<?xml version="1.0" encoding="UTF-8"?>
<?latexml RelaxNGSchema="LaTeXML"?>
<document xmlns="http://dlmf.nist.gov/LaTeXML">
  <resource src="LaTeXML.css" type="text/css"/>
  <para>
    <equation>
      <Math mode="display" tex="\matrix{a&amp;b\cr c&amp;d}" text="matrix@(Array[[a, b], [c, d]])">
        <XMath>
          <XMDual>
            <XMApp>
              <XMTok meaning="matrix"/>
              <XMRef idref="id1"/>
            </XMApp>
            <XMArray xml:id="id1">
              <XMRow>
                <XMCell align="center">
                  <XMTok font="italic" role="UNKNOWN">a</XMTok>
                </XMCell>
                <XMCell align="center">
                  <XMTok font="italic" role="UNKNOWN">b</XMTok>
                </XMCell>
              </XMRow>
              <XMRow>
                <XMCell align="center">
                  <XMTok font="italic" role="UNKNOWN">c</XMTok>
                </XMCell>
                <XMCell align="center">
                  <XMTok font="italic" role="UNKNOWN">d</XMTok>
                </XMCell>
              </XMRow>
            </XMArray>
          </XMDual>
        </XMath>
      </Math>
    </equation>
    <equation>
      <Math class="ltx_math_unparsed" mode="display" tex="\bordermatrix{&amp;A&amp;B\cr C&amp;0&amp;1\cr D&amp;2&amp;3}" text="Array[[, , A, B, ], [C, (@ , 0, 1, )@ ], [D, , 2, 3, ]]">
        <XMath>
          <XMArray>
            <XMRow>
              <XMCell/>
              <XMCell/>
              <XMCell align="center">
                <XMTok font="italic" role="UNKNOWN">A</XMTok>
              </XMCell>
              <XMCell align="center">
                <XMTok font="italic" role="UNKNOWN">B</XMTok>
              </XMCell>
              <XMCell/>
            </XMRow>
            <XMRow>
              <XMCell align="center">
                <XMTok font="italic" role="UNKNOWN">C</XMTok>
              </XMCell>
              <XMCell rowspan="2">
                <XMWrap depth="6.8pt">
                  <XMTok depth="6.8pt" height="0" role="OPEN" yoffset="-6.8pt">(</XMTok>
                  <XMTok height="6.8pt" yoffset="-6.8pt"> </XMTok>
                </XMWrap>
              </XMCell>
              <XMCell align="center">
                <XMTok meaning="0" role="NUMBER">0</XMTok>
              </XMCell>
              <XMCell align="center">
                <XMTok meaning="1" role="NUMBER">1</XMTok>
              </XMCell>
              <XMCell rowspan="2">
                <XMWrap>
                  <XMTok depth="6.8pt" height="0" role="CLOSE" yoffset="-6.8pt">)</XMTok>
                  <XMTok height="6.8pt" yoffset="-6.8pt"> </XMTok>
                </XMWrap>
              </XMCell>
            </XMRow>
            <XMRow>
              <XMCell align="center">
                <XMTok font="italic" role="UNKNOWN">D</XMTok>
              </XMCell>
              <XMCell/>
              <XMCell align="center">
                <XMTok meaning="2" role="NUMBER">2</XMTok>
              </XMCell>
              <XMCell align="center">
                <XMTok meaning="3" role="NUMBER">3</XMTok>
              </XMCell>
              <XMCell/>
            </XMRow>
          </XMArray>
        </XMath>
      </Math>
    </equation>
    <equation>
      <Math mode="display" tex="\pmatrix{a&amp;b\cr c&amp;d}" text="matrix@(Array[[a, b], [c, d]])">
        <XMath>
          <XMDual>
            <XMApp>
              <XMTok meaning="matrix"/>
              <XMRef idref="id2"/>
            </XMApp>
            <XMWrap>
              <XMTok role="OPEN" stretchy="true">(</XMTok>
              <XMArray xml:id="id2">
                <XMRow>
                  <XMCell align="center">
                    <XMTok font="italic" role="UNKNOWN">a</XMTok>
                  </XMCell>
                  <XMCell align="center">
                    <XMTok font="italic" role="UNKNOWN">b</XMTok>
                  </XMCell>
                </XMRow>
                <XMRow>
                  <XMCell align="center">
                    <XMTok font="italic" role="UNKNOWN">c</XMTok>
                  </XMCell>
                  <XMCell align="center">
                    <XMTok font="italic" role="UNKNOWN">d</XMTok>
                  </XMCell>
                </XMRow>
              </XMArray>
              <XMTok role="CLOSE" stretchy="true">)</XMTok>
            </XMWrap>
          </XMDual>
        </XMath>
      </Math>
    </equation>
  </para>
  <para>
    <equation>
      <Math mode="display" tex="s(x)=\cases{+1&amp;whatever\cr-1&amp;$x&lt;0$\cr 0}" text="s * x = cases@(+ 1, [whatever], - 1, x &lt; 0, 0, [otherwise])">
        <XMath>
          <XMApp>
            <XMTok meaning="equals" role="RELOP">=</XMTok>
            <XMApp>
              <XMTok meaning="times" role="MULOP">⁢</XMTok>
              <XMTok font="italic" role="UNKNOWN">s</XMTok>
              <XMDual>
                <XMRef idref="id8"/>
                <XMWrap>
                  <XMTok role="OPEN" stretchy="false">(</XMTok>
                  <XMTok font="italic" role="UNKNOWN" xml:id="id8">x</XMTok>
                  <XMTok role="CLOSE" stretchy="false">)</XMTok>
                </XMWrap>
              </XMDual>
            </XMApp>
            <XMDual>
              <XMApp>
                <XMTok meaning="cases"/>
                <XMRef idref="id3"/>
                <XMRef idref="id4"/>
                <XMRef idref="id5"/>
                <XMRef idref="id6"/>
                <XMRef idref="id7"/>
                <XMText><text font="italic">otherwise</text></XMText>
              </XMApp>
              <XMWrap>
                <XMTok role="OPEN" stretchy="true">{</XMTok>
                <XMArray>
                  <XMRow>
                    <XMCell align="left">
                      <XMApp xml:id="id3">
                        <XMTok meaning="plus" role="ADDOP">+</XMTok>
                        <XMTok meaning="1" role="NUMBER">1</XMTok>
                      </XMApp>
                    </XMCell>
                    <XMCell align="left">
                      <XMText xml:id="id4">whatever</XMText>
                    </XMCell>
                  </XMRow>
                  <XMRow>
                    <XMCell align="left">
                      <XMApp xml:id="id5">
                        <XMTok meaning="minus" role="ADDOP">-</XMTok>
                        <XMTok meaning="1" role="NUMBER">1</XMTok>
                      </XMApp>
                    </XMCell>
                    <XMCell align="left">
                      <XMApp xml:id="id6">
                        <XMTok meaning="less-than" role="RELOP">&lt;</XMTok>
                        <XMTok font="italic" role="UNKNOWN">x</XMTok>
                        <XMTok meaning="0" role="NUMBER">0</XMTok>
                      </XMApp>
                    </XMCell>
                  </XMRow>
                  <XMRow>
                    <XMCell align="left">
                      <XMTok meaning="0" role="NUMBER" xml:id="id7">0</XMTok>
                    </XMCell>
                    <XMCell/>
                  </XMRow>
                </XMArray>
              </XMWrap>
            </XMDual>
          </XMApp>
        </XMath>
      </Math>
    </equation>
  </para>
  <para>
    <equation>
      <Math mode="display" tex="\eqalign{x&amp;\ll y+i+\cdots+y_{n}\cr&amp;\leq z}" text="Array[[x, absent &lt;&lt; y + i + cdots + y _ n], [, absent &lt;= z]]">
        <XMath>
          <XMArray vattach="baseline">
            <XMRow>
              <XMCell align="right">
                <XMTok font="italic" role="UNKNOWN">x</XMTok>
              </XMCell>
              <XMCell align="left">
                <XMApp>
                  <XMTok meaning="much-less-than" name="ll" role="RELOP">≪</XMTok>
                  <XMTok meaning="absent"/>
                  <XMApp>
                    <XMTok meaning="plus" role="ADDOP">+</XMTok>
                    <XMTok font="italic" role="UNKNOWN">y</XMTok>
                    <XMTok font="italic" role="UNKNOWN">i</XMTok>
                    <XMTok name="cdots" role="ID">⋯</XMTok>
                    <XMApp>
                      <XMTok role="SUBSCRIPTOP" scriptpos="post5"/>
                      <XMTok font="italic" role="UNKNOWN">y</XMTok>
                      <XMTok font="italic" fontsize="70%" role="UNKNOWN">n</XMTok>
                    </XMApp>
                  </XMApp>
                </XMApp>
              </XMCell>
            </XMRow>
            <XMRow>
              <XMCell/>
              <XMCell align="left">
                <XMApp>
                  <XMTok meaning="less-than-or-equals" name="leq" role="RELOP">≤</XMTok>
                  <XMTok meaning="absent"/>
                  <XMTok font="italic" role="UNKNOWN">z</XMTok>
                </XMApp>
              </XMCell>
            </XMRow>
          </XMArray>
        </XMath>
      </Math>
    </equation>
    <equation>
      <Math mode="display" tex="\eqalign{x+y+z&amp;\ll y+i+\cdots+y_{n}\cr&amp;\leq q}" text="Array[[x + y + z, absent &lt;&lt; y + i + cdots + y _ n], [, absent &lt;= q]]">
        <XMath>
          <XMArray vattach="baseline">
            <XMRow>
              <XMCell align="right">
                <XMApp>
                  <XMTok meaning="plus" role="ADDOP">+</XMTok>
                  <XMTok font="italic" role="UNKNOWN">x</XMTok>
                  <XMTok font="italic" role="UNKNOWN">y</XMTok>
                  <XMTok font="italic" role="UNKNOWN">z</XMTok>
                </XMApp>
              </XMCell>
              <XMCell align="left">
                <XMApp>
                  <XMTok meaning="much-less-than" name="ll" role="RELOP">≪</XMTok>
                  <XMTok meaning="absent"/>
                  <XMApp>
                    <XMTok meaning="plus" role="ADDOP">+</XMTok>
                    <XMTok font="italic" role="UNKNOWN">y</XMTok>
                    <XMTok font="italic" role="UNKNOWN">i</XMTok>
                    <XMTok name="cdots" role="ID">⋯</XMTok>
                    <XMApp>
                      <XMTok role="SUBSCRIPTOP" scriptpos="post5"/>
                      <XMTok font="italic" role="UNKNOWN">y</XMTok>
                      <XMTok font="italic" fontsize="70%" role="UNKNOWN">n</XMTok>
                    </XMApp>
                  </XMApp>
                </XMApp>
              </XMCell>
            </XMRow>
            <XMRow>
              <XMCell/>
              <XMCell align="left">
                <XMApp>
                  <XMTok meaning="less-than-or-equals" name="leq" role="RELOP">≤</XMTok>
                  <XMTok meaning="absent"/>
                  <XMTok font="italic" role="UNKNOWN">q</XMTok>
                </XMApp>
              </XMCell>
            </XMRow>
          </XMArray>
        </XMath>
      </Math>
    </equation>
    <equation>
      <Math mode="display" tex="\eqalignno{x&amp;\ll y+i+\cdots+y_{n}&amp;(x)\cr&amp;\leq z}" text="Array[[x, absent &lt;&lt; y + i + cdots + y _ n, x], [, absent &lt;= z, ]]">
        <XMath>
          <XMArray vattach="baseline">
            <XMRow>
              <XMCell align="right">
                <XMTok font="italic" role="UNKNOWN">x</XMTok>
              </XMCell>
              <XMCell align="left">
                <XMApp>
                  <XMTok meaning="much-less-than" name="ll" role="RELOP">≪</XMTok>
                  <XMTok meaning="absent"/>
                  <XMApp>
                    <XMTok meaning="plus" role="ADDOP">+</XMTok>
                    <XMTok font="italic" role="UNKNOWN">y</XMTok>
                    <XMTok font="italic" role="UNKNOWN">i</XMTok>
                    <XMTok name="cdots" role="ID">⋯</XMTok>
                    <XMApp>
                      <XMTok role="SUBSCRIPTOP" scriptpos="post5"/>
                      <XMTok font="italic" role="UNKNOWN">y</XMTok>
                      <XMTok font="italic" fontsize="70%" role="UNKNOWN">n</XMTok>
                    </XMApp>
                  </XMApp>
                </XMApp>
              </XMCell>
              <XMCell align="left">
                <XMDual>
                  <XMRef idref="id9"/>
                  <XMWrap>
                    <XMTok role="OPEN" stretchy="false">(</XMTok>
                    <XMTok font="italic" role="UNKNOWN" xml:id="id9">x</XMTok>
                    <XMTok role="CLOSE" stretchy="false">)</XMTok>
                  </XMWrap>
                </XMDual>
              </XMCell>
            </XMRow>
            <XMRow>
              <XMCell/>
              <XMCell align="left">
                <XMApp>
                  <XMTok meaning="less-than-or-equals" name="leq" role="RELOP">≤</XMTok>
                  <XMTok meaning="absent"/>
                  <XMTok font="italic" role="UNKNOWN">z</XMTok>
                </XMApp>
              </XMCell>
              <XMCell/>
            </XMRow>
          </XMArray>
        </XMath>
      </Math>
    </equation>
    <equation>
      <Math mode="display" tex="\leqalignno{x&amp;\ll y+i+\cdots+y_{n}&amp;(x)\cr&amp;\leq z}" text="Array[[x, absent &lt;&lt; y + i + cdots + y _ n, x], [, absent &lt;= z, ]]">
        <XMath>
          <XMArray vattach="baseline">
            <XMRow>
              <XMCell align="right">
                <XMTok font="italic" role="UNKNOWN">x</XMTok>
              </XMCell>
              <XMCell align="left">
                <XMApp>
                  <XMTok meaning="much-less-than" name="ll" role="RELOP">≪</XMTok>
                  <XMTok meaning="absent"/>
                  <XMApp>
                    <XMTok meaning="plus" role="ADDOP">+</XMTok>
                    <XMTok font="italic" role="UNKNOWN">y</XMTok>
                    <XMTok font="italic" role="UNKNOWN">i</XMTok>
                    <XMTok name="cdots" role="ID">⋯</XMTok>
                    <XMApp>
                      <XMTok role="SUBSCRIPTOP" scriptpos="post5"/>
                      <XMTok font="italic" role="UNKNOWN">y</XMTok>
                      <XMTok font="italic" fontsize="70%" role="UNKNOWN">n</XMTok>
                    </XMApp>
                  </XMApp>
                </XMApp>
              </XMCell>
              <XMCell align="left">
                <XMDual>
                  <XMRef idref="id10"/>
                  <XMWrap>
                    <XMTok role="OPEN" stretchy="false">(</XMTok>
                    <XMTok font="italic" role="UNKNOWN" xml:id="id10">x</XMTok>
                    <XMTok role="CLOSE" stretchy="false">)</XMTok>
                  </XMWrap>
                </XMDual>
              </XMCell>
            </XMRow>
            <XMRow>
              <XMCell/>
              <XMCell align="left">
                <XMApp>
                  <XMTok meaning="less-than-or-equals" name="leq" role="RELOP">≤</XMTok>
                  <XMTok meaning="absent"/>
                  <XMTok font="italic" role="UNKNOWN">z</XMTok>
                </XMApp>
              </XMCell>
              <XMCell/>
            </XMRow>
          </XMArray>
        </XMath>
      </Math>
    </equation>
  </para>
</document>