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_jets_lp..._cm__Projective_eq_gt..._rp.html
<!DOCTYPE html> <html lang="en"> <head> <title>jets(...,Projective=>...) -- Option for jets</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="compute jets of various algebraic, geometric and combinatorial objects" href="index.html">Jets</a> » <a title="compute the jets of an object" href="_jets.html">jets</a> » <a title="Option for jets" href="_jets_lp..._cm__Projective_eq_gt..._rp.html">jets(...,Projective=>...)</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="___J__J.html">next</a> | <a href="_jets_lp__Z__Z_cm__Affine__Variety_rp.html">previous</a> | <a href="___J__J.html">forward</a> | <a href="_jets_lp__Z__Z_cm__Affine__Variety_rp.html">backward</a> | <a href="_jets.html">up</a> | <a href="master.html">index</a> | <a href="toc.html">toc</a> </div> </div> <hr> <div> <h1>jets(...,Projective=>...) -- Option for jets</h1> <div> <h2>Description</h2> <div> <p>Set the degree of each jet variable to match its order, as in Proposition 6.6 (c) of <a href="https://arxiv.org/abs/math/0407113">P. Vojta, Jets via Hasse-Schmidt Derivations</a>. This guarantees that the output of <a title="compute the jets of an object" href="_jets.html">jets</a> is homogeneous.</p> </div> </div> <div> <h2>Caveat</h2> <div> <p>With <span class="tt">Projective=>true</span> the jet variables of order zero have degree 0, therefore no heft vector exist for the ambient ring of the jets. As a result, certain computations will not be supported, and others may run more slowly. See <a href="../../Macaulay2Doc/html/_heft_spvectors.html">heft vectors</a> for more information.</p> </div> </div> <div> <h2>See also</h2> <ul> <li><span><a title="compute jets of a polynomial ring" href="_jets_lp__Z__Z_cm__Polynomial__Ring_rp.html">jets(ZZ,PolynomialRing)</a> -- compute jets of a polynomial ring</span></li> <li><span><a title="compute jets of a an ideal in a polynomial ring" href="_jets_lp__Z__Z_cm__Ideal_rp.html">jets(ZZ,Ideal)</a> -- compute jets of a an ideal in a polynomial ring</span></li> </ul> </div> <div> <div> <h2>Functions with optional argument named <span class="tt">Projective</span>:</h2> <ul> <li><span><a title="choose how to display the Hilbert polynomial" href="../../Macaulay2Doc/html/_hilbert__Polynomial_lp..._cm__Projective_eq_gt..._rp.html">hilbertPolynomial(...,Projective=>...)</a> -- choose how to display the Hilbert polynomial</span></li> <li><span><a title="Option for jets" href="_jets_lp..._cm__Projective_eq_gt..._rp.html">jets(...,Projective=>...)</a> -- Option for jets</span></li> <li><kbd>jetsProjection(...,Projective=>...)</kbd></li> </ul> </div> <div> <h2>Further information</h2> <ul> <li><span>Default value: <a href="../../Macaulay2Doc/html/_false.html">false</a></span></li> <li><span>Function: <span><a title="compute the jets of an object" href="_jets.html">jets</a> -- compute the jets of an object</span></span></li> <li><span>Option key: <span><a title="an optional argument" href="../../Macaulay2Doc/html/___Projective.html">Projective</a> -- an optional argument</span></span></li> </ul> </div> <hr> <div class="waystouse"> <p>The source of this document is in <span class="tt">Jets.m2:1666:0</span>.</p> </div> </div> </div> </body> </html>
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