<?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>standardForm -- convert to standard form</title> <link rel="stylesheet" type="text/css" href="../../../../Macaulay2/Style/doc.css"/> </head> <body> <table class="buttons"> <tr> <td><div><a href="_standard__Pairs.html">next</a> | <a href="___Standard.html">previous</a> | <a href="_standard__Pairs.html">forward</a> | <a href="___Standard.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>standardForm -- convert to standard form</h1> <div class="single"><h2>Description</h2> <div><tt>standardForm f</tt> -- converts a polynomial or monomial to a form involving hash tables.<p/> A polynomial is represented by hash tables in which the keys are hash tables representing the monomials and the values are the coefficients.<p/> The monomials themselves are represented by hash tables in which the keys are the variables and the values are the corresponding exponents.<table class="examples"><tr><td><pre>i1 : R = ZZ/101[x,y,z];</pre> </td></tr> <tr><td><pre>i2 : standardForm (x^2 - 7 + x*y*z^11 + y) o2 = HashTable{HashTable{} => -7 } HashTable{0 => 1 } => 1 1 => 1 2 => 11 HashTable{0 => 2} => 1 HashTable{1 => 1} => 1 o2 : HashTable</pre> </td></tr> </table> </div> </div> <div class="waystouse"><h2>Ways to use <tt>standardForm</tt> :</h2> <ul><li>standardForm(MonoidElement)</li> <li>standardForm(RingElement)</li> </ul> </div> </div> </body> </html>