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<!DOCTYPE html> <html lang="en"> <head> <title>schemeInProduct -- multi-graded Ideal of the image of a map to a product of projective spaces</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", 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href="../../Macaulay2Doc/html/_packages_spprovided_spwith_sp__Macaulay2.html">Packages</a> » <span><a title="The unique Gorenstein double structure on a surface scroll" href="index.html">K3Carpets</a> :: <a title="multi-graded Ideal of the image of a map to a product of projective spaces" href="_scheme__In__Product.html">schemeInProduct</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="_schreyer__Name.html">next</a> | <a href="_resonance__Scroll.html">previous</a> | <a href="_schreyer__Name.html">forward</a> | <a href="_resonance__Scroll.html">backward</a> | up | <a href="master.html">index</a> | <a href="toc.html">toc</a> </div> </div> <hr> <div> <h1>schemeInProduct -- multi-graded Ideal of the image of a map to a product of projective spaces</h1> <ul> <li> <dl class="element"> <dt>Usage: </dt> <dd><code class="language-macaulay2">J = schemeInProduct(I,maps,PP)</code></dd> <dd><code class="language-macaulay2">J = schemeInProduct(I,maps,X)</code></dd> </dl> </li> <li>Inputs: <ul> <li><span><span class="tt">I</span>, <span>an <a title="the class of all ideals" href="../../Macaulay2Doc/html/___Ideal.html">ideal</a></span>, defining the source scheme</span></li> <li><span><span class="tt">maps</span>, <span>a <a title="the class of all lists -- {...}" href="../../Macaulay2Doc/html/___List.html">list</a></span>, list of sequences of polynomials each of a single degree, in I</span></li> <li><span><span class="tt">PP</span>, <span>a <a title="the class of all rings" href="../../Macaulay2Doc/html/___Ring.html">ring</a></span>, multigraded ring of the product of projective spaces</span></li> <li><span><span class="tt">X</span>, <span>a <a title="the class of all symbols" href="../../Macaulay2Doc/html/___Symbol.html">symbol</a></span>, name of variable to use in constructing a ring PP if none is given</span></li> </ul> </li> <li>Outputs: <ul> <li><span><span class="tt">J</span>, <span>an <a title="the class of all ideals" href="../../Macaulay2Doc/html/___Ideal.html">ideal</a></span>, multi-graded ideal of the image</span></li> </ul> </li> </ul> <div> <h2>Description</h2> <table class="examples"> <tr> <td> <pre><code class="language-macaulay2">i1 : S = ZZ/101[a,b] o1 = S o1 : PolynomialRing</code></pre> </td> </tr> <tr> <td> <pre><code class="language-macaulay2">i2 : I = ideal 0_S o2 = ideal 0 o2 : Ideal of S</code></pre> </td> </tr> <tr> <td> <pre><code class="language-macaulay2">i3 : f0 = matrix"a,b" o3 = | a b | 1 2 o3 : Matrix S <-- S</code></pre> </td> </tr> <tr> <td> <pre><code class="language-macaulay2">i4 : f1 = matrix"a,b" o4 = | a b | 1 2 o4 : Matrix S <-- S</code></pre> </td> </tr> <tr> <td> <pre><code class="language-macaulay2">i5 : maps = {f0,f1} o5 = {| a b |, | a b |} o5 : List</code></pre> </td> </tr> <tr> <td> <pre><code class="language-macaulay2">i6 : schemeInProduct(I, maps, Y) warning: clearing value of symbol X to allow access to subscripted variables based on it : debug with expression debug 1308 or with command line option --debug 1308 o6 = ideal(X X - X X ) 1,0 0,1 0,0 1,1 ZZ o6 : Ideal of ---[X , X , X , X , a..b] 101 0,0 1,0 0,1 1,1</code></pre> </td> </tr> </table> </div> <div> <h2>See also</h2> <ul> <li><span><a title="Constructs the multi-graded ring of a product of copies of P^1 (pp is a synonym)" href="_product__Of__Projective__Spaces.html">productOfProjectiveSpaces</a> -- Constructs the multi-graded ring of a product of copies of P^1 (pp is a synonym)</span></li> </ul> </div> <div> <div class="waystouse"> <h2>Ways to use <span class="tt">schemeInProduct</span>:</h2> <ul> <li><kbd>schemeInProduct(Ideal,List,Ring)</kbd></li> <li><kbd>schemeInProduct(Ideal,List,Symbol)</kbd></li> </ul> </div> <div class="waystouse"> <h2>For the programmer</h2> <p>The object <a title="multi-graded Ideal of the image of a map to a product of projective spaces" href="_scheme__In__Product.html">schemeInProduct</a> is <span>a <a title="a type of method function" href="../../Macaulay2Doc/html/___Method__Function.html">method function</a></span>.</p> </div> <hr> <div class="waystouse"> <p>The source of this document is in <span class="tt">K3Carpets.m2:1962:0</span>.</p> </div> </div> </div> </body> </html>