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<!DOCTYPE html> <html lang="en"> <head> <title>monoid(...,Heft=>...) -- specify a heft vector</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="_polynomial_springs.html">polynomial rings</a> » <a href="_monomial_sporderings.html">monomial orderings</a> » <a title="make or retrieve a monoid" href="_monoid.html">monoid</a> » <a title="specify a heft vector" href="_monoid_lp..._cm__Heft_eq_gt..._rp.html">monoid(...,Heft=>...)</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="_monoid_lp..._cm__Join_eq_gt..._rp.html">next</a> | <a href="_monoid_lp..._cm__Degree__Lift_eq_gt..._rp.html">previous</a> | <a href="_monoid_lp..._cm__Join_eq_gt..._rp.html">forward</a> | <a href="_monoid_lp..._cm__Degree__Lift_eq_gt..._rp.html">backward</a> | <a href="_monoid.html">up</a> | <a href="master.html">index</a> | <a href="toc.html">toc</a> </div> </div> <hr> <div> <h1>monoid(...,Heft=>...) -- specify a heft vector</h1> <ul> <li> <dl class="element"> <dt>Usage: </dt> <dd><code class="language-macaulay2">monoid[a,b, Heft => {...}]</code></dd> </dl> </li> </ul> <div> <h2>Description</h2> <div> <p>The <span class="tt">Heft</span> option can be used to provide a <a href="_heft_spvectors.html">heft vector</a> as a list of integers such that the dot product with the degree of each variable will be positive. This is used as a computational aid in certain routines. If no value for this option is specified, one will be computed automatically if possible, hence there is no need to provide one unless the time spent computing one is onerous; if no heft vector exists, certain computations will not be supported, and others may take more time.</p> </div> <table class="examples"> <tr> <td> <pre><code class="language-macaulay2">i1 : R = ZZ[x,y, Degrees => {-1,-2}, Heft => {-1}] o1 = R o1 : PolynomialRing</code></pre> </td> </tr> </table> <div> <p>This option may also be used when creating a new ring from an existing ring, creating a tensor product ring, or symmetric algebra.</p> </div> </div> <div> <h2>See also</h2> <ul> <li><span><a title="make or retrieve a monoid" href="_monoid.html">monoid</a> -- make or retrieve a monoid</span></li> <li><span><a title="make a copy of a ring, with some features changed" href="_new__Ring.html">newRing</a> -- make a copy of a ring, with some features changed</span></li> <li><span><a title="tensor product of monoids" href="_tensor_lp__Monoid_cm__Monoid_rp.html">tensor(Ring,Ring)</a> -- tensor product of monoids</span></li> <li><span><a title="the symmetric algebra of a module" href="_symmetric__Algebra.html">symmetricAlgebra</a> -- the symmetric algebra of a module</span></li> </ul> </div> <div> <div> <h2>Functions with optional argument named <span class="tt">Heft</span>:</h2> <ul> <li><span><a title="specify a heft vector" href="_monoid_lp..._cm__Heft_eq_gt..._rp.html">monoid(...,Heft=>...)</a> -- specify a heft vector</span></li> <li><span><kbd>newRing(...,Heft=>...)</kbd> -- see <span><a title="make a copy of a ring, with some features changed" href="_new__Ring.html">newRing</a> -- make a copy of a ring, with some features changed</span></span></li> <li><span><kbd>symmetricAlgebra(...,Heft=>...)</kbd> -- see <span><a title="the symmetric algebra of a module" href="_symmetric__Algebra.html">symmetricAlgebra</a> -- the symmetric algebra of a module</span></span></li> <li><span><kbd>tensor(Monoid,Monoid,Heft=>...)</kbd> -- see <span><a title="tensor product of monoids" href="_tensor_lp__Monoid_cm__Monoid_rp.html">tensor(Monoid,Monoid)</a> -- tensor product of monoids</span></span></li> <li><span><kbd>tensor(Ring,Ring,Heft=>...)</kbd> -- see <span><a title="tensor product of monoids" href="_tensor_lp__Monoid_cm__Monoid_rp.html">tensor(Monoid,Monoid)</a> -- tensor product of monoids</span></span></li> </ul> </div> <div> <h2>Further information</h2> <ul> <li><span>Default value: <span class="tt">null</span></span></li> <li><span>Function: <span><a title="make or retrieve a monoid" href="_monoid.html">monoid</a> -- make or retrieve a monoid</span></span></li> <li><span>Option key: <span><a title="an optional argument" href="___Heft.html">Heft</a> -- an optional argument</span></span></li> </ul> </div> <hr> <div class="waystouse"> <p>The source of this document is in <span class="tt">Macaulay2Doc/functions/monoid-doc.m2:563:0</span>.</p> </div> </div> </div> </body> </html>