One Hat Cyber Team
Your IP :
216.73.216.80
Server IP :
194.44.31.54
Server :
Linux zen.imath.kiev.ua 4.18.0-553.77.1.el8_10.x86_64 #1 SMP Fri Oct 3 14:30:23 UTC 2025 x86_64
Server Software :
Apache/2.4.37 (Rocky Linux) OpenSSL/1.1.1k
PHP Version :
5.6.40
Buat File
|
Buat Folder
Eksekusi
Dir :
~
/
usr
/
share
/
doc
/
Macaulay2
/
Macaulay2Doc
/
html
/
View File Name :
_some__Terms.html
<!DOCTYPE html> <html lang="en"> <head> <title>someTerms -- select some terms of a polynomial</title> <meta content="text/html; charset=utf-8" http-equiv="Content-Type"> <link type="text/css" rel="stylesheet" href="../../../../Macaulay2/Style/doc.css"> <link rel="stylesheet" href="../../../../Macaulay2/Style/katex/katex.min.css"> <script defer="defer" src="../../../../Macaulay2/Style/katex/katex.min.js"></script> <script defer="defer" src="../../../../Macaulay2/Style/katex/contrib/auto-render.min.js"></script> <script> var macros = { "\\break": "\\\\", "\\ZZ": "\\mathbb{Z}", "\\NN": "\\mathbb{N}", "\\QQ": "\\mathbb{Q}", "\\RR": "\\mathbb{R}", "\\CC": "\\mathbb{C}", "\\PP": "\\mathbb{P}" }, delimiters = [ { left: "$$", right: "$$", display: true}, { left: "\\[", right: "\\]", display: true}, { left: "$", right: "$", display: false}, { left: "\\(", right: "\\)", display: false} ], ignoredTags = [ "kbd", "var", "samp", "script", "noscript", "style", "textarea", "pre", "code", "option" ]; document.addEventListener("DOMContentLoaded", function() { renderMathInElement(document.body, { delimiters: delimiters, macros: macros, ignoredTags: ignoredTags, trust: true }); }); </script> <style>.katex { font-size: 1em; }</style> <script defer="defer" src="../../../../Macaulay2/Style/katex/contrib/copy-tex.min.js"></script> <script defer="defer" src="../../../../Macaulay2/Style/katex/contrib/render-a11y-string.min.js"></script> <script src="../../../../Macaulay2/Style/prism.js"></script> <script>var current_version = '1.25.06';</script> <script src="../../../../Macaulay2/Style/version-select.js"></script> <link type="image/x-icon" rel="icon" href="../../../../Macaulay2/Style/icon.gif"> </head> <body> <div id="buttons"> <div> <a href="https://macaulay2.com/">Macaulay2</a> <span id="version-select-container"></span> » <a title="Macaulay2 documentation" href="index.html">Documentation </a> <br><a href="_packages_spprovided_spwith_sp__Macaulay2.html">Packages</a> » <span><a title="Macaulay2 documentation" href="index.html">Macaulay2Doc</a> » <a href="_rings.html">rings</a> » <a href="_manipulating_sppolynomials.html">manipulating polynomials</a> » <a title="select some terms of a polynomial" href="_some__Terms.html">someTerms</a></span> </div> <div class="right"> <form method="get" action="https://www.google.com/search"> <input placeholder="Search" type="text" name="q" value=""> <input type="hidden" name="q" value="site:macaulay2.com/doc"> </form> <a href="_terms.html">next</a> | <a href="_parts.html">previous</a> | <a href="_terms.html">forward</a> | <a href="_parts.html">backward</a> | <a href="_manipulating_sppolynomials.html">up</a> | <a href="master.html">index</a> | <a href="toc.html">toc</a> </div> </div> <hr> <div> <h1>someTerms -- select some terms of a polynomial</h1> <ul> <li> <dl class="element"> <dt>Usage: </dt> <dd><code class="language-macaulay2">someTerms(f,i,n)</code></dd> </dl> </li> <li>Inputs: <ul> <li><span><span class="tt">f</span>, <span>a <a title="the class of all ring elements handled by the engine" href="___Ring__Element.html">ring element</a></span>, in a polynomial ring</span></li> <li><span><span class="tt">i</span>, <span>an <a title="the class of all integers" href="___Z__Z.html">integer</a></span>, the starting index</span></li> <li><span><span class="tt">n</span>, <span>an <a title="the class of all integers" href="___Z__Z.html">integer</a></span>, the number of terms to select</span></li> </ul> </li> <li>Outputs: <ul> <li><span><span>a <a title="the class of all ring elements handled by the engine" href="___Ring__Element.html">ring element</a></span>, the <span class="tt">n</span> terms of the polynomial <span class="tt">f</span> starting with the <span class="tt">i</span>-th one</span></li> </ul> </li> </ul> <div> <h2>Description</h2> The index i is 0-based, and a negative number refers to location from the end of the polynomial. <table class="examples"> <tr> <td> <pre><code class="language-macaulay2">i1 : R = ZZ[a..d];</code></pre> </td> </tr> <tr> <td> <pre><code class="language-macaulay2">i2 : f = (a+2*b-3)^2 2 2 o2 = a + 4a*b + 4b - 6a - 12b + 9 o2 : R</code></pre> </td> </tr> <tr> <td> <pre><code class="language-macaulay2">i3 : someTerms(f,0,1) -- the lead term 2 o3 = a o3 : R</code></pre> </td> </tr> <tr> <td> <pre><code class="language-macaulay2">i4 : someTerms(f,-1,1) -- the last term o4 = 9 o4 : R</code></pre> </td> </tr> <tr> <td> <pre><code class="language-macaulay2">i5 : someTerms(f,-2,2) -- the last 2 terms o5 = - 12b + 9 o5 : R</code></pre> </td> </tr> </table> Here is an example where the coefficient ring is also a polynomial ring. <table class="examples"> <tr> <td> <pre><code class="language-macaulay2">i6 : S = R[x,y,z];</code></pre> </td> </tr> <tr> <td> <pre><code class="language-macaulay2">i7 : f = (x*(a-b)+y^2+a-1)^2 4 2 2 2 2 2 2 o7 = y + (2a - 2b)x*y + (a - 2a*b + b )x + (2a - 2)y + (2a - 2a*b - 2a ------------------------------------------------------------------------ 2 + 2b)x + a - 2a + 1 o7 : S</code></pre> </td> </tr> <tr> <td> <pre><code class="language-macaulay2">i8 : someTerms(f,-1,1) -- the last term 2 o8 = a - 2a + 1 o8 : S</code></pre> </td> </tr> <tr> <td> <pre><code class="language-macaulay2">i9 : someTerms(f,-2,2) -- the last 2 terms 2 2 o9 = (2a - 2a*b - 2a + 2b)x + a - 2a + 1 o9 : S</code></pre> </td> </tr> </table> </div> <div> <h2>See also</h2> <ul> <li><span><a title="matrix of monomials in a ring element or matrix" href="_monomials.html">monomials</a> -- matrix of monomials in a ring element or matrix</span></li> <li><span><a title="get the monomials and coefficients of a polynomial or matrix" href="_coefficients.html">coefficients</a> -- get the monomials and coefficients of a polynomial or matrix</span></li> <li><span><a title="provide a list of terms of a polynomial" href="_terms.html">terms</a> -- provide a list of terms of a polynomial</span></li> <li><span><a title="get the greatest term" href="_lead__Term.html">leadTerm</a> -- get the greatest term</span></li> </ul> </div> <div> <div class="waystouse"> <h2>Ways to use <span class="tt">someTerms</span>:</h2> <ul> <li><kbd>someTerms(RingElement,ZZ,ZZ)</kbd></li> </ul> </div> <div class="waystouse"> <h2>For the programmer</h2> <p>The object <a title="select some terms of a polynomial" href="_some__Terms.html">someTerms</a> is <span>a <a title="a type of method function" href="___Method__Function.html">method function</a></span>.</p> </div> <hr> <div class="waystouse"> <p>The source of this document is in <span class="tt">Macaulay2Doc/functions/someTerms-doc.m2:35:0</span>.</p> </div> </div> </div> </body> </html>