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    <title>elementaryQuotient -- associated to a modular cut or linear subclass</title>
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o1 = | 1 0 0 1 1  |
     | 0 1 0 1 -1 |
     | 0 0 1 0 0  |

3       5
o1 : Matrix ZZ  &lt;-- ZZ</code></pre>
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              <pre><code class="language-macaulay2">i2 : M = matroid A

o2 = a &quot;matroid&quot; of rank 3 on 5 elements

o2 : Matroid</code></pre>
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              <pre><code class="language-macaulay2">i3 : K = {{2}, {2, 4}, {2, 3}, {1, 2}, {0, 2}, {0, 1, 2, 3, 4}};</code></pre>
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              <pre><code class="language-macaulay2">i4 : isModularCut(M, K)

o4 = true</code></pre>
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              <pre><code class="language-macaulay2">i5 : Q1 = elementaryQuotient(M, K)

o5 = a &quot;matroid&quot; of rank 2 on 5 elements

o5 : Matroid</code></pre>
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        <p>Equivalently since, a modular cut K of the matroid M is completely determined by a collection of hyperplanes of M called a linear subclass, we can form an elementary quotient by specifying a much shorter list of hyperplanes as follows.  See <a title="whether a list of hyperplanes of a matroid is a linear subclass" href="_is__Linear__Subclass.html">isLinearSubclass</a> for more details about linear subclasses.</p>
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              <pre><code class="language-macaulay2">i6 : H = linearSubclass(M, K)

o6 = {set {2, 3}, set {0, 2}, set {4, 2}, set {1, 2}}

o6 : List</code></pre>
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              <pre><code class="language-macaulay2">i7 : Q2 = elementaryQuotient(M, H, EntryMode => &quot;hyperplanes&quot;)

o7 = a &quot;matroid&quot; of rank 2 on 5 elements

o7 : Matroid</code></pre>
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              <pre><code class="language-macaulay2">i8 : Q1 == Q2

o8 = true</code></pre>
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        <h2>See also</h2>
        <ul>
          <li><span><a title="whether a matroid is an elementary quotient of another matroid" href="_is__Elementary__Quotient.html">isElementaryQuotient</a> -- whether a matroid is an elementary quotient of another matroid</span></li>
          <li><span><a title="whether a list of hyperplanes of a matroid is a linear subclass" href="_is__Linear__Subclass.html">isLinearSubclass</a> -- whether a list of hyperplanes of a matroid is a linear subclass</span></li>
          <li><span><a title="whether a list of flats of a matroid is a modular cut" href="_is__Modular__Cut.html">isModularCut</a> -- whether a list of flats of a matroid is a modular cut</span></li>
          <li><span><a title="whether a matroid is a quotient of another matroid" href="_is__Quotient.html">isQuotient</a> -- whether a matroid is a quotient of another matroid</span></li>
          <li><span><a title="associated to an elementary quotient or modular cut" href="_linear__Subclass.html">linearSubclass</a> -- associated to an elementary quotient or modular cut</span></li>
          <li><span><a title="associated to an elementary quotient or linear subclass" href="_modular__Cut.html">modularCut</a> -- associated to an elementary quotient or linear subclass</span></li>
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        <div class="waystouse">
          <h2>Ways to use <span class="tt">elementaryQuotient</span>:</h2>
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            <li><kbd>elementaryQuotient(Matroid,List)</kbd></li>
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          <h2>For the programmer</h2>
          <p>The object <a title="associated to a modular cut or linear subclass" href="_elementary__Quotient.html">elementaryQuotient</a> is <span>a <a title="a type of method function" href="../../Macaulay2Doc/html/___Method__Function__With__Options.html">method function with options</a></span>.</p>
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        <div class="waystouse">
          <p>The source of this document is in <span class="tt">Matroids/doc-Matroids.m2:3793:0</span>.</p>
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