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<HTML><HEAD><TITLE>7.2 Sets over Integers</TITLE><LINK href="ozdoc.css" rel="stylesheet" type="text/css"></HEAD><BODY><TABLE align="center" border="0" cellpadding="6" cellspacing="6" class="nav"><TR bgcolor="#DDDDDD"><TD><A href="node34.html#section.fs.genral"><< Prev</A></TD><TD><A href="node33.html">- Up -</A></TD><TD><A href="node36.html#section.fs.standard">Next >></A></TD></TR></TABLE><DIV id="section.fs.integers"><H2><A name="section.fs.integers">7.2 Sets over Integers</A></H2><P></P><DL><DT><A name="label327"></A> <CODE>int<SPAN class="keyword">.</SPAN>min</CODE></DT><DD><BLOCKQUOTE class="synopsis"><P></P><BLOCKQUOTE class="code"><CODE>{FS<SPAN class="keyword">.</SPAN>int<SPAN class="keyword">.</SPAN>min <SPAN class="keyword">*</SPAN>M $D}</CODE></BLOCKQUOTE><P></P></BLOCKQUOTE></DD><DD><P><CODE>D</CODE> is the minimal element within <CODE>M</CODE>. </P></DD><DT><A name="label329"></A> <CODE>int<SPAN class="keyword">.</SPAN>max</CODE></DT><DD><BLOCKQUOTE class="synopsis"><P></P><BLOCKQUOTE class="code"><CODE>{FS<SPAN class="keyword">.</SPAN>int<SPAN class="keyword">.</SPAN>max <SPAN class="keyword">*</SPAN>M $D}</CODE></BLOCKQUOTE><P></P></BLOCKQUOTE></DD><DD><P><CODE>D</CODE> is the maximal element within <CODE>M</CODE>. </P></DD><DT><A name="label331"></A> <CODE>int<SPAN class="keyword">.</SPAN>convex</CODE></DT><DD><BLOCKQUOTE class="synopsis"><P></P><BLOCKQUOTE class="code"><CODE>{FS<SPAN class="keyword">.</SPAN>int<SPAN class="keyword">.</SPAN>convex <SPAN class="keyword">*</SPAN>M}</CODE></BLOCKQUOTE><P></P></BLOCKQUOTE></DD><DD><P>Whenever <CODE>I1</CODE> and <CODE>I2</CODE> are elements of <CODE>M</CODE>, then every <CODE>I</CODE> between <CODE>I1</CODE> and <CODE>I2</CODE>, <CODE>I1 <SPAN class="keyword"><</SPAN> I <SPAN class="keyword"><</SPAN> I2</CODE>, is also in <CODE>M</CODE>. </P></DD><DT><A name="label333"></A> <CODE>int<SPAN class="keyword">.</SPAN>match</CODE></DT><DD><BLOCKQUOTE class="synopsis"><P></P><BLOCKQUOTE class="code"><CODE>{FS<SPAN class="keyword">.</SPAN>int<SPAN class="keyword">.</SPAN>match <SPAN class="keyword">*</SPAN>M <SPAN class="keyword">*</SPAN>Dv}</CODE></BLOCKQUOTE><P></P></BLOCKQUOTE></DD><DD><P><CODE>Dv</CODE> is a vector of integer variables that denotes the elements of <CODE>M</CODE> in ascending order. </P></DD><DT><A name="label335"></A> <CODE>int<SPAN class="keyword">.</SPAN>minN</CODE></DT><DD><BLOCKQUOTE class="synopsis"><P></P><BLOCKQUOTE class="code"><CODE>{FS<SPAN class="keyword">.</SPAN>int<SPAN class="keyword">.</SPAN>minN <SPAN class="keyword">*</SPAN>M <SPAN class="keyword">*</SPAN>Dv}</CODE></BLOCKQUOTE><P></P></BLOCKQUOTE></DD><DD><P><CODE>Dv</CODE> is a vector of <I>n</I> integer variables that denotes the <I>n</I> minimal elements of <CODE>M</CODE> in ascending order. </P></DD><DT><A name="label337"></A> <CODE>int<SPAN class="keyword">.</SPAN>maxN</CODE></DT><DD><BLOCKQUOTE class="synopsis"><P></P><BLOCKQUOTE class="code"><CODE>{FS<SPAN class="keyword">.</SPAN>int<SPAN class="keyword">.</SPAN>maxN <SPAN class="keyword">*</SPAN>M <SPAN class="keyword">*</SPAN>Dv}</CODE></BLOCKQUOTE><P></P></BLOCKQUOTE></DD><DD><P><CODE>Dv</CODE> is a vector of <I>n</I> integer variables that denotes the <I>n</I> maximal elements of <CODE>M</CODE> in ascending order. </P></DD><DT><A name="label339"></A> <CODE>int<SPAN class="keyword">.</SPAN>seq</CODE></DT><DD><BLOCKQUOTE class="synopsis"><P></P><BLOCKQUOTE class="code"><CODE>{FS<SPAN class="keyword">.</SPAN>int<SPAN class="keyword">.</SPAN>seq <SPAN class="keyword">*</SPAN>Mv}</CODE></BLOCKQUOTE><P></P></BLOCKQUOTE></DD><DD><P><CODE>Mv</CODE> is a vector of disjoint sets such that for distinct sets <CODE>M1</CODE> and <CODE>M2</CODE>, where <CODE>M1</CODE> precedes <CODE>M2</CODE> in <CODE>Mv</CODE>, all elements of <CODE>M1</CODE> are smaller than any element of <CODE>M2</CODE>.</P></DD></DL><P></P></DIV><TABLE align="center" border="0" cellpadding="6" cellspacing="6" class="nav"><TR bgcolor="#DDDDDD"><TD><A href="node34.html#section.fs.genral"><< Prev</A></TD><TD><A href="node33.html">- Up -</A></TD><TD><A href="node36.html#section.fs.standard">Next >></A></TD></TR></TABLE><HR><ADDRESS><A href="http://www.ps.uni-sb.de/~duchier/">Denys Duchier</A>, <A href="http://www.ps.uni-sb.de/~kornstae/">Leif Kornstaedt</A>, <A href="http://www.ps.uni-sb.de/~homik/">Martin Homik</A>, <A href="http://www.ps.uni-sb.de/~tmueller/">Tobias Müller</A>, <A href="http://www.ps.uni-sb.de/~schulte/">Christian Schulte</A> and <A href="http://www.info.ucl.ac.be/~pvr">Peter Van Roy</A><BR><SPAN class="version">Version 1.4.0 (20110908185330)</SPAN></ADDRESS></BODY></HTML>
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