<?xml version="1.0" encoding="utf-8" ?> <!-- for emacs: -*- coding: utf-8 -*- --> <!-- Apache may like this line in the file .htaccess: AddCharset utf-8 .html --> <!DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.1 plus MathML 2.0 plus SVG 1.1//EN" "http://www.w3.org/2002/04/xhtml-math-svg/xhtml-math-svg-flat.dtd" > <html xmlns="http://www.w3.org/1999/xhtml" xml:lang="en"> <head><title>: -- a binary operator, uses include repetition; ideal quotients</title> <link rel="stylesheet" type="text/css" href="../../../../Macaulay2/Style/doc.css"/> </head> <body> <table class="buttons"> <tr> <td><div><a href="_...html">next</a> | <a href="__lp_st_rp.html">previous</a> | <a href="_...html">forward</a> | <a href="__lp_st_rp.html">backward</a> | <a href="_operators.html">up</a> | <a href="index.html">top</a> | <a href="master.html">index</a> | <a href="toc.html">toc</a> | <a href="http://www.math.uiuc.edu/Macaulay2/">Macaulay2 web site</a></div> </td> </tr> </table> <div><a href="index.html" title="">Macaulay2Doc</a> > <a href="___The_sp__Macaulay2_splanguage.html" title="">The Macaulay2 language</a> > <a href="_operators.html" title="">operators</a> > <a href="__co.html" title="a binary operator, uses include repetition; ideal quotients">:</a></div> <hr/> <div><h1>: -- a binary operator, uses include repetition; ideal quotients</h1> <div><!--empty documentation body--></div> <div class="waystouse"><h2>Ways to use <tt>:</tt> :</h2> <ul><li><span>Ideal : Ideal, see <span><a href="_quotient_lp__Ideal_cm__Ideal_rp.html" title="ideal or submodule quotient">quotient(Ideal,Ideal)</a> -- ideal or submodule quotient</span></span></li> <li><span>Ideal : RingElement, see <span><a href="_quotient_lp__Ideal_cm__Ideal_rp.html" title="ideal or submodule quotient">quotient(Ideal,Ideal)</a> -- ideal or submodule quotient</span></span></li> <li><span>Module : Ideal, see <span><a href="_quotient_lp__Ideal_cm__Ideal_rp.html" title="ideal or submodule quotient">quotient(Ideal,Ideal)</a> -- ideal or submodule quotient</span></span></li> <li><span>Module : Module, see <span><a href="_quotient_lp__Ideal_cm__Ideal_rp.html" title="ideal or submodule quotient">quotient(Ideal,Ideal)</a> -- ideal or submodule quotient</span></span></li> <li><span>Module : RingElement, see <span><a href="_quotient_lp__Ideal_cm__Ideal_rp.html" title="ideal or submodule quotient">quotient(Ideal,Ideal)</a> -- ideal or submodule quotient</span></span></li> <li><span>MonomialIdeal : MonomialIdeal, see <span><a href="_quotient_lp__Ideal_cm__Ideal_rp.html" title="ideal or submodule quotient">quotient(Ideal,Ideal)</a> -- ideal or submodule quotient</span></span></li> <li><span><a href="___Z__Z_sp_co_sp__Thing.html" title="repeat an item">ZZ : Thing</a> -- repeat an item</span></li> </ul> </div> <div class="waystouse"><h2>For the programmer</h2> <p>The object <a href="__co.html" title="a binary operator, uses include repetition; ideal quotients">:</a> is <span>a <a href="___Keyword.html">keyword</a></span>.</p> <div><div><p>This operator may be used as a binary operator in an expression like <tt>x:y</tt>. The user may install <a href="_binary_spmethods.html" title="">binary methods</a> for handling such expressions with code such as</p> <pre> X : Y := (x,y) -> ...</pre> <p>where <tt>X</tt> is the class of <tt>x</tt> and <tt>Y</tt> is the class of <tt>y</tt>.</p> </div> </div> </div> </div> </body> </html>