One Hat Cyber Team
Your IP :
216.73.216.135
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
/
DiffAlg
/
html
/
View File Name :
___Diff__Alg__Element.html
<!DOCTYPE html> <html lang="en"> <head> <title>DiffAlgElement -- the class of all differential forms and vector fields</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="../../Macaulay2Doc/html/index.html">Documentation </a> <br><a href="../../Macaulay2Doc/html/_packages_spprovided_spwith_sp__Macaulay2.html">Packages</a> » <span><a title="differential algebra" href="index.html">DiffAlg</a> :: <a title="the class of all differential forms and vector fields" href="___Diff__Alg__Element.html">DiffAlgElement</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="___Diff__Alg__Element_sp_st_sp__Ring__Element.html">next</a> | <a href="___Diff__Alg__Distribution.html">previous</a> | <a href="___Diff__Alg__Element_sp_st_sp__Ring__Element.html">forward</a> | <a href="___Diff__Alg__Distribution.html">backward</a> | up | <a href="master.html">index</a> | <a href="toc.html">toc</a> </div> </div> <hr> <div> <h1>DiffAlgElement -- the class of all differential forms and vector fields</h1> <div> <!--empty documentation body--> </div> <div> <div class="waystouse"> <h2>Types of <span class="tt">DiffAlgElement</span>:</h2> <ul> <li><span><a title="the class of all vector fields" href="___Diff__Alg__Field.html">DiffAlgField</a> -- the class of all vector fields</span></li> <li><span><a title="the class of all differential forms" href="___Diff__Alg__Form.html">DiffAlgForm</a> -- the class of all differential forms</span></li> </ul> <h2>Functions and methods returning an object of class DiffAlgElement:</h2> <ul> <li><span><a title="negation of a differential form or vector field" href="_-_sp__Diff__Alg__Element.html">- DiffAlgElement</a> -- negation of a differential form or vector field</span></li> <li><span><kbd>DiffAlgElement * QQ</kbd> -- see <span><a title="scalar multiplication" href="___Diff__Alg__Element_sp_st_sp__Ring__Element.html">DiffAlgElement * RingElement</a> -- scalar multiplication</span></span></li> <li><span><a title="scalar multiplication" href="___Diff__Alg__Element_sp_st_sp__Ring__Element.html">DiffAlgElement * RingElement</a> -- scalar multiplication</span></li> <li><span><kbd>DiffAlgElement * ZZ</kbd> -- see <span><a title="scalar multiplication" href="___Diff__Alg__Element_sp_st_sp__Ring__Element.html">DiffAlgElement * RingElement</a> -- scalar multiplication</span></span></li> <li><span><kbd>QQ * DiffAlgElement</kbd> -- see <span><a title="scalar multiplication" href="___Diff__Alg__Element_sp_st_sp__Ring__Element.html">DiffAlgElement * RingElement</a> -- scalar multiplication</span></span></li> <li><span><kbd>RingElement * DiffAlgElement</kbd> -- see <span><a title="scalar multiplication" href="___Diff__Alg__Element_sp_st_sp__Ring__Element.html">DiffAlgElement * RingElement</a> -- scalar multiplication</span></span></li> <li><span><kbd>ZZ * DiffAlgElement</kbd> -- see <span><a title="scalar multiplication" href="___Diff__Alg__Element_sp_st_sp__Ring__Element.html">DiffAlgElement * RingElement</a> -- scalar multiplication</span></span></li> <li><span><a title="addition" href="___Diff__Alg__Element_sp_pl_sp__Diff__Alg__Element.html">DiffAlgElement + DiffAlgElement</a> -- addition</span></li> <li><span><a title="subtraction" href="___Diff__Alg__Element_sp-_sp__Diff__Alg__Element.html">DiffAlgElement - DiffAlgElement</a> -- subtraction</span></li> <li><span><kbd>DiffAlgElement / QQ</kbd> -- see <span><a title="scalar division" href="___Diff__Alg__Element_sp_sl_sp__Ring__Element.html">DiffAlgElement / RingElement</a> -- scalar division</span></span></li> <li><span><a title="scalar division" href="___Diff__Alg__Element_sp_sl_sp__Ring__Element.html">DiffAlgElement / RingElement</a> -- scalar division</span></li> <li><span><kbd>DiffAlgElement / ZZ</kbd> -- see <span><a title="scalar division" href="___Diff__Alg__Element_sp_sl_sp__Ring__Element.html">DiffAlgElement / RingElement</a> -- scalar division</span></span></li> <li><span><a title="homogenize a differential form or vector field" href="_homogenize_lp__Diff__Alg__Element_rp.html">homogenize(DiffAlgElement)</a> -- homogenize a differential form or vector field</span></li> <li><span><kbd>linearComb(List,String)</kbd> -- see <span><a title="generic linear combination of elements" href="_linear__Comb.html">linearComb</a> -- generic linear combination of elements</span></span></li> <li><span><kbd>projectivize(DiffAlgElement)</kbd> -- see <span><a title="projectivize a differential form or vector field" href="_projectivize.html">projectivize</a> -- projectivize a differential form or vector field</span></span></li> <li><span><kbd>random(DiffAlgElement)</kbd> -- see <span><a title="replaces the variables of the coefficient ring of a differential form or a vector field with random values" href="_random_lp__Diff__Alg__Element_cm__Ring_rp.html">random(DiffAlgElement,Ring)</a> -- replaces the variables of the coefficient ring of a differential form or a vector field with random values</span></span></li> <li><span><a title="replaces the variables of the coefficient ring of a differential form or a vector field with random values" href="_random_lp__Diff__Alg__Element_cm__Ring_rp.html">random(DiffAlgElement,Ring)</a> -- replaces the variables of the coefficient ring of a differential form or a vector field with random values</span></li> </ul> <h2>Methods that use an object of class DiffAlgElement:</h2> <ul> <li><span><a title="degree of a differential form or a vector field" href="_degree_lp__Diff__Alg__Element_rp.html">degree(DiffAlgElement)</a> -- degree of a differential form or a vector field</span></li> <li><span><a title="concatenate a string with a differential form or vector field" href="___Diff__Alg__Element_sp_vb_sp__String.html">DiffAlgElement | String</a> -- concatenate a string with a differential form or vector field</span></li> <li><span><kbd>String | DiffAlgElement</kbd> -- see <span><a title="concatenate a string with a differential form or vector field" href="___Diff__Alg__Element_sp_vb_sp__String.html">DiffAlgElement | String</a> -- concatenate a string with a differential form or vector field</span></span></li> <li><span><kbd>genIm(DiffAlgElement,DiffAlgElement)</kbd> -- see <span><a title="a basis of the image of a linear expression" href="_gen__Im.html">genIm</a> -- a basis of the image of a linear expression</span></span></li> <li><span><kbd>genKer(DiffAlgElement,DiffAlgElement)</kbd> -- see <span><a title="basis of the kernel of a linear expression" href="_gen__Ker.html">genKer</a> -- basis of the kernel of a linear expression</span></span></li> <li><span><a title="tests if a form (or field) is homogeneous" href="_is__Homogeneous_lp__Diff__Alg__Element_rp.html">isHomogeneous(DiffAlgElement)</a> -- tests if a form (or field) is homogeneous</span></li> <li><span><kbd>moduliIdeal(DiffAlgElement)</kbd> -- see <span><a title="ideal generated by the coefficients of a differential form or vector field" href="_moduli__Ideal.html">moduliIdeal</a> -- ideal generated by the coefficients of a differential form or vector field</span></span></li> <li><span><a title="ring of the differential form or vector field" href="_ring_lp__Diff__Alg__Element_rp.html">ring(DiffAlgElement)</a> -- ring of the differential form or vector field</span></li> <li><span><kbd>singularIdeal(DiffAlgElement)</kbd> -- see <span><a title="ideal generated by the polynomial coefficients of a differential form or vector field" href="_singular__Ideal.html">singularIdeal</a> -- ideal generated by the polynomial coefficients of a differential form or vector field</span></span></li> <li><span><a title="gets the RingElement of a differential form or vector field in a ring" href="_substitute_lp__Diff__Alg__Element_cm__Ring_rp.html">substitute(DiffAlgElement,Ring)</a> -- gets the RingElement of a differential form or vector field in a ring</span></li> </ul> </div> <div class="waystouse"> <h2>For the programmer</h2> <p>The object <a title="the class of all differential forms and vector fields" href="___Diff__Alg__Element.html">DiffAlgElement</a> is <span>a <a title="the class of all mutable types" href="../../Macaulay2Doc/html/___Type.html">type</a></span>, with ancestor classes <a title="the class of all hash tables" href="../../Macaulay2Doc/html/___Hash__Table.html">HashTable</a> < <a title="the class of all things" href="../../Macaulay2Doc/html/___Thing.html">Thing</a>.</p> </div> <hr> <div class="waystouse"> <p>The source of this document is in <span class="tt">DiffAlg.m2:503:0</span>.</p> </div> </div> </div> </body> </html>