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    <title>carpet -- Ideal of the unique Gorenstein double structure on a 2-dimensional scroll</title>
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0  1  2  3  4  5 6
o1 = total: 1 15 49 70 49 15 1
         0: 1  .  .  .  .  . .
         1: . 15 35 35 14  . .
         2: .  . 14 35 35 15 .
         3: .  .  .  .  .  . 1

o1 : BettiTally</code></pre>
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              <pre><code class="language-macaulay2">i2 : S = ZZ/101[a..j]

o2 = S

o2 : PolynomialRing</code></pre>
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              <pre><code class="language-macaulay2">i3 : m = genericMatrix(S,a,2,5)

o3 = | a c e g i |
     | b d f h j |

2      5
o3 : Matrix S  &lt;-- S</code></pre>
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              <pre><code class="language-macaulay2">i4 : I = carpet(2,3,m)

o4 = ideal (b*c - a*d, b*e - a*f, d*e - c*f, d*g - c*h - b*i + a*j, f*g - e*h
     ------------------------------------------------------------------------
     - d*i + c*j, h*i - g*j)

o4 : Ideal of S</code></pre>
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              <pre><code class="language-macaulay2">i5 : L = primaryDecomposition I;</code></pre>
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              <pre><code class="language-macaulay2">i6 : betti freeResolution L_0

0  1  2  3 4
o6 = total: 1 10 20 15 4
         0: 1  .  .  . .
         1: . 10 20 15 4

o6 : BettiTally</code></pre>
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              <pre><code class="language-macaulay2">i7 : betti freeResolution L_1

0  1  2  3  4 5
o7 = total: 1 15 40 45 24 5
         0: 1  .  .  .  . .
         1: . 15 40 45 24 5

o7 : BettiTally</code></pre>
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          <p></p>
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        <h2>Caveat</h2>
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          <p>We require $a1,a2 \ge 1$. If $a1>a2$ then the blocks are reversed, so that the smaller block always comes first. The script generalizeScroll is a more general tool that can do the same things.</p>
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        <h2>See also</h2>
        <ul>
          <li><span><a title="Carpet of given genus and Clifford index" href="_canonical__Carpet.html">canonicalCarpet</a> -- Carpet of given genus and Clifford index</span></li>
          <li><span><a title="attempts to produce a Gorenstein double structure J subset I" href="_gorenstein__Double.html">gorensteinDouble</a> -- attempts to produce a Gorenstein double structure J subset I</span></li>
          <li><span><a title="Union of planes joining points of rational normal curves according to a given correspondence" href="_correspondence__Scroll.html">correspondenceScroll</a> -- Union of planes joining points of rational normal curves according to a given correspondence</span></li>
        </ul>
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        <div class="waystouse">
          <h2>Ways to use <span class="tt">carpet</span>:</h2>
          <ul>
            <li><kbd>carpet(ZZ,ZZ)</kbd></li>
            <li><kbd>carpet(ZZ,ZZ,Matrix)</kbd></li>
          </ul>
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        <div class="waystouse">
          <h2>For the programmer</h2>
          <p>The object <a title="Ideal of the unique Gorenstein double structure on a 2-dimensional scroll" href="_carpet.html">carpet</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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        <hr>
        <div class="waystouse">
          <p>The source of this document is in <span class="tt">K3Carpets.m2:1199:0</span>.</p>
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