One Hat Cyber Team

Edit File: _same.html

<!DOCTYPE html>
<html lang="en">
  <head>
    <title>same -- whether everything in a list is the same</title>
    <meta content="text/html; charset=utf-8" http-equiv="Content-Type">
    <link type="text/css" rel="stylesheet" href="../../../../Macaulay2/Style/doc.css">

o1 = true</code></pre>
            </td>
          </tr>
          <tr>
            <td>
              <pre><code class="language-macaulay2">i2 : same {1, 2, 1, 1}

o2 = false</code></pre>
            </td>
          </tr>
        </table>
        <div>
          <p>The comparison is done with &quot;===&quot;, which is quick, but not always intuitive. Here is a simple example of what can go wrong:</p>
        </div>
        <table class="examples">
          <tr>
            <td>
              <pre><code class="language-macaulay2">i3 : R = QQ[x,y,z];</code></pre>
            </td>
          </tr>
          <tr>
            <td>
              <pre><code class="language-macaulay2">i4 : L = {gcd{x,y}, x/x, 1}

o4 = {1, 1, 1}

o4 : List</code></pre>
            </td>
          </tr>
          <tr>
            <td>
              <pre><code class="language-macaulay2">i5 : same L

o5 = false</code></pre>
            </td>
          </tr>
        </table>
        <div>
          <p>We can see the problem by asking <span class="tt">Macaulay2</span> to display the class of each element of <span class="tt">L</span>. (Or use the function <a title="whether all elements of a list are the same class" href="_uniform.html">uniform</a>, which returns whether or not the elements of a list are all of the same class.)</p>
        </div>
        <table class="examples">
          <tr>
            <td>
              <pre><code class="language-macaulay2">i6 : apply(L, class)

o6 = {R, frac R, ZZ}

o6 : List</code></pre>
            </td>
          </tr>
          <tr>
            <td>
              <pre><code class="language-macaulay2">i7 : uniform L

o7 = false</code></pre>
            </td>
          </tr>
        </table>
        <div>
          <p>The first <span class="tt">1</span> is an element of the ring <span class="tt">R</span>, the second <span class="tt">1</span> is an element of the fraction field of <span class="tt">R</span>, and the third <span class="tt">1</span> is an integer. Thus <span class="tt">Macaulay2</span> thinks of these three elements as being pairwise unequal, with respect to the operator &quot;===&quot;.</p>
        </div>
      </div>
      <div>
        <h2>See also</h2>
        <ul>
          <li><span><a title="the most common elements of a list or tally" href="_commonest.html">commonest</a> -- the most common elements of a list or tally</span></li>
          <li><span><a title="count how many elements of a list satisfy a condition" href="_number.html">number</a> -- count how many elements of a list satisfy a condition</span></li>
          <li><span><a title="make a set" href="_set.html">set</a> -- make a set</span></li>
          <li><span><a title="whether all elements of a list are the same class" href="_uniform.html">uniform</a> -- whether all elements of a list are the same class</span></li>
          <li><span><a title="eliminate duplicates from a list" href="_unique.html">unique</a> -- eliminate duplicates from a list</span></li>
          <li><span><a title="a detailed overview of lists and sequences in Macaulay2" href="_lists_spand_spsequences.html">lists and sequences</a> -- a detailed overview of lists and sequences in Macaulay2</span></li>
        </ul>
      </div>
      <div>
        <div class="waystouse">
          <h2>For the programmer</h2>
          <p>The object <a title="whether everything in a list is the same" href="_same.html">same</a> is <span>a <a title="the class of all function closures" href="___Function__Closure.html">function closure</a></span>.</p>
        </div>
        <hr>
        <div class="waystouse">
          <p>The source of this document is in <span class="tt">Macaulay2Doc/functions/same-doc.m2:48:0</span>.</p>
        </div>
      </div>
    </div>
  </body>

</html>