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___Tensor.html
<!DOCTYPE html> <html lang="en"> <head> <title>Tensor -- a mutable hash table representing a tensor</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="a package for computing equilibria in game theory" href="index.html">GameTheory</a> :: <a title="a mutable hash table representing a tensor" href="___Tensor.html">Tensor</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="_to__Markov__Ring.html">next</a> | <a href="_spohn__Matrices.html">previous</a> | <a href="_to__Markov__Ring.html">forward</a> | <a href="_spohn__Matrices.html">backward</a> | up | <a href="master.html">index</a> | <a href="toc.html">toc</a> </div> </div> <hr> <div> <h1>Tensor -- a mutable hash table representing a tensor</h1> <ul> <li> <dl class="element"> <dt>Usage: </dt> <dd><code class="language-macaulay2">T = zeroTensor(R, d)</code></dd> </dl> </li> <li>Outputs: <ul> <li><span><span>an instance of the type <a title="a mutable hash table representing a tensor" href="___Tensor.html">Tensor</a></span>, A Tensor object storing values at multi-indices.</span></li> </ul> </li> </ul> <div> <h2>Description</h2> <div> <p>The type `Tensor` is a mutable hash table with additional metadata to represent multi-dimensional arrays. Each tensor has an associated format (list of dimensions), a coefficient ring, and a set of index keys.</p> <p></p> </div> <table class="examples"> <tr> <td> <pre><code class="language-macaulay2">i1 : T = zeroTensor(QQ, {2,2});</code></pre> </td> </tr> <tr> <td> <pre><code class="language-macaulay2">i2 : T#{0,0} = 1;</code></pre> </td> </tr> <tr> <td> <pre><code class="language-macaulay2">i3 : T#{1,1} = 5;</code></pre> </td> </tr> <tr> <td> <pre><code class="language-macaulay2">i4 : format T o4 = {2, 2} o4 : List</code></pre> </td> </tr> <tr> <td> <pre><code class="language-macaulay2">i5 : coefficientRing T o5 = QQ o5 : Ring</code></pre> </td> </tr> <tr> <td> <pre><code class="language-macaulay2">i6 : indexset T o6 = {{0, 0}, {0, 1}, {1, 0}, {1, 1}} o6 : List</code></pre> </td> </tr> </table> </div> <div> <h2>See also</h2> <ul> <li><span><a title="construct a tensor with zero entries from a given ring." href="_zero__Tensor.html">zeroTensor</a> -- construct a tensor with zero entries from a given ring.</span></li> <li><span><a title="construct a tensor with random entries from a given ring" href="_random__Tensor.html">randomTensor</a> -- construct a tensor with random entries from a given ring</span></li> </ul> </div> <div> <div class="waystouse"> <h2>Methods that use an object of class Tensor:</h2> <ul> <li><span><kbd>assemblePlayeriPolynomials(Ring,Tensor,ZZ)</kbd> -- see <span><a title="get all incentive constraint polynomials for a player" href="_assemble__Playeri__Polynomials.html">assemblePlayeriPolynomials</a> -- get all incentive constraint polynomials for a player</span></span></li> <li><span><kbd>assemblePolynomial(Ring,Tensor,List)</kbd> -- see <span><a title="compute incentive constraint polynomial for deviation" href="_assemble__Polynomial.html">assemblePolynomial</a> -- compute incentive constraint polynomial for deviation</span></span></li> <li><span><span class="tt">coefficientRing(Tensor)</span> (missing documentation)<!--tag: (coefficientRing,Tensor)--> </span></li> <li><span><span class="tt">format(Tensor)</span> (missing documentation)<!--tag: (format,Tensor)--> </span></li> <li><span><kbd>indexset(Tensor)</kbd> -- see <span><a title="get the list of index tuples of a tensor" href="_indexset.html">indexset</a> -- get the list of index tuples of a tensor</span></span></li> <li><span><kbd>slice(Tensor,List,List)</kbd> -- see <span><a title="extract a slice of a tensor" href="_slice.html">slice</a> -- extract a slice of a tensor</span></span></li> </ul> </div> <div class="waystouse"> <h2>For the programmer</h2> <p>The object <a title="a mutable hash table representing a tensor" href="___Tensor.html">Tensor</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 mutable hash tables" href="../../Macaulay2Doc/html/___Mutable__Hash__Table.html">MutableHashTable</a> < <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">GameTheory.m2:986:0</span>.</p> </div> </div> </div> </body> </html>
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