One Hat Cyber Team
Your IP :
216.73.216.115
Server IP :
194.44.31.54
Server :
Linux zen.imath.kiev.ua 4.18.0-553.77.1.el8_10.x86_64 #1 SMP Fri Oct 3 14:30:23 UTC 2025 x86_64
Server Software :
Apache/2.4.37 (Rocky Linux) OpenSSL/1.1.1k
PHP Version :
5.6.40
Buat File
|
Buat Folder
Eksekusi
Dir :
~
/
usr
/
share
/
doc
/
Macaulay2
/
Bertini
/
html
/
View File Name :
_make__B_sq__Slice.html
<!DOCTYPE html> <html lang="en"> <head> <title>makeB'Slice -- makeB'Slice creates a hash table that represents a linear slice.</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="software for numerical algebraic geometry" href="index.html">Bertini</a> :: <a title="makeB'Slice creates a hash table that represents a linear slice." href="_make__B_sq__Slice.html">makeB'Slice</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="_move__B_sq__File.html">next</a> | <a href="_make__B_sq__Section.html">previous</a> | <a href="_move__B_sq__File.html">forward</a> | <a href="_make__B_sq__Section.html">backward</a> | up | <a href="master.html">index</a> | <a href="toc.html">toc</a> </div> </div> <hr> <div> <h1>makeB'Slice -- makeB'Slice creates a hash table that represents a linear slice.</h1> <ul> <li> <dl class="element"> <dt>Usage: </dt> <dd><code class="language-macaulay2">makeB'Slice(sliceType,variableGroups)</code></dd> </dl> </li> <li>Inputs: <ul> <li><span><span class="tt">sliceType</span>, <span>a <a title="the class of all lists -- {...}" href="../../Macaulay2Doc/html/___List.html">list</a></span>, A list of integers or integer.</span></li> <li><span><span class="tt">variableGroups</span>, <span>a <a title="the class of all lists -- {...}" href="../../Macaulay2Doc/html/___List.html">list</a></span>, A list of list of variables or list of variables.</span></li> </ul> </li> <li><a href="../../Macaulay2Doc/html/_using_spfunctions_spwith_spoptional_spinputs.html">Optional inputs</a>: <ul> <li><span><a title="makeB'Section creates a hash table that represents a hyperplane." href="_make__B_sq__Section.html">B'Homogenization</a><span class="tt"> => </span><span class="tt">...</span>, <span>default value {}</span>, <span>makeB'Section creates a hash table that represents a hyperplane.</span></span></li> <li><span><span class="tt">B'NumberCoefficients</span><span class="tt"> => </span><span class="tt">...</span>, <span>default value {}</span></span></li> <li><span><span class="tt">ContainsMultiProjectivePoint</span><span class="tt"> => </span><span class="tt">...</span>, <span>default value {}</span></span></li> <li><span><span class="tt">ContainsPoint</span><span class="tt"> => </span><span class="tt">...</span>, <span>default value {}</span></span></li> <li><span><span class="tt">NameB'Slice</span><span class="tt"> => </span><span class="tt">...</span>, <span>default value null</span></span></li> <li><span><span class="tt">RandomCoefficientGenerator</span><span class="tt"> => </span><span class="tt">...</span>, <span>default value FunctionClosure[../Bertini.m2:2356:37-2356:66]</span></span></li> </ul> </li> </ul> <div> <h2>Description</h2> <div> <p>makeB'Slice allows for easy creation of equations that define linear spaces, i.e. slices. The default creates a hash table with two keys: B'NumberCoefficients and B'SectionString. When we have a multiprojective variety we can different types of slices. To make a slice we need to specify the type of slice we want followed by variable groups.</p> </div> <table class="examples"> <tr> <td> <pre><code class="language-macaulay2">i1 : sliceType={1,1} o1 = {1, 1} o1 : List</code></pre> </td> </tr> <tr> <td> <pre><code class="language-macaulay2">i2 : variableGroups={{x0,x1},{y0,y1,y2}} o2 = {{x0, x1}, {y0, y1, y2}} o2 : List</code></pre> </td> </tr> <tr> <td> <pre><code class="language-macaulay2">i3 : xySlice=makeB'Slice(sliceType,variableGroups) o3 = B'Slice{...4...} o3 : B'Slice</code></pre> </td> </tr> <tr> <td> <pre><code class="language-macaulay2">i4 : peek xySlice o4 = B'Slice{B'NumberCoefficients => {{1.49144+.713846*ii, -.840113+1.1986*ii}, {.014842+1.23548*ii, -.214468+.911293*ii, -.486176+.400577*ii}} } B'SectionString => {(1.49144+.713846*ii)*(x0)+(-.840113+1.1986*ii)*(x1), (.014842+1.23548*ii)*(y0)+(-.214468+.911293*ii)*(y1)+(-.486176+.400577*ii)*(y2)} ListB'Sections => {B'Section{...2...}, B'Section{...2...}} NameB'Slice => null</code></pre> </td> </tr> <tr> <td> <pre><code class="language-macaulay2">i5 : for i in xySlice#B'SectionString do print i (1.49144+.713846*ii)*(x0)+(-.840113+1.1986*ii)*(x1) (.014842+1.23548*ii)*(y0)+(-.214468+.911293*ii)*(y1)+(-.486176+.400577*ii)*(y2)</code></pre> </td> </tr> </table> <table class="examples"> <tr> <td> <pre><code class="language-macaulay2">i6 : aSlice=makeB'Slice(3,{x,y,z,1},NameB'Slice=>"f");</code></pre> </td> </tr> <tr> <td> <pre><code class="language-macaulay2">i7 : aSlice#NameB'Slice o7 = {f0, f1, f2} o7 : List</code></pre> </td> </tr> <tr> <td> <pre><code class="language-macaulay2">i8 : makeB'InputFile(storeBM2Files,AffVariableGroup=>{x,y,z},B'Functions=>{aSlice},NamePolynomials=>{"f0","f1","f2"});</code></pre> </td> </tr> </table> <table class="examples"> <tr> <td> <pre><code class="language-macaulay2">i9 : f1="x0*y0+x1*y0+x2*y2" o9 = x0*y0+x1*y0+x2*y2</code></pre> </td> </tr> <tr> <td> <pre><code class="language-macaulay2">i10 : f2="x0*y0^2+x1*y1*y2+x2*y0*y2" o10 = x0*y0^2+x1*y1*y2+x2*y0*y2</code></pre> </td> </tr> <tr> <td> <pre><code class="language-macaulay2">i11 : variableGroups={{x0,x1,x2},{y0,y1,y2}} o11 = {{x0, x1, x2}, {y0, y1, y2}} o11 : List</code></pre> </td> </tr> <tr> <td> <pre><code class="language-macaulay2">i12 : xxSlice=makeB'Slice({2,0},variableGroups) o12 = B'Slice{...4...} o12 : B'Slice</code></pre> </td> </tr> <tr> <td> <pre><code class="language-macaulay2">i13 : xySlice=makeB'Slice({1,1},variableGroups) o13 = B'Slice{...4...} o13 : B'Slice</code></pre> </td> </tr> <tr> <td> <pre><code class="language-macaulay2">i14 : yySlice=makeB'Slice({0,2},variableGroups) o14 = B'Slice{...4...} o14 : B'Slice</code></pre> </td> </tr> <tr> <td> <pre><code class="language-macaulay2">i15 : makeB'InputFile(storeBM2Files, HomVariableGroup=>variableGroups, B'Polynomials=>{f1,f2}|xxSlice#ListB'Sections);</code></pre> </td> </tr> <tr> <td> <pre><code class="language-macaulay2">i16 : runBertini(storeBM2Files)</code></pre> </td> </tr> <tr> <td> <pre><code class="language-macaulay2">i17 : xxDegree=#importSolutionsFile(storeBM2Files) o17 = 2</code></pre> </td> </tr> <tr> <td> <pre><code class="language-macaulay2">i18 : makeB'InputFile(storeBM2Files, HomVariableGroup=>variableGroups, B'Polynomials=>{f1,f2}|xySlice#ListB'Sections);</code></pre> </td> </tr> <tr> <td> <pre><code class="language-macaulay2">i19 : runBertini(storeBM2Files)</code></pre> </td> </tr> <tr> <td> <pre><code class="language-macaulay2">i20 : xyDegree=#importSolutionsFile(storeBM2Files) o20 = 3</code></pre> </td> </tr> <tr> <td> <pre><code class="language-macaulay2">i21 : makeB'InputFile(storeBM2Files, HomVariableGroup=>variableGroups, B'Polynomials=>{f1,f2}|yySlice#ListB'Sections);</code></pre> </td> </tr> <tr> <td> <pre><code class="language-macaulay2">i22 : runBertini(storeBM2Files)</code></pre> </td> </tr> <tr> <td> <pre><code class="language-macaulay2">i23 : yyDegree=#importSolutionsFile(storeBM2Files) o23 = 1</code></pre> </td> </tr> </table> </div> <div> <div class="waystouse"> <h2>Ways to use <span class="tt">makeB'Slice</span>:</h2> <ul> <li><kbd>makeB'Slice(Thing,List)</kbd></li> </ul> </div> <div class="waystouse"> <h2>For the programmer</h2> <p>The object <a title="makeB'Slice creates a hash table that represents a linear slice." href="_make__B_sq__Slice.html">makeB'Slice</a> is <span>a <a title="a type of method function" href="../../Macaulay2Doc/html/___Method__Function__With__Options.html">method function with options</a></span>.</p> </div> <hr> <div class="waystouse"> <p>The source of this document is in <span class="tt">Bertini.m2:3676:0</span>.</p> </div> </div> </div> </body> </html>