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set_theory.html
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<html>
<head>
<title>
SET_THEORY - MATLAB Commands for Set Operations
</title>
</head>
<body bgcolor="#EEEEEE" link="#CC0000" alink="#FF3300" vlink="#000055">
<h1 align = "center">
SET_THEORY <br> MATLAB Commands for Set Operations
</h1>
<hr>
<p>
<b>SET_THEORY</b>
is a MATLAB library which
demonstrates how set-theoretic operations can be carried out,
primarily using built-in MATLAB commands.
</p>
<p>
We assume that a set is represented by a strictly ascending sequence
of positive integers. We might think of a universal set U = 1 : N
in cases where all our subsets will have elements between 1 and N.
</p>
<p>
Set theoretic operations include
<ul>
<li>
<i>definition</i> using a numeric property: A = <b>find</b> ( mod ( U, 3 ) = 1 );
</li>
<li>
<i>definition</i> using an explicit list: A = <b>[</b> 1, 3, 8<b>]</b>;
</li>
<li>
<i>unique</i>: creating a set from the unique elements of a list:
A = <b>unique</b> ( [ 1, 3, 8, 3, 3, 1, 7, 3, 1, 1 ] );
</li>
<li>
<i>union</i>: C = <b>union</b> ( A, B );
</li>
<li>
<i>intersection</i>: C = <b>intersect</b> ( A, B );
</li>
<li>
<i>symmetric difference</i>: C = <b>setxor</b> ( A, B );
</li>
<li>
<i>complement</i> with respect to the universal set: B = <b>setdiff</b> ( U, A );
</li>
<li>
<i>complement</i> with respect to another set: C = <b>setdiff</b> ( B, A );
</li>
<li>
<i>cardinality</i>: n = <b>length</b> ( A );
</li>
<li>
<i>membership</i>: true/false = <b>ismember</b> ( a, A );
</li>
<li>
<i>subset</i>: true/false = <b>ismember</b> ( B, A );
</li>
<li>
<i>addition of one element</i>: A = <b>unique</b> ( [ A; a ] );
</li>
<li>
<i>deletion of one element</i>: A = <b>setxor</b> ( A, a );
</li>
<li>
<i>indexing one element</i>: i = <b>find</b> ( A == a );
</li>
</ul>
</p>
<h3 align = "center">
Licensing:
</h3>
<p>
The computer code and data files described and made available on this web page
are distributed under
<a href = "../../txt/gnu_lgpl.txt">the GNU LGPL license.</a>
</p>
<h3 align = "center">
Languages:
</h3>
<p>
<b>SET_THEORY</b> is available in
<a href = "../../c_src/set_theory/set_theory.html">a C version</a> and
<a href = "../../cpp_src/set_theory/set_theory.html">a C++ version</a> and
<a href = "../../f77_src/set_theory/set_theory.html">a FORTRAN77 version</a> and
<a href = "../../f_src/set_theory/set_theory.html">a FORTRAN90 version</a> and
<a href = "../../m_src/set_theory/set_theory.html">a MATLAB version</a>.
</p>
<h3 align = "center">
Related Data and Programs:
</h3>
<p>
<a href = "../../m_src/combo/combo.html">
COMBO</a>,
a MATLAB library which
handles combinatorial problems, by Kreher and Stinson;
</p>
<p>
<a href = "../../m_src/subset/subset.html">
SUBSET</a>,
a MATLAB library which
ranks, unranks, and generates random subsets, combinations, permutations, and so on;
</p>
<h3 align = "center">
Reference:
</h3>
<p>
<ol>
<li>
Charles Pinter,<br>
Set Theory,<br>
Addison-Wesley, 1971,<br>
LC: QA248.P55.
</li>
</ol>
</p>
<h3 align = "center">
Source Code:
</h3>
<p>
<ul>
<li>
<a href = "i4vec_transpose_print.m">i4vec_transpose_print.m</a>
prints an I4VEC "transposed";
</li>
<li>
<a href = "timestamp.m">timestamp.m</a>
prints the current YMDHMS date as a time stamp.
</li>
</ul>
</p>
<h3 align = "center">
Examples and Tests:
</h3>
<p>
<ul>
<li>
<a href = "set_theory_test.m">set_theory_test.m</a>,
runs all the tests;
</li>
<li>
<a href = "set_theory_test01.m">set_theory_test01.m</a>,
demonstrates standard set theory operations in which the
sets are represented as subsets of the integers 1 to N.
</li>
<li>
<a href = "set_theory_test_output.txt">set_theory_test_output.txt</a>,
the output from the tests.
</li>
</ul>
</p>
<p>
You can go up one level to <a href = "../m_src.html">
the MATLAB source codes</a>.
</p>
<hr>
<i>
Last revised on 14 August 2011.
</i>
<!-- John Burkardt -->
</body>
</html>