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    <title>Sub -- format ring actors as one-row substitution matrices</title>
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o1 = R

o1 : PolynomialRing</code></pre>
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              <pre><code class="language-macaulay2">i2 : I = ideal apply(subsets(gens R,2),product)

o2 = ideal (x x , x x , x x , x x , x x , x x )
             1 2   1 3   2 3   1 4   2 4   3 4

o2 : Ideal of R</code></pre>
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              <pre><code class="language-macaulay2">i3 : RI = freeResolution I

1      6      8      3
o3 = R  &lt;-- R  &lt;-- R  &lt;-- R
                           
     0      1      2      3

o3 : Complex</code></pre>
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              <pre><code class="language-macaulay2">i4 : G = { (id_(R^4))_{1,2,3,0},
           (id_(R^4))_{1,2,0,3},
           (id_(R^4))_{1,0,3,2},
           (id_(R^4))_{1,0,2,3},
            id_(R^4) }

o4 = {| 0 0 0 1 |, | 0 0 1 0 |, | 0 1 0 0 |, | 0 1 0 0 |, | 1 0 0 0 |}
      | 1 0 0 0 |  | 1 0 0 0 |  | 1 0 0 0 |  | 1 0 0 0 |  | 0 1 0 0 |
      | 0 1 0 0 |  | 0 1 0 0 |  | 0 0 0 1 |  | 0 0 1 0 |  | 0 0 1 0 |
      | 0 0 1 0 |  | 0 0 0 1 |  | 0 0 1 0 |  | 0 0 0 1 |  | 0 0 0 1 |

o4 : List</code></pre>
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              <pre><code class="language-macaulay2">i5 : A = action(RI,G,Sub=>false)

o5 = Complex with 5 actors

o5 : ActionOnComplex</code></pre>
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          <p>Similarly, setting <span class="tt">Sub=>false</span> causes <a title="get action on ring generators" href="_ring__Actors.html">ringActors</a> and <a title="get inverse of action on ring generators" href="_inverse__Ring__Actors.html">inverseRingActors</a> to return the group elements acting on the ring as square matrices. With the default setting <span class="tt">Sub=>true</span>, the same elements are returned as one-row substitution matrices.</p>
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              <pre><code class="language-macaulay2">i6 : ringActors(A,Sub=>false)

o6 = {| 0 0 0 1 |, | 0 0 1 0 |, | 0 1 0 0 |, | 0 1 0 0 |, | 1 0 0 0 |}
      | 1 0 0 0 |  | 1 0 0 0 |  | 1 0 0 0 |  | 1 0 0 0 |  | 0 1 0 0 |
      | 0 1 0 0 |  | 0 1 0 0 |  | 0 0 0 1 |  | 0 0 1 0 |  | 0 0 1 0 |
      | 0 0 1 0 |  | 0 0 0 1 |  | 0 0 1 0 |  | 0 0 0 1 |  | 0 0 0 1 |

o6 : List</code></pre>
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              <pre><code class="language-macaulay2">i7 : inverseRingActors(A,Sub=>false)

o7 = {| 0 1 0 0 |, | 0 1 0 0 |, | 0 1 0 0 |, | 0 1 0 0 |, | 1 0 0 0 |}
      | 0 0 1 0 |  | 0 0 1 0 |  | 1 0 0 0 |  | 1 0 0 0 |  | 0 1 0 0 |
      | 0 0 0 1 |  | 1 0 0 0 |  | 0 0 0 1 |  | 0 0 1 0 |  | 0 0 1 0 |
      | 1 0 0 0 |  | 0 0 0 1 |  | 0 0 1 0 |  | 0 0 0 1 |  | 0 0 0 1 |

o7 : List</code></pre>
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              <pre><code class="language-macaulay2">i8 : ringActors(A)

o8 = {| x_2 x_3 x_4 x_1 |, | x_2 x_3 x_1 x_4 |, | x_2 x_1 x_4 x_3 |, | x_2
     ------------------------------------------------------------------------
     x_1 x_3 x_4 |, | x_1 x_2 x_3 x_4 |}

o8 : List</code></pre>
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              <pre><code class="language-macaulay2">i9 : inverseRingActors(A)

o9 = {| x_4 x_1 x_2 x_3 |, | x_3 x_1 x_2 x_4 |, | x_2 x_1 x_4 x_3 |, | x_2
     ------------------------------------------------------------------------
     x_1 x_3 x_4 |, | x_1 x_2 x_3 x_4 |}

o9 : List</code></pre>
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          <h2>Functions with optional argument named <span class="tt">Sub</span>:</h2>
          <ul>
            <li><kbd>action(...,Sub=>...)</kbd></li>
            <li><kbd>inverseRingActors(...,Sub=>...)</kbd></li>
            <li><kbd>ringActors(...,Sub=>...)</kbd></li>
          </ul>
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        <div class="waystouse">
          <h2>For the programmer</h2>
          <p>The object <a title="format ring actors as one-row substitution matrices" href="___Sub.html">Sub</a> is <span>a <a title="the class of all symbols" href="../../Macaulay2Doc/html/___Symbol.html">symbol</a></span>.</p>
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        <div class="waystouse">
          <p>The source of this document is in <span class="tt">BettiCharacters.m2:2846:0</span>.</p>
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