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    <title>compose -- composition as a pairing on Hom-modules</title>
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o1 = R

o1 : PolynomialRing</code></pre>
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              <pre><code class="language-macaulay2">i2 : M = image vars R ++ R^2

o2 = image | x y 0 0 |
           | 0 0 1 0 |
           | 0 0 0 1 |

3
o2 : R-module, submodule of R</code></pre>
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              <pre><code class="language-macaulay2">i3 : f = compose(M,M,M);

o3 : Matrix</code></pre>
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              <pre><code class="language-macaulay2">i4 : H = Hom(M,M);</code></pre>
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              <pre><code class="language-macaulay2">i5 : g = H_{0}

o5 = {0} | 1 |
     {0} | 0 |
     {0} | 0 |
     {0} | 0 |
     {0} | 0 |
     {0} | 0 |
     {0} | 0 |
     {1} | 0 |
     {1} | 0 |
     {1} | 0 |
     {1} | 0 |

1
o5 : Matrix H &lt;-- R</code></pre>
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              <pre><code class="language-macaulay2">i6 : h = homomorphism g

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

o6 : Matrix M &lt;-- M</code></pre>
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              <pre><code class="language-macaulay2">i7 : f * (g ** g)

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

1
o7 : Matrix H &lt;-- R</code></pre>
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              <pre><code class="language-macaulay2">i8 : h' = homomorphism oo

o8 = {1} | 1 0 0 0 |
     {1} | 0 1 0 0 |
     {0} | 0 0 0 0 |
     {0} | 0 0 0 0 |

o8 : Matrix M &lt;-- M</code></pre>
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              <pre><code class="language-macaulay2">i9 : h' === h * h

o9 = true</code></pre>
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              <pre><code class="language-macaulay2">i10 : assert oo</code></pre>
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          <p>The modules should be defined over the same ring.</p>
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        <h2>See also</h2>
        <ul>
          <li><span><a title="module of homomorphisms" href="___Hom.html">Hom</a> -- module of homomorphisms</span></li>
          <li><span><a title="get the homomorphism from element of Hom" href="_homomorphism.html">homomorphism</a> -- get the homomorphism from element of Hom</span></li>
          <li><span><a title="get the element of Hom from a homomorphism" href="_homomorphism_sq.html">homomorphism'</a> -- get the element of Hom from a homomorphism</span></li>
          <li><span><a title="the tensor-Hom adjunction maps" href="_adjoint.html">adjoint</a> -- the tensor-Hom adjunction maps</span></li>
          <li><span><a title="isomorphism map of commutativity of tensor product" href="_flip.html">flip</a> -- isomorphism map of commutativity of tensor product</span></li>
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        <div class="waystouse">
          <h2>Ways to use <span class="tt">compose</span>:</h2>
          <ul>
            <li><kbd>compose(Module,Module,Module)</kbd></li>
          </ul>
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          <h2>For the programmer</h2>
          <p>The object <a title="composition as a pairing on Hom-modules" href="_compose.html">compose</a> is <span>a <a title="a type of method function" href="___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">Macaulay2Doc/functions/Hom-doc.m2:431:0</span>.</p>
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