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<!DOCTYPE html> <html lang="en"> <head> <title>- -- a unary or binary operator, usually used for negation or subtraction</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="___The_sp__Macaulay2_splanguage.html">The Macaulay2 language</a> » <a href="_operators.html">operators</a> » <a title="a unary or binary operator, usually used for negation or subtraction" href="_-.html">-</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="__st.html">next</a> | <a href="__pl.html">previous</a> | <a href="__st.html">forward</a> | <a href="__pl.html">backward</a> | <a href="_operators.html">up</a> | <a href="master.html">index</a> | <a href="toc.html">toc</a> </div> </div> <hr> <div> <h1>- -- a unary or binary operator, usually used for negation or subtraction</h1> <ul> <li> <dl class="element"> <dt>Usage: </dt> <dd><code class="language-macaulay2">-y </code></dd> <dd><code class="language-macaulay2">x-y</code></dd> </dl> </li> </ul> <div> <h2>Description</h2> In most cases, this operator refers to standard negation or subtraction. <p></p> In many cases, the integer 1 can be used as the identity, and scalars function as multiples of the identity. For example, the 1 below refers to the identity matrix and the 2 to twice the identity matrix. <table class="examples"> <tr> <td> <pre><code class="language-macaulay2">i1 : M = matrix{{1,2,3},{2,3,4},{3,4,6}} o1 = | 1 2 3 | | 2 3 4 | | 3 4 6 | 3 3 o1 : Matrix ZZ <-- ZZ</code></pre> </td> </tr> <tr> <td> <pre><code class="language-macaulay2">i2 : M-1, M-2 o2 = (| 0 2 3 |, | -1 2 3 |) | 2 2 4 | | 2 1 4 | | 3 4 5 | | 3 4 4 | o2 : Sequence</code></pre> </td> </tr> </table> <h3>Intervals</h3> <p>If one of the inputs is an <a title="the class of all real intervals" href="___R__Ri.html">RRi</a>, the output is an interval containing all differences of pairs in the inputs.</p> <table class="examples"> <tr> <td> <pre><code class="language-macaulay2">i3 : 2-interval(1,3) o3 = [-1,1] o3 : RRi (of precision 53)</code></pre> </td> </tr> <tr> <td> <pre><code class="language-macaulay2">i4 : interval(1,3)-interval(-1,2) o4 = [-1,4] o4 : RRi (of precision 53)</code></pre> </td> </tr> <tr> <td> <pre><code class="language-macaulay2">i5 : interval(-1,1)-interval(-1,1) o5 = [-2,2] o5 : RRi (of precision 53)</code></pre> </td> </tr> </table> </div> <div> <h2>See also</h2> <ul> <li><span><a title="difference" href="_difference.html">difference</a> -- difference</span></li> <li><span><a title="additive inverse" href="_minus.html">minus</a> -- additive inverse</span></li> </ul> </div> <div> <div class="waystouse"> <h2>Ways to use <span class="tt">symbol -</span>:</h2> <ul> <li><kbd>- CC</kbd></li> <li><kbd>- Constant</kbd></li> <li><kbd>- InfiniteNumber</kbd></li> <li><kbd>- List</kbd></li> <li><kbd>- Matrix</kbd></li> <li><kbd>- MutableMatrix</kbd></li> <li><kbd>- QQ</kbd></li> <li><kbd>- RingElement</kbd></li> <li><kbd>- RR</kbd></li> <li><kbd>- RRi</kbd></li> <li><kbd>- Tally</kbd></li> <li><kbd>- Vector</kbd></li> <li><kbd>- ZZ</kbd></li> <li><kbd>CC - CC</kbd></li> <li><kbd>CC - InfiniteNumber</kbd></li> <li><kbd>CC - QQ</kbd></li> <li><kbd>CC - RR</kbd></li> <li><kbd>CC - ZZ</kbd></li> <li><kbd>Constant - Constant</kbd></li> <li><kbd>Constant - InexactNumber</kbd></li> <li><kbd>Constant - Number</kbd></li> <li><kbd>Constant - RingElement</kbd></li> <li><kbd>InexactNumber - Constant</kbd></li> <li><kbd>InexactNumber - RingElement</kbd></li> <li><kbd>InfiniteNumber - CC</kbd></li> <li><kbd>InfiniteNumber - InfiniteNumber</kbd></li> <li><kbd>InfiniteNumber - Number</kbd></li> <li><kbd>Matrix - Matrix</kbd></li> <li><kbd>Matrix - Number</kbd></li> <li><kbd>Matrix - RingElement</kbd></li> <li><kbd>MutableMatrix - MutableMatrix</kbd></li> <li><kbd>Number - Constant</kbd></li> <li><kbd>Number - InfiniteNumber</kbd></li> <li><kbd>Number - Matrix</kbd></li> <li><kbd>Number - RingElement</kbd></li> <li><kbd>Number - Vector</kbd></li> <li><kbd>QQ - CC</kbd></li> <li><kbd>QQ - QQ</kbd></li> <li><kbd>QQ - RR</kbd></li> <li><kbd>QQ - RRi</kbd></li> <li><kbd>QQ - ZZ</kbd></li> <li><kbd>RingElement - Constant</kbd></li> <li><kbd>RingElement - InexactNumber</kbd></li> <li><kbd>RingElement - Matrix</kbd></li> <li><kbd>RingElement - Number</kbd></li> <li><kbd>RingElement - RingElement</kbd></li> <li><kbd>RingElement - Vector</kbd></li> <li><kbd>RR - CC</kbd></li> <li><kbd>RR - QQ</kbd></li> <li><kbd>RR - RR</kbd></li> <li><kbd>RR - RRi</kbd></li> <li><kbd>RR - ZZ</kbd></li> <li><kbd>RRi - QQ</kbd></li> <li><kbd>RRi - RR</kbd></li> <li><kbd>RRi - RRi</kbd></li> <li><kbd>RRi - ZZ</kbd></li> <li><kbd>Vector - Number</kbd></li> <li><kbd>Vector - RingElement</kbd></li> <li><kbd>Vector - Vector</kbd></li> <li><kbd>ZZ - CC</kbd></li> <li><kbd>ZZ - QQ</kbd></li> <li><kbd>ZZ - RR</kbd></li> <li><kbd>ZZ - RRi</kbd></li> <li><kbd>ZZ - ZZ</kbd></li> <li><span><a title="negation of a virtual tally" href="_-_sp__Virtual__Tally.html">- VirtualTally</a> -- negation of a virtual tally</span></li> <li><span><a title="difference of two vectors" href="___List_sp-_sp__List.html">List - List</a> -- difference of two vectors</span></li> <li><span><a title="monomial ideal difference" href="___Monomial__Ideal_sp-_sp__Monomial__Ideal.html">MonomialIdeal - MonomialIdeal</a> -- monomial ideal difference</span></li> <li><span><kbd>List - Set</kbd> -- see <span><a title="set difference" href="___Set_sp-_sp__Set.html">Set - Set</a> -- set difference</span></span></li> <li><span><kbd>Set - List</kbd> -- see <span><a title="set difference" href="___Set_sp-_sp__Set.html">Set - Set</a> -- set difference</span></span></li> <li><span><a title="set difference" href="___Set_sp-_sp__Set.html">Set - Set</a> -- set difference</span></li> <li><span><a title="difference of tallies" href="___Tally_sp-_sp__Tally.html">Tally - Tally</a> -- difference of tallies</span></li> <li><span><a href="___Virtual__Tally_sp-_sp__Virtual__Tally.html">VirtualTally - VirtualTally</a></span></li> </ul> </div> <div class="waystouse"> <h2>For the programmer</h2> <p>The object <a title="a unary or binary operator, usually used for negation or subtraction" href="_-.html">-</a> is <span>a <a title="the class of all keywords" href="___Keyword.html">keyword</a></span>.</p> <div> <p>This operator may be used as a binary operator in an expression like <span class="tt">x-y</span>. The user may install <a href="_binary_spmethods.html">binary methods</a> for handling such expressions with code such as</p> <pre> X - Y := (x,y) -> ...</pre> <p>where <span class="tt">X</span> is the class of <span class="tt">x</span> and <span class="tt">Y</span> is the class of <span class="tt">y</span>.</p> <p>This operator may be used as a prefix unary operator in an expression like <span class="tt">-y</span>. The user may <a href="_installing_spmethods.html">install a method</a> for handling such expressions with code such as</p> <pre> - Y := (y) -> ...</pre> <p>where <span class="tt">Y</span> is the class of <span class="tt">y</span>.</p> </div> </div> <hr> <div class="waystouse"> <p>The source of this document is in <span class="tt">Macaulay2Doc/operators/minus.m2:113:0</span>.</p> </div> </div> </div> </body> </html>