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<div class="chlinktop"><span class="chlink1">Goto Chapter: </span><a href="chap0.html">Top</a>  <a href="chap1.html">1</a>  <a href="chap2.html">2</a>  <a href="chap3.html">3</a>  <a href="chap4.html">4</a>  <a href="chapA.html">A</a>  <a href="chapBib.html">Bib</a>  <a href="chapInd.html">Ind</a>  </div>

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<p id="mathjaxlink" class="pcenter"><a href="chap4_mj.html">[MathJax on]</a></p>
<p><a id="X8394FA997C62A89C" name="X8394FA997C62A89C"></a></p>
<div class="ChapSects"><a href="chap4.html#X8394FA997C62A89C">4 <span class="Heading"><strong class="pkg">SCO</strong> methods and
functions</span></a>
<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap4.html#X822BCAB878B669A5">4.1 <span class="Heading">Methods and functions for orbifold
triangulations</span></a>
</span>
<div class="ContSSBlock">
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap4.html#X817F45D6780F45F7">4.1-1 OrbifoldTriangulation</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap4.html#X79E4BB4F849AC8A1">4.1-2 Vertices</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap4.html#X7AC3235E8044172B">4.1-3 Simplices</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap4.html#X7D9F409380816CB5">4.1-4 Isotropy</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap4.html#X795D2855804A5855">4.1-5 Mu</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap4.html#X83926F268523C541">4.1-6 MuData</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap4.html#X7E845DE47C817088">4.1-7 InfoString</a></span>
</div></div>
<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap4.html#X7B0172DD7CD92CD8">4.2 <span class="Heading">Methods and functions for simplicial sets</span></a>
</span>
<div class="ContSSBlock">
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap4.html#X7DD68A0E7E3A4A51">4.2-1 SimplicialSet</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap4.html#X7DC060057E853275">4.2-2 SimplicialSet</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap4.html#X80091ADD7F0D80F2">4.2-3 ComputeNextDimension</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap4.html#X7BAB245A8009088D">4.2-4 Extend</a></span>
</div></div>
<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap4.html#X87335B4B8437DA4B">4.3 <span class="Heading">Methods and functions for matrix creation and
computation</span></a>
</span>
<div class="ContSSBlock">
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap4.html#X7F28FA7B83B681E8">4.3-1 BoundaryOperator</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap4.html#X80C3C6867CE9FE3E">4.3-2 CreateBoundaryMatrices</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap4.html#X85A9D5CB8605329C">4.3-3 Homology</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap4.html#X8320B03E7FEB2BA8">4.3-4 CreateCoboundaryMatrices</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap4.html#X84CFC57B7E9CCCF7">4.3-5 Cohomology</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap4.html#X85874A8979FF9E82">4.3-6 SCO_Examples</a></span>
</div></div>
</div>

<h3>4 <span class="Heading"><strong class="pkg">SCO</strong> methods and
functions</span></h3>

<p><a id="X822BCAB878B669A5" name="X822BCAB878B669A5"></a></p>

<h4>4.1 <span class="Heading">Methods and functions for orbifold
triangulations</span></h4>

<p><a id="X817F45D6780F45F7" name="X817F45D6780F45F7"></a></p>

<h5>4.1-1 OrbifoldTriangulation</h5>

<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ OrbifoldTriangulation</code>( <var class="Arg">M</var>[, <var class="Arg">I</var>, <var class="Arg">mu_data</var>, <var class="Arg">info</var>] )</td><td class="tdright">( function )</td></tr></table></div>
<p>Returns: OrbifoldTriangulation</p>

<p>The constructor for OrbifoldTriangulations. Needs the list <var class="Arg">M</var> of maximal simplices, the Isotropy at certain vertices as a record <var class="Arg">I</var>, and the list <var class="Arg">mu_data</var> that encodes the function mu. If only one argument is given, <var class="Arg">I</var> and <var class="Arg">mu_data</var> are supposed to be empty. In case of two arguments, <var class="Arg">mu_data</var> is supposed to be empty. If the last argument <var class="Arg">info</var> is given as a string, it is stored in the info component of the orbifold triangulation and does not count towards the total number of arguments.</p>


<div class="example"><pre>
<span class="GAPprompt">gap></span> <span class="GAPinput">M := [ [1,2,3], [1,2,4], [1,3,4], [2,3,4] ];;</span>
<span class="GAPprompt">gap></span> <span class="GAPinput">S2 := OrbifoldTriangulation( M, "S^2" );</span>
<OrbifoldTriangulation "S^2" of dimension 2. 4 simplices on 4 vertices without\
 Isotropy>
<span class="GAPprompt">gap></span> <span class="GAPinput">I := rec( 1 := Group( (1,2) ) );;</span>
<span class="GAPprompt">gap></span> <span class="GAPinput">mu_data := [</span>
<span class="GAPprompt">></span> <span class="GAPinput">[ [2], [1,2], [1,2,3], [1,2,4], x->x*(1,2) ],</span>
<span class="GAPprompt">></span> <span class="GAPinput">[ [2], [1,2], [1,2,4], [1,2,3], x->x*(1,2) ]</span>
<span class="GAPprompt">></span> <span class="GAPinput">];;</span>
<span class="GAPprompt">gap></span> <span class="GAPinput">Teardrop := OrbifoldTriangulation( M, I, mu_data, "Teardrop" );</span>
<OrbifoldTriangulation "Teardrop" of dimension 2. 4 simplices on 4 vertices wi\
th Isotropy on 1 vertex and nontrivial mu-maps>
</pre></div>

<p><a id="X79E4BB4F849AC8A1" name="X79E4BB4F849AC8A1"></a></p>

<h5>4.1-2 Vertices</h5>

<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ Vertices</code>( <var class="Arg">ot</var> )</td><td class="tdright">( method )</td></tr></table></div>
<p>Returns: List <var class="Arg">V</var></p>

<p>This returns the list of vertices <var class="Arg">V</var> of the orbifold triangulation <var class="Arg">ot</var>. Should be preferred to the equivalent <code class="code">ot!.vertices</code>.</p>

<p><a id="X7AC3235E8044172B" name="X7AC3235E8044172B"></a></p>

<h5>4.1-3 Simplices</h5>

<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ Simplices</code>( <var class="Arg">ot</var> )</td><td class="tdright">( method )</td></tr></table></div>
<p>Returns: List <var class="Arg">M</var></p>

<p>This returns the list of maximal simplices <var class="Arg">M</var> of the orbifold triangulation <var class="Arg">ot</var>. Should be preferred to the equivalent <code class="code">ot!.max_simplices</code>.</p>

<p><a id="X7D9F409380816CB5" name="X7D9F409380816CB5"></a></p>

<h5>4.1-4 Isotropy</h5>

<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ Isotropy</code>( <var class="Arg">ot</var> )</td><td class="tdright">( method )</td></tr></table></div>
<p>Returns: Record <var class="Arg">I</var></p>

<p>This returns the isotropy record <var class="Arg">I</var> of the orbifold triangulation <var class="Arg">ot</var>. Should be preferred to the equivalent <code class="code">ot!.isotropy</code>.</p>

<p><a id="X795D2855804A5855" name="X795D2855804A5855"></a></p>

<h5>4.1-5 Mu</h5>

<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ Mu</code>( <var class="Arg">ot</var> )</td><td class="tdright">( method )</td></tr></table></div>
<p>Returns: Function <var class="Arg">mu</var></p>

<p>This returns the function <var class="Arg">mu</var> of the orbifold triangulation <var class="Arg">ot</var>. Should be preferred to the equivalent <code class="code">ot!.mu</code>.</p>

<p><a id="X83926F268523C541" name="X83926F268523C541"></a></p>

<h5>4.1-6 MuData</h5>

<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ MuData</code>( <var class="Arg">ot</var> )</td><td class="tdright">( method )</td></tr></table></div>
<p>Returns: List <var class="Arg">mu_data</var></p>

<p>This returns the list <var class="Arg">mu_data</var> that encodes the function mu of the orbifold triangulation <var class="Arg">ot</var>. Should be preferred to the equivalent <code class="code">ot!.mu_data</code>.</p>

<p><a id="X7E845DE47C817088" name="X7E845DE47C817088"></a></p>

<h5>4.1-7 InfoString</h5>

<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ InfoString</code>( <var class="Arg">ot</var> )</td><td class="tdright">( method )</td></tr></table></div>
<p>Returns: String <var class="Arg">info</var></p>

<p>This return the string <var class="Arg">info</var> of the orbifold triangulation <var class="Arg">ot</var>. Should be preferred to the equivalent <code class="code">ot!.info</code>.</p>

<p><a id="X7B0172DD7CD92CD8" name="X7B0172DD7CD92CD8"></a></p>

<h4>4.2 <span class="Heading">Methods and functions for simplicial sets</span></h4>

<p><a id="X7DD68A0E7E3A4A51" name="X7DD68A0E7E3A4A51"></a></p>

<h5>4.2-1 SimplicialSet</h5>

<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ SimplicialSet</code>( <var class="Arg">ot</var> )</td><td class="tdright">( method )</td></tr></table></div>
<p>Returns: SimplicialSet</p>

<p>The constructor for simplicial sets based on an orbifold triangulation <var class="Arg">ot</var>. This just sets up the object without any computations. These can be triggered later, either explicitly or by <code class="func">SimplicialSet</code> (<a href="chap4.html#X7DC060057E853275"><span class="RefLink">4.2-2</span></a>).</p>


<div class="example"><pre>
<span class="GAPprompt">gap></span> <span class="GAPinput">Teardrop;</span>
<OrbifoldTriangulation "Teardrop" of dimension 2. 4 simplices on 4 vertices wi\
th Isotropy on 1 vertex and nontrivial mu-maps>
<span class="GAPprompt">gap></span> <span class="GAPinput">S := SimplicialSet( Teardrop );</span>
<The simplicial set of the orbifold triangulation "Teardrop", computed up to d\
imension 0 with Length vector [ 4 ]>
</pre></div>

<p><a id="X7DC060057E853275" name="X7DC060057E853275"></a></p>

<h5>4.2-2 SimplicialSet</h5>

<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ SimplicialSet</code>( <var class="Arg">S</var>, <var class="Arg">i</var> )</td><td class="tdright">( method )</td></tr></table></div>
<p>Returns: List <var class="Arg">S</var>_<var class="Arg">i</var></p>

<p>This returns the components of dimension <var class="Arg">i</var> of the simplicial set <var class="Arg">S</var>. Should be used to access existing data instead of using <code class="code">S!.simplicial_set[ i + 1 ]</code>, as it has the additional side effect of computing <var class="Arg">S</var> up to dimension <var class="Arg">i</var>, thus always returning the desired result.</p>


<div class="example"><pre>
<span class="GAPprompt">gap></span> <span class="GAPinput">S := SimplicialSet( Teardrop );</span>
<The simplicial set of the orbifold triangulation "Teardrop", computed up to d\
imension 0 with Length vector [ 4 ]>
<span class="GAPprompt">gap></span> <span class="GAPinput">S!.simplicial_set[1];</span>
[ [ [ 1, 2, 3 ] ], [ [ 1, 2, 4 ] ], [ [ 1, 3, 4 ] ], [ [ 2, 3, 4 ] ] ]
<span class="GAPprompt">gap></span> <span class="GAPinput">S!.simplicial_set[2];;</span>
Error, List Element: <list>[2] must have an assigned value
<span class="GAPprompt">gap></span> <span class="GAPinput">SimplicialSet( S, 0 );</span>
[ [ [ 1, 2, 3 ] ], [ [ 1, 2, 4 ] ], [ [ 1, 3, 4 ] ], [ [ 2, 3, 4 ] ] ]
<span class="GAPprompt">gap></span> <span class="GAPinput">SimplicialSet( S, 1 );;</span>
<span class="GAPprompt">gap></span> <span class="GAPinput">S;</span>
<The simplicial set of the orbifold triangulation "Teardrop", computed up to d\
imension 1 with Length vector [ 4, 12 ]>
</pre></div>

<p><a id="X80091ADD7F0D80F2" name="X80091ADD7F0D80F2"></a></p>

<h5>4.2-3 ComputeNextDimension</h5>

<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ ComputeNextDimension</code>( <var class="Arg">S</var> )</td><td class="tdright">( method )</td></tr></table></div>
<p>Returns: <var class="Arg">S</var></p>

<p>This computes the component of the next dimension of the simplicial set <var class="Arg">S</var>. <var class="Arg">S</var> is extended as a side effect.</p>


<div class="example"><pre>
<span class="GAPprompt">gap></span> <span class="GAPinput">S;</span>
<The simplicial set of the orbifold triangulation "Teardrop", computed up to d\
imension 1 with Length vector [ 4, 12 ]>
<span class="GAPprompt">gap></span> <span class="GAPinput">ComputeNextDimension( S );</span>
<The simplicial set of the orbifold triangulation "Teardrop", computed up to d\
imension 2 with Length vector [ 4, 12, 22 ]>
</pre></div>

<p><a id="X7BAB245A8009088D" name="X7BAB245A8009088D"></a></p>

<h5>4.2-4 Extend</h5>

<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ Extend</code>( <var class="Arg">S</var>, <var class="Arg">i</var> )</td><td class="tdright">( method )</td></tr></table></div>
<p>Returns: <var class="Arg">S</var></p>

<p>This computes the components of the simplicial set <var class="Arg">S</var> up to dimension <var class="Arg">i</var>. <var class="Arg">S</var> is extended as a side effect. This method is equivalent to calling <code class="func">ComputeNextDimension</code> (<a href="chap4.html#X80091ADD7F0D80F2"><span class="RefLink">4.2-3</span></a>) the appropriate number of times.</p>


<div class="example"><pre>
<span class="GAPprompt">gap></span> <span class="GAPinput">S;</span>
<The simplicial set of the orbifold triangulation "Teardrop", computed up to d\
imension 2 with Length vector [ 4, 12, 22 ]>
<span class="GAPprompt">gap></span> <span class="GAPinput">Extend( S, 5 );</span>
<The simplicial set of the orbifold triangulation "Teardrop", computed up to d\
imension 5 with Length vector [ 4, 12, 22, 33, 51, 73 ]>
</pre></div>

<p><a id="X87335B4B8437DA4B" name="X87335B4B8437DA4B"></a></p>

<h4>4.3 <span class="Heading">Methods and functions for matrix creation and
computation</span></h4>

<p><a id="X7F28FA7B83B681E8" name="X7F28FA7B83B681E8"></a></p>

<h5>4.3-1 BoundaryOperator</h5>

<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ BoundaryOperator</code>( <var class="Arg">i</var>, <var class="Arg">L</var>, <var class="Arg">mu</var> )</td><td class="tdright">( function )</td></tr></table></div>
<p>Returns: List B</p>

<p>This returns the <var class="Arg">i</var>th boundary of <var class="Arg">L</var>, which has to be an element of a simplicial set. <var class="Arg">mu</var> is the function <span class="SimpleMath">μ</span> that has to be taken into account when computing orbifold boundaries. This function is used for matrix creation, there should not be much reason for calling it independently.</p>

<p><a id="X80C3C6867CE9FE3E" name="X80C3C6867CE9FE3E"></a></p>

<h5>4.3-2 CreateBoundaryMatrices</h5>

<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ CreateBoundaryMatrices</code>( <var class="Arg">S</var>, <var class="Arg">d</var>, <var class="Arg">R</var> )</td><td class="tdright">( method )</td></tr></table></div>
<p>Returns: List <var class="Arg">M</var></p>

<p>This returns the list <var class="Arg">M</var> of homalg matrices over the homalg ring <var class="Arg">R</var> up to dimension <var class="Arg">d</var>, corresponding to the boundary matrices induced by the simplicial set <var class="Arg">S</var>. If <var class="Arg">d</var> is not given, the current dimension of <var class="Arg">S</var> is used.</p>


<div class="example"><pre>
<span class="GAPprompt">gap></span> <span class="GAPinput">S := SimplicialSet( Teardrop );</span>
<The simplicial set of the orbifold triangulation "Teardrop", computed up to d\
imension 0 with Length vector [ 4 ]>
<span class="GAPprompt">gap></span> <span class="GAPinput">M := CreateBoundaryMatrices( S, 4, HomalgRingOfIntegers() );;</span>
<span class="GAPprompt">gap></span> <span class="GAPinput">S;</span>
<The simplicial set of the orbifold triangulation "Teardrop", computed up to d\
imension 5 with Length vector [ 4, 12, 22, 33, 51, 73 ]>
</pre></div>

<p><a id="X85A9D5CB8605329C" name="X85A9D5CB8605329C"></a></p>

<h5>4.3-3 Homology</h5>

<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ Homology</code>( <var class="Arg">M</var>[, <var class="Arg">R</var>] )</td><td class="tdright">( method )</td></tr></table></div>
<p>Returns: a <strong class="pkg">homalg</strong> complex</p>

<p>This returns the homology complex of a list <var class="Arg">M</var> of <strong class="pkg">homalg</strong> matrices over the <strong class="pkg">homalg</strong> ring <var class="Arg">R</var>.</p>


<div class="example"><pre>
<span class="GAPprompt">gap></span> <span class="GAPinput">S := SimplicialSet( Teardrop );</span>
<The simplicial set of the orbifold triangulation "Teardrop", computed up to d\
imension 0 with Length vector [ 4 ]>
<span class="GAPprompt">gap></span> <span class="GAPinput">R := HomalgRingOfIntegers();</span>
Z
<span class="GAPprompt">gap></span> <span class="GAPinput">M := CreateBoundaryMatrices( S, 4, R );;</span>
<span class="GAPprompt">gap></span> <span class="GAPinput">Homology( M, R );</span>
----------------------------------------------->>>>  Z^(1 x 1)
----------------------------------------------->>>>  0
----------------------------------------------->>>>  Z^(1 x 1)
----------------------------------------------->>>>  Z/< 2 >
----------------------------------------------->>>>  0
<A graded homology object consisting of 5 left modules at degrees [ 0 .. 4 ]>
</pre></div>

<p><a id="X8320B03E7FEB2BA8" name="X8320B03E7FEB2BA8"></a></p>

<h5>4.3-4 CreateCoboundaryMatrices</h5>

<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ CreateCoboundaryMatrices</code>( <var class="Arg">S</var>[, <var class="Arg">d</var>], <var class="Arg">R</var> )</td><td class="tdright">( method )</td></tr></table></div>
<p>Returns: List <var class="Arg">M</var></p>

<p>This returns the list <var class="Arg">M</var> of homalg matrices over the homalg ring <var class="Arg">R</var> up to dimension <var class="Arg">d</var>, corresponding to the coboundary matrices induced by the simplicial set <var class="Arg">S</var>. If <var class="Arg">d</var> is not given, the current dimension of <var class="Arg">S</var> is used.</p>


<div class="example"><pre>
<span class="GAPprompt">gap></span> <span class="GAPinput">S := SimplicialSet( Teardrop );</span>
<The simplicial set of the orbifold triangulation "Teardrop", computed up to d\
imension 0 with Length vector [ 4 ]>
<span class="GAPprompt">gap></span> <span class="GAPinput">M := CreateCoboundaryMatrices( S, 4, HomalgRingOfIntegers() );;</span>
<span class="GAPprompt">gap></span> <span class="GAPinput">S;</span>
<The simplicial set of the orbifold triangulation "Teardrop", computed up to d\
imension 5 with Length vector [ 4, 12, 22, 33, 51, 73 ]>
</pre></div>

<p><a id="X84CFC57B7E9CCCF7" name="X84CFC57B7E9CCCF7"></a></p>

<h5>4.3-5 Cohomology</h5>

<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ Cohomology</code>( <var class="Arg">M</var>[, <var class="Arg">R</var>] )</td><td class="tdright">( method )</td></tr></table></div>
<p>Returns: a <strong class="pkg">homalg</strong> complex</p>

<p>This returns the cohomology complex of a list <var class="Arg">M</var> of <strong class="pkg">homalg</strong> matrices over the <strong class="pkg">homalg</strong> ring <var class="Arg">R</var>.</p>


<div class="example"><pre>
<span class="GAPprompt">gap></span> <span class="GAPinput">S := SimplicialSet( Teardrop );</span>
<The simplicial set of the orbifold triangulation "Teardrop", computed up to d\
imension 0 with Length vector [ 4 ]>
<span class="GAPprompt">gap></span> <span class="GAPinput">R := HomalgRingOfIntegers();</span>
Z
<span class="GAPprompt">gap></span> <span class="GAPinput">M := CreateCoboundaryMatrices( S, 4, R );;</span>
<span class="GAPprompt">gap></span> <span class="GAPinput">Cohomology( M, R );</span>
----------------------------------------------->>>>  Z^(1 x 1)
----------------------------------------------->>>>  0
----------------------------------------------->>>>  Z^(1 x 1)
----------------------------------------------->>>>  0
----------------------------------------------->>>>  Z/< 2 >
<A graded cohomology object consisting of 5 left modules at degrees
[ 0 .. 4 ]>
</pre></div>

<p><a id="X85874A8979FF9E82" name="X85874A8979FF9E82"></a></p>

<h5>4.3-6 SCO_Examples</h5>

<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ SCO_Examples</code>(  )</td><td class="tdright">( function )</td></tr></table></div>
<p>Returns: nothing</p>

<p>This is just an easy way to call the script <code class="file">examples.g</code>, which is located in <code class="file">gap/pkg/SCO/examples/</code>.</p>


<div class="example"><pre>
<span class="GAPprompt">gap></span> <span class="GAPinput">SCO_Examples();</span>
@@@@@@@@ SCO @@@@@@@@

Select base ring:
 1) Integers (default)
 2) Rationals
 3) Z/nZ
:1

Select Computer Algebra System:
 1) GAP (default)
 2) External GAP
 3) MAGMA
 4) Maple
 5) Sage
:3
---------------------------------------------------------------
Magma V2.14-14    Tue Aug 19 2008 08:36:19 on evariste [Seed = 1054613462]
Type ? for help.  Type <Ctrl>-D to quit.
----------------------------------------------------------------


Select Method:
 1) Full syzygy computation (default)
 2) matrix creation and rank computation only
:1

Select orbifold (default="C2")
:Torus
  
Select mode:
 1) Cohomology (default)
 2) Homology
:1

Select dimension (default = 4)
:4
Creating the coboundary matrices ...
Starting cohomology computation ...
----------------------------------------------->>>>  Z^(1 x 1)
----------------------------------------------->>>>  Z^(1 x 2)
----------------------------------------------->>>>  Z^(1 x 1)
----------------------------------------------->>>>  0
----------------------------------------------->>>>  0    
</pre></div>


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