<?xml version="1.0" encoding="UTF-8" ?>DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.0 Strict//EN" "http://www.w3.org/TR/xhtml1/DTD/xhtml1-strict.dtd " >html xmlns="http://www.w3.org/1999/xhtml " xml:lang="en" >head >script type="text/javascript" "https://cdn.jsdelivr.net/npm/mathjax@2/MathJax.js?config=TeX-AMS-MML_HTMLorMML " >script >title >GAP (4ti2Interface) - Contents</title >meta http-equiv="content-type" content="text/html; charset=UTF-8" />meta name="generator" content="GAPDoc2HTML" />link rel="stylesheet" type="text/css" href="manual.css" />script src="manual.js" type="text/javascript" ></script >script type="text/javascript" >overwriteStyle();</script >head >body class="chap0" onload="jscontent()" >div class="chlinktop" ><span class="chlink1" >Goto Chapter: </span ><a href="chap0_mj.html" >Top</a> <a href="chap1_mj.html" >1</a> <a href="chap2_mj.html" >2</a> <a href="chap3_mj.html" >3</a> <a href="chap4_mj.html" >4</a> <a href="chapInd_mj.html" >Ind</a> </div >div class="chlinkprevnexttop" > <a href="chap0_mj.html" >[Top of Book]</a> <a href="chap0_mj.html#contents" >[Contents]</a> <a href="chap1_mj.html" >[Next Chapter]</a> </div >"mathjaxlink" class="pcenter" ><a href="chap0.html" >[MathJax off]</a></p>"X7D2C85EC87DD46E5" name="X7D2C85EC87DD46E5" ></a></p>div class="pcenter" >h1 >4ti2Interface</h1 >link to 4ti2</h2>div >br />Email: <span class="URL" ><a href="mailto:gutsche@mathematik.uni-siegen.de" >gutsche@mathematik.uni-siegen.de</a></span >br />Homepage: <span class="URL" ><a href="https://sebasguts.github.io " >https://sebasguts.github.io</a></span >br />Address : <br />Department Mathematik<br /> Universität Siegen<br /> Walter-Flex-Straße 3<br /> 57072 Siegen<br /> Germany<br />"X8537FEB07AF2BEC8" name="X8537FEB07AF2BEC8" ></a></p>div class="contents" >"contents" name="contents" ></a></h3>div class="ContChap" ><a href="chap1_mj.html#X7DFB63A97E67C0A1" >1 <span class="Heading" >Introduction</span ></a>div class="ContSect" ><span class="tocline" ><span class="nocss" > </span ><a href="chap1_mj.html#X82A882D87ABF47EB" >1.1 <span class="Heading" >What is the idea of 4ti2Interface</span ></a>span >div >div >div class="ContChap" ><a href="chap2_mj.html#X8360C04082558A12" >2 <span class="Heading" >Installation</span ></a>div class="ContSect" ><span class="tocline" ><span class="nocss" > </span ><a href="chap2_mj.html#X81A5946683F0AD7D" >2.1 <span class="Heading" >How to install this package</span ></a>span >div >div >div class="ContChap" ><a href="chap3_mj.html#X876DE76280B7AB01" >3 <span class="Heading" >4ti2 functions</span ></a>div class="ContSect" ><span class="tocline" ><span class="nocss" > </span ><a href="chap3_mj.html#X7C635ACB7DD200CF" >3.1 <span class="Heading" >Groebner</span ></a>span >div class="ContSSBlock" >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap3_mj.html#X7CCB80AD7BA246B0" >3.1-1 4ti2Interface_groebner_matrix</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap3_mj.html#X86736FF783E8F6AF" >3.1-2 4ti2Interface_groebner_basis</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap3_mj.html#X8485878A84333E15" >3.1-3 <span class="Heading" >Defining ideal of toric variety</span ></a>span >div ></div >div class="ContSect" ><span class="tocline" ><span class="nocss" > </span ><a href="chap3_mj.html#X7F5D3AAB7834A607" >3.2 <span class="Heading" >Hilbert</span ></a>span >div class="ContSSBlock" >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap3_mj.html#X7DDFDF9D7DE9A29D" >3.2-1 4ti2Interface_hilbert_inequalities</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap3_mj.html#X7F9E586C817E3C08" >3.2-2 4ti2Interface_hilbert_equalities_in_positive_orthant</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap3_mj.html#X80878F7E7F1DDDDE" >3.2-3 4ti2Interface_hilbert_equalities_and_inequalities</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap3_mj.html#X7822ED3E7DC13FAE" >3.2-4 <span class="Heading" >Generators of semigroup</span ></a>span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap3_mj.html#X7C9AE7868537AB0A" >3.2-5 <span class="Heading" >Hilbert basis of dual cone</span ></a>span >div ></div >div class="ContSect" ><span class="tocline" ><span class="nocss" > </span ><a href="chap3_mj.html#X84237872798DB501" >3.3 <span class="Heading" >ZSolve</span ></a>span >div class="ContSSBlock" >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap3_mj.html#X82FD0D9F7B7EA6F8" >3.3-1 4ti2Interface_zsolve_equalities_and_inequalities</a></span >div ></div >div class="ContSect" ><span class="tocline" ><span class="nocss" > </span ><a href="chap3_mj.html#X7D34D2A17EE6F480" >3.4 <span class="Heading" >Graver</span ></a>span >div class="ContSSBlock" >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap3_mj.html#X84F90D9B79886CA6" >3.4-1 4ti2Interface_graver_equalities</a></span >div ></div >div >div class="ContChap" ><a href="chap4_mj.html#X7A15CCB67FBCF3E3" >4 <span class="Heading" >Tool functions</span ></a>div class="ContSect" ><span class="tocline" ><span class="nocss" > </span ><a href="chap4_mj.html#X86BDFBD07D23807E" >4.1 <span class="Heading" >Read and write matrix</span ></a>span >div class="ContSSBlock" >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap4_mj.html#X7B786D5E8267CBD0" >4.1-1 4ti2Interface_Read_Matrix_From_File</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap4_mj.html#X847592CF87F6DBEC" >4.1-2 4ti2Interface_Write_Matrix_To_File</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap4_mj.html#X80F4C48487375746" >4.1-3 4ti2Interface_Cut_Vector</a></span >div ></div >div >div class="ContChap" ><a href="chapInd_mj.html" ><span class="Heading" >Index</span ></a></div >br />div >div class="chlinkprevnextbot" > <a 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