>
    </tags>
    <title><tag close=" ">3</tag>Cases</title>
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      <equation xml:id="S3.Ex7">
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                        <XMTok font="italic" role="ID">b</XMTok>
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    </para>
    <para xml:id="S3.p2">
      <equation xml:id="S3.Ex8">
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                      <XMTok font="italic" role="ID">c</XMTok>
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        </Math>
      </equation>
      <equation xml:id="S3.Ex9">
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              <XMWrap>
                <XMTok role="OPEN" stretchy="false">(</XMTok>
                <XMApp xml:id="S3.Ex9.m1.2">
                  <XMTok meaning="plus" role="ADDOP">+</XMTok>
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                            <XMTok font="italic" role="ID">d</XMTok>
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                <XMTok role="CLOSE" stretchy="false">)</XMTok>
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          </XMath>
        </Math>
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    </para>
  </section>
  <section inlist="toc" xml:id="S4">
    <tags>
      <tag>4</tag>
      <tag role="refnum">4</tag>
      <tag role="typerefnum">§4</tag>
    </tags>
    <title><tag close=" ">4</tag>Atop</title>
    <para xml:id="S4.p1">
      <equation xml:id="S4.Ex10">
        <Math mode="display" tex="a+{b\atop c}+d" text="a + b FRACOP c + d" xml:id="S4.Ex10.m1">
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              <XMTok font="italic" role="ID">a</XMTok>
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                <XMTok font="italic" role="ID">b</XMTok>
                <XMTok font="italic" role="ID">c</XMTok>
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              <XMTok font="italic" role="ID">d</XMTok>
            </XMApp>
          </XMath>
        </Math>
      </equation>
      <equation xml:id="S4.Ex11">
        <Math mode="display" tex="a+\left[b\atop c\right]+d" text="a + delimited-[]@(b FRACOP c) + d" xml:id="S4.Ex11.m1">
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                    <XMTok font="italic" role="ID">b</XMTok>
                    <XMTok font="italic" role="ID">c</XMTok>
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              <XMTok font="italic" role="ID">d</XMTok>
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    </para>
  </section>
  <section inlist="toc" xml:id="S5">
    <tags>
      <tag>5</tag>
      <tag role="refnum">5</tag>
      <tag role="typerefnum">§5</tag>
    </tags>
    <title><tag close=" ">5</tag>Delimiters</title>
    <para xml:id="S5.p1">
      <equation xml:id="S5.Ex12">
        <Math mode="display" tex="\left({a\over b}\right)" text="a / b" xml:id="S5.Ex12.m1">
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                <XMTok role="OPEN" stretchy="true">(</XMTok>
                <XMApp xml:id="S5.Ex12.m1.1">
                  <XMTok mathstyle="display" meaning="divide" role="FRACOP"/>
                  <XMTok font="italic" role="ID">a</XMTok>
                  <XMTok font="italic" role="ID">b</XMTok>
                </XMApp>
                <XMTok role="CLOSE" stretchy="true">)</XMTok>
              </XMWrap>
            </XMDual>
          </XMath>
        </Math>
      </equation>
      <equation xml:id="S5.Ex13">
        <Math mode="display" tex="\left[{a\over b}\right]" text="delimited-[]@(a / b)" xml:id="S5.Ex13.m1">
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                <XMTok meaning="delimited-[]"/>
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              <XMWrap>
                <XMTok role="OPEN" stretchy="true">[</XMTok>
                <XMApp xml:id="S5.Ex13.m1.1">
                  <XMTok mathstyle="display" meaning="divide" role="FRACOP"/>
                  <XMTok font="italic" role="ID">a</XMTok>
                  <XMTok font="italic" role="ID">b</XMTok>
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                <XMTok role="CLOSE" stretchy="true">]</XMTok>
              </XMWrap>
            </XMDual>
          </XMath>
        </Math>
      </equation>
      <equation xml:id="S5.Ex14">
        <Math mode="display" tex="\left[{a\over b}\right]" text="delimited-[]@(a / b)" xml:id="S5.Ex14.m1">
          <XMath>
            <XMDual>
              <XMApp>
                <XMTok meaning="delimited-[]"/>
                <XMRef idref="S5.Ex14.m1.1"/>
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              <XMWrap>
                <XMTok role="OPEN" stretchy="true">[</XMTok>
                <XMApp xml:id="S5.Ex14.m1.1">
                  <XMTok mathstyle="display" meaning="divide" role="FRACOP"/>
                  <XMTok font="italic" role="ID">a</XMTok>
                  <XMTok font="italic" role="ID">b</XMTok>
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                <XMTok role="CLOSE" stretchy="true">]</XMTok>
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        </Math>
      </equation>
      <equation xml:id="S5.Ex15">
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                <XMTok role="CLOSE" stretchy="true">}</XMTok>
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        </Math>
      </equation>
      <equation xml:id="S5.Ex16">
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                  <XMTok font="italic" role="ID">b</XMTok>
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                <XMTok role="CLOSE" stretchy="true">}</XMTok>
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          </XMath>
        </Math>
      </equation>
      <equation xml:id="S5.Ex17">
        <Math mode="display" tex="\left\lfloor{a\over b}\right\rfloor" text="floor@(a / b)" xml:id="S5.Ex17.m1">
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                <XMTok name="lfloor" role="OPEN" stretchy="true">⌊</XMTok>
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                  <XMTok mathstyle="display" meaning="divide" role="FRACOP"/>
                  <XMTok font="italic" role="ID">a</XMTok>
                  <XMTok font="italic" role="ID">b</XMTok>
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                <XMTok name="rfloor" role="CLOSE" stretchy="true">⌋</XMTok>
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            </XMDual>
          </XMath>
        </Math>
      </equation>
      <equation xml:id="S5.Ex18">
        <Math mode="display" tex="\left\lceil{a\over b}\right\rceil" text="ceiling@(a / b)" xml:id="S5.Ex18.m1">
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                <XMTok name="lceil" role="OPEN" stretchy="true">⌈</XMTok>
                <XMApp xml:id="S5.Ex18.m1.1">
                  <XMTok mathstyle="display" meaning="divide" role="FRACOP"/>
                  <XMTok font="italic" role="ID">a</XMTok>
                  <XMTok font="italic" role="ID">b</XMTok>
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                <XMTok name="rceil" role="CLOSE" stretchy="true">⌉</XMTok>
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            </XMDual>
          </XMath>
        </Math>
      </equation>
      <equation xml:id="S5.Ex19">
        <Math mode="display" tex="\left&lt;{a\over b}\right&gt;" text="delimited-⟨⟩@(a / b)" xml:id="S5.Ex19.m1">
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            <XMDual>
              <XMApp>
                <XMTok meaning="delimited-⟨⟩"/>
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              <XMWrap>
                <XMTok name="langle" role="OPEN" stretchy="true">⟨</XMTok>
                <XMApp xml:id="S5.Ex19.m1.1">
                  <XMTok mathstyle="display" meaning="divide" role="FRACOP"/>
                  <XMTok font="italic" role="ID">a</XMTok>
                  <XMTok font="italic" role="ID">b</XMTok>
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                <XMTok name="rangle" role="CLOSE" stretchy="true">⟩</XMTok>
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          </XMath>
        </Math>
      </equation>
      <equation xml:id="S5.Ex20">
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                <XMTok meaning="delimited-⟨⟩"/>
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                  <XMTok font="italic" role="ID">b</XMTok>
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                <XMTok name="rangle" role="CLOSE" stretchy="true">⟩</XMTok>
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            </XMDual>
          </XMath>
        </Math>
      </equation>
      <equation xml:id="S5.Ex21">
        <Math mode="display" tex="\left|{a\over b}\right|" text="absolute-value@(a / b)" xml:id="S5.Ex21.m1">
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            <XMDual>
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              <XMWrap>
                <XMTok role="VERTBAR" stretchy="true">|</XMTok>
                <XMApp xml:id="S5.Ex21.m1.1">
                  <XMTok mathstyle="display" meaning="divide" role="FRACOP"/>
                  <XMTok font="italic" role="ID">a</XMTok>
                  <XMTok font="italic" role="ID">b</XMTok>
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                <XMTok role="VERTBAR" stretchy="true">|</XMTok>
              </XMWrap>
            </XMDual>
          </XMath>
        </Math>
      </equation>
      <equation xml:id="S5.Ex22">
        <Math mode="display" tex="\left|{a\over b}\right|" text="absolute-value@(a / b)" xml:id="S5.Ex22.m1">
          <XMath>
            <XMDual>
              <XMApp>
                <XMTok meaning="absolute-value"/>
                <XMRef idref="S5.Ex22.m1.1"/>
              </XMApp>
              <XMWrap>
                <XMTok role="VERTBAR" stretchy="true">|</XMTok>
                <XMApp xml:id="S5.Ex22.m1.1">
                  <XMTok mathstyle="display" meaning="divide" role="FRACOP"/>
                  <XMTok font="italic" role="ID">a</XMTok>
                  <XMTok font="italic" role="ID">b</XMTok>
                </XMApp>
                <XMTok role="VERTBAR" stretchy="true">|</XMTok>
              </XMWrap>
            </XMDual>
          </XMath>
        </Math>
      </equation>
      <equation xml:id="S5.Ex23">
        <Math mode="display" tex="\left\|{a\over b}\right\|" text="norm@(a / b)" xml:id="S5.Ex23.m1">
          <XMath>
            <XMDual>
              <XMApp>
                <XMTok meaning="norm"/>
                <XMRef idref="S5.Ex23.m1.1"/>
              </XMApp>
              <XMWrap>
                <XMTok role="VERTBAR" stretchy="true">∥</XMTok>
                <XMApp xml:id="S5.Ex23.m1.1">
                  <XMTok mathstyle="display" meaning="divide" role="FRACOP"/>
                  <XMTok font="italic" role="ID">a</XMTok>
                  <XMTok font="italic" role="ID">b</XMTok>
                </XMApp>
                <XMTok role="VERTBAR" stretchy="true">∥</XMTok>
              </XMWrap>
            </XMDual>
          </XMath>
        </Math>
      </equation>
      <equation xml:id="S5.Ex24">
        <Math mode="display" tex="\left\|{a\over b}\right\|" text="norm@(a / b)" xml:id="S5.Ex24.m1">
          <XMath>
            <XMDual>
              <XMApp>
                <XMTok meaning="norm"/>
                <XMRef idref="S5.Ex24.m1.1"/>
              </XMApp>
              <XMWrap>
                <XMTok role="VERTBAR" stretchy="true">∥</XMTok>
                <XMApp xml:id="S5.Ex24.m1.1">
                  <XMTok mathstyle="display" meaning="divide" role="FRACOP"/>
                  <XMTok font="italic" role="ID">a</XMTok>
                  <XMTok font="italic" role="ID">b</XMTok>
                </XMApp>
                <XMTok role="VERTBAR" stretchy="true">∥</XMTok>
              </XMWrap>
            </XMDual>
          </XMath>
        </Math>
      </equation>
      <equation xml:id="S5.Ex25">
        <Math mode="display" tex="\left\uparrow{a\over b}\right\downarrow" text="delimited-↑↓@(a / b)" xml:id="S5.Ex25.m1">
          <XMath>
            <XMDual>
              <XMApp>
                <XMTok meaning="delimited-↑↓"/>
                <XMRef idref="S5.Ex25.m1.1"/>
              </XMApp>
              <XMWrap>
                <XMTok name="uparrow" role="OPEN" stretchy="true">↑</XMTok>
                <XMApp xml:id="S5.Ex25.m1.1">
                  <XMTok mathstyle="display" meaning="divide" role="FRACOP"/>
                  <XMTok font="italic" role="ID">a</XMTok>
                  <XMTok font="italic" role="ID">b</XMTok>
                </XMApp>
                <XMTok name="downarrow" role="CLOSE" stretchy="true">↓</XMTok>
              </XMWrap>
            </XMDual>
          </XMath>
        </Math>
      </equation>
      <equation xml:id="S5.Ex26">
        <Math mode="display" tex="\left\Uparrow{a\over b}\right\Downarrow" text="delimited-⇑⇓@(a / b)" xml:id="S5.Ex26.m1">
          <XMath>
            <XMDual>
              <XMApp>
                <XMTok meaning="delimited-⇑⇓"/>
                <XMRef idref="S5.Ex26.m1.1"/>
              </XMApp>
              <XMWrap>
                <XMTok name="Uparrow" role="OPEN" stretchy="true">⇑</XMTok>
                <XMApp xml:id="S5.Ex26.m1.1">
                  <XMTok mathstyle="display" meaning="divide" role="FRACOP"/>
                  <XMTok font="italic" role="ID">a</XMTok>
                  <XMTok font="italic" role="ID">b</XMTok>
                </XMApp>
                <XMTok name="Downarrow" role="CLOSE" stretchy="true">⇓</XMTok>
              </XMWrap>
            </XMDual>
          </XMath>
        </Math>
      </equation>
      <equation xml:id="S5.Ex27">
        <Math mode="display" tex="\left\updownarrow{a\over b}\right\Updownarrow" text="delimited-↕⇕@(a / b)" xml:id="S5.Ex27.m1">
          <XMath>
            <XMDual>
              <XMApp>
                <XMTok meaning="delimited-↕⇕"/>
                <XMRef idref="S5.Ex27.m1.1"/>
              </XMApp>
              <XMWrap>
                <XMTok name="updownarrow" role="OPEN" stretchy="true">↕</XMTok>
                <XMApp xml:id="S5.Ex27.m1.1">
                  <XMTok mathstyle="display" meaning="divide" role="FRACOP"/>
                  <XMTok font="italic" role="ID">a</XMTok>
                  <XMTok font="italic" role="ID">b</XMTok>
                </XMApp>
                <XMTok name="Updownarrow" role="CLOSE" stretchy="true">⇕</XMTok>
              </XMWrap>
            </XMDual>
          </XMath>
        </Math>
      </equation>
    </para>
    <para xml:id="S5.p2">
      <equation xml:id="S5.Ex28">
        <Math mode="display" tex="a+\left\langle{b\over c}\right\rangle+d" text="a + delimited-⟨⟩@(b / c) + d" xml:id="S5.Ex28.m1">
          <XMath>
            <XMApp>
              <XMTok meaning="plus" role="ADDOP">+</XMTok>
              <XMTok font="italic" role="ID">a</XMTok>
              <XMDual>
                <XMApp>
                  <XMTok meaning="delimited-⟨⟩"/>
                  <XMRef idref="S5.Ex28.m1.1"/>
                </XMApp>
                <XMWrap>
                  <XMTok name="langle" role="OPEN" stretchy="true">⟨</XMTok>
                  <XMApp xml:id="S5.Ex28.m1.1">
                    <XMTok mathstyle="display" meaning="divide" role="FRACOP"/>
                    <XMTok font="italic" role="ID">b</XMTok>
                    <XMTok font="italic" role="ID">c</XMTok>
                  </XMApp>
                  <XMTok name="rangle" role="CLOSE" stretchy="true">⟩</XMTok>
                </XMWrap>
              </XMDual>
              <XMTok font="italic" role="ID">d</XMTok>
            </XMApp>
          </XMath>
        </Math>
      </equation>
    </para>
    <para xml:id="S5.p3">
      <equation xml:id="S5.Ex29">
        <Math mode="display" tex="{a\over b}\left/{c\over d}\right." text="(a / b) / (c / d)" xml:id="S5.Ex29.m1">
          <XMath>
            <XMApp>
              <XMTok role="MULOP" stretchy="true">/</XMTok>
              <XMApp>
                <XMTok mathstyle="display" meaning="divide" role="FRACOP"/>
                <XMTok font="italic" role="ID">a</XMTok>
                <XMTok font="italic" role="ID">b</XMTok>
              </XMApp>
              <XMApp>
                <XMTok mathstyle="display" meaning="divide" role="FRACOP"/>
                <XMTok font="italic" role="ID">c</XMTok>
                <XMTok font="italic" role="ID">d</XMTok>
              </XMApp>
            </XMApp>
          </XMath>
        </Math>
      </equation>
    </para>
  </section>
</document>
