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    <title>minor -- minor of matroid</title>
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o1 = a &quot;matroid&quot; of rank 3 on 6 elements

o1 : Matroid</code></pre>
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              <pre><code class="language-macaulay2">i2 : M_*

o2 = {| 8 |, | 7 |, | 3 |, | 8 |, | 8 |, | 3 |}
      | 1 |  | 8 |  | 7 |  | 5 |  | 5 |  | 6 |
      | 3 |  | 3 |  | 8 |  | 7 |  | 2 |  | 3 |

o2 : List</code></pre>
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              <pre><code class="language-macaulay2">i3 : M.groundSet

o3 = set {0, 1, 2, 3, 4, 5}

o3 : Set</code></pre>
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              <pre><code class="language-macaulay2">i4 : (X, Y) = (set{3}, set{0,1})

o4 = (set {3}, set {0, 1})

o4 : Sequence</code></pre>
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              <pre><code class="language-macaulay2">i5 : (X1, Y1) = (M_X, M_Y)/toList

o5 = ({| 8 |}, {| 7 |, | 8 |})
       | 5 |    | 8 |  | 1 |
       | 7 |    | 3 |  | 3 |

o5 : Sequence</code></pre>
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              <pre><code class="language-macaulay2">i6 : N = minor(M, X, Y)

o6 = a &quot;matroid&quot; of rank 2 on 3 elements

o6 : Matroid</code></pre>
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              <pre><code class="language-macaulay2">i7 : peek N

o7 = Matroid{bases => {set {0, 1}, set {0, 2}, set {1, 2}}}
             cache => CacheTable{...1...}
             groundSet => set {0, 1, 2}
             rank => 2</code></pre>
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              <pre><code class="language-macaulay2">i8 : N == minor(M, X1, Y1)

o8 = true</code></pre>
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          <p></p>
          <p>Note that there is potential ambiguity for the second argument - namely, whether or not Y is treated with respect to the ground set of M or M / X (which are different). This method assumes that the indices of Y (and X) are taken with respect to the ground set of M.</p>
          <p>If one already has the indices Y0 of Y in M / X (or the indices X0 of X in M \ Y), one can simply use the notation M <a title="contraction of subset of matroid" href="_contraction.html">/</a> X <a title="deletion of subset of matroid" href="_deletion.html">\</a> Y0 (or (M \ Y) / X0). Thus this method serves purely as a convenience, to save the user the (trivial) task of computing Y0 from Y.</p>
          <p>If X and Y are not disjoint, then an error is thrown (thus one should <a title="set difference" href="../../Macaulay2Doc/html/___Set_sp-_sp__Set.html">subtract</a> X from Y beforehand).</p>
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              <pre><code class="language-macaulay2">i9 : M5 = matroid completeGraph 5

o9 = a &quot;matroid&quot; of rank 4 on 10 elements

o9 : Matroid</code></pre>
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              <pre><code class="language-macaulay2">i10 : M5.groundSet

o10 = set {0, 1, 2, 3, 4, 5, 6, 7, 8, 9}

o10 : Set</code></pre>
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              <pre><code class="language-macaulay2">i11 : N = minor(M5, set{8}, set{3,4,9})

o11 = a &quot;matroid&quot; of rank 3 on 6 elements

o11 : Matroid</code></pre>
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              <pre><code class="language-macaulay2">i12 : areIsomorphic(N, matroid completeGraph 4)

o12 = true</code></pre>
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              <pre><code class="language-macaulay2">i13 : N == (M5 \ set{3,4,9}) / set{6} -- after deleting 3,4 (and 9), index 8 -> 6

o13 = true</code></pre>
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              <pre><code class="language-macaulay2">i14 : N == M5 / set{8} \ set{3,4,8} -- after contracting 8, index 9 -> 8

o14 = true</code></pre>
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              <pre><code class="language-macaulay2">i15 : (try minor(M5, set{8}, set{3,4,8,9})) === null

o15 = true</code></pre>
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              <pre><code class="language-macaulay2">i16 : minor(M5, set{8}, set{3,4,8,9} - set{8})

o16 = a &quot;matroid&quot; of rank 3 on 6 elements

o16 : Matroid</code></pre>
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        <h2>See also</h2>
        <ul>
          <li><span><a title="deletion of subset of matroid" href="_deletion.html">deletion</a> -- deletion of subset of matroid</span></li>
          <li><span><a title="contraction of subset of matroid" href="_contraction.html">contraction</a> -- contraction of subset of matroid</span></li>
          <li><span><a title="whether a matroid has a given minor" href="_has__Minor.html">hasMinor</a> -- whether a matroid has a given minor</span></li>
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        <div class="waystouse">
          <h2>Ways to use <span class="tt">minor</span>:</h2>
          <ul>
            <li><kbd>minor(Matroid,List,List)</kbd></li>
            <li><kbd>minor(Matroid,Set,Set)</kbd></li>
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        <div class="waystouse">
          <h2>For the programmer</h2>
          <p>The object <a title="minor of matroid" href="_minor.html">minor</a> is <span>a <a title="a type of method function" href="../../Macaulay2Doc/html/___Method__Function.html">method function</a></span>.</p>
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        <div class="waystouse">
          <p>The source of this document is in <span class="tt">Matroids/doc-Matroids.m2:1486:0</span>.</p>
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