<?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>degree</title> <link rel="stylesheet" type="text/css" href="../../../../Macaulay2/Style/doc.css"/> </head> <body> <table class="buttons"> <tr> <td><div><a href="_degree_lp__Ideal_rp.html">next</a> | <a href="___Degree.html">previous</a> | <a href="_degree_lp__Ideal_rp.html">forward</a> | <a href="___Degree.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>degree</h1> <div class="single"><h2>Description</h2> <div>Degree is a common name, meaning different things for different kinds of mathematical objects. In Macaulay2, there are currently three related, yet different notions of degree: <h3>Degree of polynomials or vectors of such</h3> <ul><li><span><a href="_degree_lp__Ring__Element_rp.html" title="">degree(RingElement)</a></span></li> <li><span><a href="_degree_lp__Ring__Element_rp.html" title="">degree(Vector)</a></span></li> <li><span><a href="_degree_lp__Ring__Element_cm__Ring__Element_rp.html" title="degree with respect to a variable">degree(RingElement,RingElement)</a> -- degree with respect to a variable</span></li> <li><span><a href="_degree_lp__Projective__Hilbert__Polynomial_rp.html" title="">degree(ProjectiveHilbertPolynomial)</a></span></li> </ul> <h3>Degree of ideals, varieties and modules</h3> <ul><li><span><a href="_degree_lp__Ideal_rp.html" title="">degree(Ideal)</a></span></li> <li><span><a href="_degree_lp__Ring_rp.html" title="">degree(Ring)</a></span></li> <li><span><a href="_degree_lp__Module_rp.html" title="">degree(Module)</a></span></li> <li><span><a href="_degree_lp__Projective__Variety_rp.html" title="">degree(ProjectiveVariety)</a></span></li> </ul> <h3>Degree of homomorphisms</h3> <ul><li><span><a href="_degree_lp__Matrix_rp.html" title="">degree(Matrix)</a></span></li> <li><span><a href="_degree_lp__Matrix_rp.html" title="">degree(ChainComplexMap)</a></span></li> <li><span><a href="_degree_lp__Matrix_rp.html" title="">degree(GradedModuleMap)</a></span></li> </ul> </div> </div> <div class="single"><h2>See also</h2> <ul><li><span><a href="_degree__Length.html" title="the number of degrees">degreeLength</a> -- the number of degrees</span></li> <li><span><a href="_degrees__Ring.html" title="the ring of degrees">degreesRing</a> -- the ring of degrees</span></li> </ul> </div> <div class="waystouse"><h2>Ways to use <tt>degree</tt> :</h2> <ul><li><span>degree(BettiTally), see <span><a href="___Betti__Tally.html" title="the class of all Betti tallies">BettiTally</a> -- the class of all Betti tallies</span></span></li> <li><span><a href="_degree_lp__Ideal_rp.html" title="">degree(Ideal)</a></span></li> <li><span>degree(ChainComplexMap), see <span><a href="_degree_lp__Matrix_rp.html" title="">degree(Matrix)</a></span></span></li> <li><span>degree(GradedModuleMap), see <span><a href="_degree_lp__Matrix_rp.html" title="">degree(Matrix)</a></span></span></li> <li><span><a href="_degree_lp__Matrix_rp.html" title="">degree(Matrix)</a></span></li> <li><span><a href="_degree_lp__Module_rp.html" title="">degree(Module)</a></span></li> <li><span><a href="_degree_lp__Projective__Hilbert__Polynomial_rp.html" title="">degree(ProjectiveHilbertPolynomial)</a></span></li> <li><span><a href="_degree_lp__Projective__Variety_rp.html" title="">degree(ProjectiveVariety)</a></span></li> <li><span><a href="_degree_lp__Ring_rp.html" title="">degree(Ring)</a></span></li> <li><span><a href="_degree_lp__Ring__Element_rp.html" title="">degree(RingElement)</a></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><a href="_degree_lp__Ring__Element_cm__Ring__Element_rp.html" title="degree with respect to a variable">degree(RingElement,RingElement)</a> -- degree with respect to a variable</span></li> </ul> </div> </div> </body> </html>