<?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>Vector -- the class of all elements of free modules that are handled by the engine</title>
<link rel="stylesheet" type="text/css" href="../../../../Macaulay2/Style/doc.css"/>
</head>
<body>
<table class="buttons">
<tr>
<td><div><a href="_vector.html">next</a> | <a href="_vars_lp__Ring_rp.html">previous</a> | <a href="_vector.html">forward</a> | <a href="_vars_lp__Ring_rp.html">backward</a> | up | <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>
<hr/>
<div><h1>Vector -- the class of all elements of free modules that are handled by the engine</h1>
<div class="single"><h2>Description</h2>
<div>If <tt>R</tt> is a ring handled by the engine, and <tt>M</tt> is a free module over <tt>R</tt>, then M is a subclass of Vector.<p/>
</div>
</div>
<div class="single"><h2>See also</h2>
<ul><li><span><a href="_engine.html" title="">engine</a></span></li>
<li><span><a href="___Module.html" title="the class of all modules">Module</a> -- the class of all modules</span></li>
</ul>
</div>
<div class="waystouse"><h2>Functions and methods returning a vector :</h2>
<ul><li><span>Matrix * Vector, see <span><a href="__st.html" title="a binary operator, usually used for multiplication">*</a> -- a binary operator, usually used for multiplication</span></span></li>
<li><span>Matrix _ ZZ, see <span><a href="_generators_spof_spideals_spand_spmodules.html" title="">generators of ideals and modules</a></span></span></li>
<li><span>Module _ ZZ, see <span><a href="_generators_spof_spideals_spand_spmodules.html" title="">generators of ideals and modules</a></span></span></li>
<li><span>homogenize(Vector,RingElement), see <span><a href="_homogenize.html" title="homogenize with respect to a variable">homogenize</a> -- homogenize with respect to a variable</span></span></li>
<li><span>homogenize(Vector,RingElement,List), see <span><a href="_homogenize.html" title="homogenize with respect to a variable">homogenize</a> -- homogenize with respect to a variable</span></span></li>
<li><span>RingMap Vector, see <span><a href="___Ring__Map_sp__Ring__Element.html" title="apply a ring map">RingMap RingElement</a> -- apply a ring map</span></span></li>
<li><span>substitute(Vector,List), see <span><a href="_substitute.html" title="substituting values for variables">substitute</a> -- substituting values for variables</span></span></li>
<li><span>substitute(Vector,Matrix), see <span><a href="_substitute.html" title="substituting values for variables">substitute</a> -- substituting values for variables</span></span></li>
<li><span>substitute(Vector,Ring), see <span><a href="_substitute.html" title="substituting values for variables">substitute</a> -- substituting values for variables</span></span></li>
<li><span>substitute(Vector,RingFamily), see <span><a href="_substitute.html" title="substituting values for variables">substitute</a> -- substituting values for variables</span></span></li>
<li><span><a href="___Z__Z_sp_us_sp__Module.html" title="integers or zero element">ZZ _ Module</a> -- integers or zero element</span></li>
</ul>
<h2>Methods that use a vector :</h2>
<ul><li><span>Ideal * Vector, see <span><a href="__st.html" title="a binary operator, usually used for multiplication">*</a> -- a binary operator, usually used for multiplication</span></span></li>
<li><span>Ring * Vector, see <span><a href="__st.html" title="a binary operator, usually used for multiplication">*</a> -- a binary operator, usually used for multiplication</span></span></li>
<li><span>RingElement * Vector, see <span><a href="__st.html" title="a binary operator, usually used for multiplication">*</a> -- a binary operator, usually used for multiplication</span></span></li>
<li><span>Vector + Vector, see <span><a href="__pl.html" title="a unary or binary operator, usually used for addition">+</a> -- a unary or binary operator, usually used for addition</span></span></li>
<li><span>Vector - Vector, see <span><a href="_-.html" title="a unary or binary operator, usually used for negation or subtraction">-</a> -- a unary or binary operator, usually used for negation or subtraction</span></span></li>
<li><span>Vector == Vector, see <span><a href="__eq_eq.html" title="equality">==</a> -- equality</span></span></li>
<li><span>contract(Matrix,Vector), see <span><a href="_contract_lp__Matrix_cm__Matrix_rp.html" title="contract a matrix by a matrix">contract(Matrix,Matrix)</a> -- contract a matrix by a matrix</span></span></li>
<li><span>contract(Number,Vector), see <span><a href="_contract_lp__Matrix_cm__Matrix_rp.html" title="contract a matrix by a matrix">contract(Matrix,Matrix)</a> -- contract a matrix by a matrix</span></span></li>
<li><span>contract(RingElement,Vector), see <span><a href="_contract_lp__Matrix_cm__Matrix_rp.html" title="contract a matrix by a matrix">contract(Matrix,Matrix)</a> -- contract a matrix by a matrix</span></span></li>
<li><span>contract(Vector,Matrix), see <span><a href="_contract_lp__Matrix_cm__Matrix_rp.html" title="contract a matrix by a matrix">contract(Matrix,Matrix)</a> -- contract a matrix by a matrix</span></span></li>
<li><span>contract(Vector,Number), see <span><a href="_contract_lp__Matrix_cm__Matrix_rp.html" title="contract a matrix by a matrix">contract(Matrix,Matrix)</a> -- contract a matrix by a matrix</span></span></li>
<li><span>contract(Vector,RingElement), see <span><a href="_contract_lp__Matrix_cm__Matrix_rp.html" title="contract a matrix by a matrix">contract(Matrix,Matrix)</a> -- contract a matrix by a matrix</span></span></li>
<li><span>contract(Vector,Vector), see <span><a href="_contract_lp__Matrix_cm__Matrix_rp.html" title="contract a matrix by a matrix">contract(Matrix,Matrix)</a> -- contract a matrix by a matrix</span></span></li>
<li><span>degree(Vector), see <span><a href="_degree_lp__Ring__Element_rp.html" title="">degree(RingElement)</a></span></span></li>
<li><span>diff(Matrix,Vector), see <span><a href="_diff_lp__Matrix_cm__Matrix_rp.html" title="differentiate a matrix by a matrix">diff(Matrix,Matrix)</a> -- differentiate a matrix by a matrix</span></span></li>
<li><span>diff(RingElement,Vector), see <span><a href="_diff_lp__Matrix_cm__Matrix_rp.html" title="differentiate a matrix by a matrix">diff(Matrix,Matrix)</a> -- differentiate a matrix by a matrix</span></span></li>
<li><span>diff(Vector,Matrix), see <span><a href="_diff_lp__Matrix_cm__Matrix_rp.html" title="differentiate a matrix by a matrix">diff(Matrix,Matrix)</a> -- differentiate a matrix by a matrix</span></span></li>
<li><span>diff(Vector,RingElement), see <span><a href="_diff_lp__Matrix_cm__Matrix_rp.html" title="differentiate a matrix by a matrix">diff(Matrix,Matrix)</a> -- differentiate a matrix by a matrix</span></span></li>
<li><span>diff(Vector,Vector), see <span><a href="_diff_lp__Matrix_cm__Matrix_rp.html" title="differentiate a matrix by a matrix">diff(Matrix,Matrix)</a> -- differentiate a matrix by a matrix</span></span></li>
<li><span><a href="_entries_lp__Vector_rp.html" title="lists the entries of a vector">entries(Vector)</a> -- lists the entries of a vector</span></li>
<li><span>isHomogeneous(Vector), see <span><a href="_is__Homogeneous.html" title="whether something is homogeneous (graded)">isHomogeneous</a> -- whether something is homogeneous (graded)</span></span></li>
<li><span>leadComponent(Vector), see <span><a href="_lead__Component.html" title="the leading component of a vector or matrix">leadComponent</a> -- the leading component of a vector or matrix</span></span></li>
<li><span>leadTerm(Vector), see <span><a href="_lead__Term_lp__Matrix_rp.html" title="get the greatest term of each column">leadTerm(Matrix)</a> -- get the greatest term of each column</span></span></li>
<li><span><a href="_matrix_lp__Vector_rp.html" title="">matrix(Vector)</a></span></li>
<li><span>Module / Vector, see <span><a href="___Module_sp_sl_sp__Module.html" title="quotient module">Module / Module</a> -- quotient module</span></span></li>
<li><span><a href="_module_lp__Vector_rp.html" title="the module of a vector">module(Vector)</a> -- the module of a vector</span></li>
<li><span>norm(Vector), see <span><a href="_norm.html" title="">norm</a></span></span></li>
<li><span>ring(Vector), see <span><a href="_ring.html" title="get the associated ring of an object">ring</a> -- get the associated ring of an object</span></span></li>
<li><span>substitute(Vector,Option), see <span><a href="_substitute.html" title="substituting values for variables">substitute</a> -- substituting values for variables</span></span></li>
<li><span><a href="___Vector_sp_st_st_sp__Vector.html" title="tensor product">Vector ** Vector</a> -- tensor product</span></li>
</ul>
</div>
<div class="waystouse"><h2>For the programmer</h2>
<p>The object <a href="___Vector.html" title="the class of all elements of free modules that are handled by the engine">Vector</a> is <span>a <a href="___Type.html">type</a></span>, with ancestor classes <a href="___Basic__List.html" title="the class of all basic lists">BasicList</a> < <a href="___Thing.html" title="the class of all things">Thing</a>.</p>
</div>
</div>
</body>
</html>
