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<!DOCTYPE html> <html lang="en"> <head> <title>** -- a binary operator, usually used for tensor product or Cartesian product</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 binary operator, usually used for tensor product or Cartesian product" href="__st_st.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="_%5E_st_st.html">next</a> | <a href="__pl_pl.html">previous</a> | <a href="_%5E_st_st.html">forward</a> | <a href="__pl_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 binary operator, usually used for tensor product or Cartesian product</h1> <div> <!--empty documentation body--> </div> <div> <h2>See also</h2> <ul> <li><span><a title="a binary operator, usually used for tensor or Cartesian power" href="_%5E_st_st.html">^**</a> -- a binary operator, usually used for tensor or Cartesian power</span></li> </ul> </div> <div> <div class="waystouse"> <h2>Ways to use <span class="tt">symbol **</span>:</h2> <ul> <li><span><kbd>BettiTally ** BettiTally</kbd> -- see <span><a title="the class of all Betti tallies" href="___Betti__Tally.html">BettiTally</a> -- the class of all Betti tallies</span></span></li> <li><span><a title="Cartesian product of two lists" href="___List_sp_st_st_sp__List.html">List ** List</a> -- Cartesian product of two lists</span></li> <li><span><a title="tensor product" href="___Matrix_sp_st_st_sp__Ring.html">Matrix ** Ring</a> -- tensor product</span></li> <li><span><kbd>Ring ** Matrix</kbd> -- see <span><a title="tensor product" href="___Matrix_sp_st_st_sp__Ring.html">Matrix ** Ring</a> -- tensor product</span></span></li> <li><span><a href="___Matrix_sp_st_st_sp__Ring__Element.html">Matrix ** RingElement</a></span></li> <li><span><kbd>Ideal ** Ring</kbd> -- see <span><a title="tensor product" href="___Module_sp_st_st_sp__Ring.html">Module ** Ring</a> -- tensor product</span></span></li> <li><span><a title="tensor product" href="___Module_sp_st_st_sp__Ring.html">Module ** Ring</a> -- tensor product</span></li> <li><span><kbd>Ring ** Ideal</kbd> -- see <span><a title="tensor product" href="___Module_sp_st_st_sp__Ring.html">Module ** Ring</a> -- tensor product</span></span></li> <li><span><kbd>Ring ** Module</kbd> -- see <span><a title="tensor product" href="___Module_sp_st_st_sp__Ring.html">Module ** Ring</a> -- tensor product</span></span></li> <li><span><a title="Cartesian product" href="___Set_sp_st_st_sp__Set.html">Set ** Set</a> -- Cartesian product</span></li> <li><span><kbd>Matrix ** Matrix</kbd> -- see <span><a title="tensor product" href="_tensor_lp__Matrix_cm__Matrix_rp.html">tensor(Matrix,Matrix)</a> -- tensor product</span></span></li> <li><span><kbd>Matrix ** Module</kbd> -- see <span><a title="tensor product" href="_tensor_lp__Matrix_cm__Module_rp.html">tensor(Matrix,Module)</a> -- tensor product</span></span></li> <li><span><kbd>Module ** Matrix</kbd> -- see <span><a title="tensor product" href="_tensor_lp__Matrix_cm__Module_rp.html">tensor(Matrix,Module)</a> -- tensor product</span></span></li> <li><span><kbd>Module ** Module</kbd> -- see <span><a title="tensor product of modules" href="_tensor_lp__Module_cm__Module_rp.html">tensor(Module,Module)</a> -- tensor product of modules</span></span></li> <li><span><kbd>Monoid ** Monoid</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>Ring ** Ring</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>RingMap ** Matrix</kbd> -- see <span><a title="tensor product via a ring map" href="_tensor_lp__Ring__Map_cm__Matrix_rp.html">tensor(RingMap,Matrix)</a> -- tensor product via a ring map</span></span></li> <li><span><kbd>RingMap ** Module</kbd> -- see <span><a title="tensor product via a ring map" href="_tensor_lp__Ring__Map_cm__Matrix_rp.html">tensor(RingMap,Matrix)</a> -- tensor product via a ring map</span></span></li> <li><span><a title="tensor product" href="___Vector_sp_st_st_sp__Vector.html">Vector ** Vector</a> -- tensor product</span></li> <li><span><a title="Cartesian product of tallies" href="___Virtual__Tally_sp_st_st_sp__Virtual__Tally.html">VirtualTally ** VirtualTally</a> -- Cartesian product of tallies</span></li> </ul> </div> <div class="waystouse"> <h2>For the programmer</h2> <p>The object <a title="a binary operator, usually used for tensor product or Cartesian product" href="__st_st.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> </div> </div> <hr> <div class="waystouse"> <p>The source of this document is in <span class="tt">Macaulay2Doc/operators/tensor.m2:21:0</span>.</p> </div> </div> </div> </body> </html>