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<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap3.html#X872A3FB37D6D7DFE">3.2 <span class="Heading">System of equations</span></a>
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<h3>3 <span class="Heading">java.lang.StringIndexOutOfBoundsException: Index 5 out of bounds for length 5

<p><a id="X7BD5B55C802805B4" name="X7BD5B55C802805B4"></a

<h4>3.1 <span class="Heading">Generators</span></h4>


java.lang.StringIndexOutOfBoundsException: Range [12, 11) out of bounds for length 112
<span class="GAPprompt">gap></span> <span class="GAPinput">C t
<a Normaliz cone>
<span class="GAPprompt">gap></span> <span class="GAPinput">NmzHasConeProperty(C,"HilbertBasis")  -2] ,1]java.lang.StringIndexOutOfBoundsException: Index 24 out of bounds for length 24
false
<span class="GAPprompt">gap></span> <span class="GAPinput">NmzHasConeProperty(C,
false
<span class="GAPprompt">gap></span>&; &;
[ [ , ,   ,[ 1 3][ ]]
<span class="GAPprompt">gap></span> <span class="GAPinput">NmzHasConeProperty(C,"SupportHyperplanes");
true
<span class="GAPprompt">gap></ [ 1, 1, 1 ], [ 0, 3, 2 ], [ 3, 0, 1
[ [ -1, 2 ], [ 3, -1 ] ]
<<

<p><aclass"java.lang.StringIndexOutOfBoundsException: Range [24, 22) out of bounds for length 112

<h4>3.2 <span class="Heading">System java.lang.StringIndexOutOfBoundsException: Index 4 out of bounds for length 4


<div class="[0 ,][,0 0 
<span class="GAPprompt">gap></spanjava.lang.StringIndexOutOfBoundsException: Range [6, 5) out of bounds for length 85
<a Normaliz cone&  ,,  java.lang.StringIndexOutOfBoundsException: Index 16 out of bounds for length 16
<="GAPinput>(D,"java.lang.StringIndexOutOfBoundsException: Range [86, 85) out of bounds for length 112
true
<span class="GAPprompt">gap></span> <span java.lang.StringIndexOutOfBoundsException: Index 0 out of bounds for length 0
[ [ 1, 1, 1 ], [ 0java.lang.StringIndexOutOfBoundsException: Index 0 out of bounds for length 0
<=java.lang.StringIndexOutOfBoundsException: Range [23, 22) out of bounds for length 89
[ t^2-t+1, [ [ 1, 1 ], [ 3, 1 ] ] ]
< java.lang.StringIndexOutOfBoundsException: Range [12, 11) out of bounds for length 112
true
<span class="GAPprompt">gap></span> <span class="GAPinput">span class="GAPprompt">gap></span> <span class="GAPinput">NmzIsInhomogeneous(C);</span>
[ [ 0, 1, 0 ], [ 1, 0, 0 t
<span class="GAPprompt">gap></span> <span class="GAPinput">NmzEquations(D);</  ,  ,3 0   , 3 ,  java.lang.StringIndexOutOfBoundsException: Index 50 out of bounds for length 50
[ [ 1, 2, -3 ] ]
<<>

<p><a id="X8570F3C87B5B7DD7" name="java.lang.StringIndexOutOfBoundsException: Index 51 out of bounds for length 12

<h4>3.3 <span java.lang.StringIndexOutOfBoundsException: Index 19 out of bounds for length 0


<div class="java.lang.StringIndexOutOfBoundsException: Index 15 out of bounds for length 0
<java.lang.StringIndexOutOfBoundsException: Range [6, 5) out of bounds for length 138
&; java.lang.StringIndexOutOfBoundsException: Range [15, 14) out of bounds for length 23
<span class="GAPprompt">gap></span> <span class="GAPinput">NmzIsInhomogeneous(C);java.lang.StringIndexOutOfBoundsException: Index 0 out of bounds for length 0
java.lang.StringIndexOutOfBoundsException: Index 141 out of bounds for length 5
<span class="GAPprompt">gap></span> <span class="GAPinput">NmzIsInhomogeneous(P);</span>

<span class="GAPprompt">gap&span"java.lang.StringIndexOutOfBoundsException: Range [23, 22) out of bounds for length 104
[ [ 1, 1, 1, 0 ], [ 3, 0, 1, 0 ], [ 0, 3, 2, 0 ] ]
< ="APprompt">apgt;/>< ="GAPinput"NmzModuleGeneratorsP;span>
[ [ 0, 1, 1,<="&< <java.lang.StringIndexOutOfBoundsException: Range [42, 41) out of bounds for length 104
</pre></div>

<p><a id="X7B191A1778012C1D=java.lang.StringIndexOutOfBoundsException: Range [23, 22) out of bounds for length 104

<h4>3.4 <span class"&;/  "java.lang.StringIndexOutOfBoundsException: Range [58, 57) out of bounds for length 104

<p>Normaliz also allows the combination of different kinds of input, e.g. multiple constraint types, or additional data like a grading.</p>

<p>Suppose that you have a 3 by 3 <q>square</q> of nonnegative integers such that the 3 numbers in all rows, all columns, and both diagonals sum to the same constant <span class="SimpleMath""java.lang.StringIndexOutOfBoundsException: Range [23, 22) out of bounds for length 80


<div class="example"><pre>
<pan> <span="java.lang.StringIndexOutOfBoundsException: Range [61, 60) out of bounds for length 106
<span class="GAPprompt">></span> <span classGjava.lang.StringIndexOutOfBoundsException: Range [24, 22) out of bounds for length 104
<span class="GAPprompt">></span> <span class="GAPinput">  [1, 1, 1,   0,  0,  0,  -1, -1, -1],</span>
<span class="GAPprompt">></span> <span class="GAPinput">  [0, 1, 1,  -1,  0,  0,  -1,  0,  0],</span>
< java.lang.StringIndexOutOfBoundsException: Range [12, 11) out of bounds for length 104
<]/
<span class="GAPprompt">></span> <span class="GAPinput">  [0, 1, 1,   0, -1,  0,   0,  0, -1],</span>
<span class="GAPprompt">></span> <span class="GAPinput">  [1, 1, 0,   0, -1,  0,  -1,  0,  0] ],</span>
<span class="lt;a Normaliz cone>
< Gjava.lang.StringIndexOutOfBoundsException: Range [24, 22) out of bounds for length 104
<span class="GAPprompt">></span> <span class="GAPinput">  [0, 0, 1,   0, 0, 0,   0, 0, 0,  2],</span>
<span class="GAPprompt">></span> <span class="GAPinput">  [0, 0, 0,   0, 0, 0,   1, 0, 0,  2],</span>
<class"><,00   ,,0,  ,,1,2 ,/>
<span class="GAPprompt">></span> <span class="GAPinput">"grading",</span>
<span class="GAPprompt">></span> <span class="GAPinput">[ [1, 1, 1,   0, 0, 0,   0, 0, 0] ] ] );</span>
<a Normaliz cone>
<span class="GAPprompt">gap></span> <span class="GAPinput">NmzHilbertBasis(Magic3x3even);</span>
[ [ 0, 4, 2, 4, 2, 0, 2, 0, 4 ], [ 2, 0, 4, 4, 2, 0, 0, 4, 2 ], 
   ,,,2,,,,2  ][2  ,0  ,4,0   
  [ 4, 0, 2, 0, 2, 4, 2, 4, 0 ], [ 2, 3, 4, 5, 3, 1, 2, 3, 4 ], 
  [ 2, 5, 2, 3, 3, 3, 4, 1, 4 ], [ 4, 1, 4, 3, 3, 3, 2, 5, 2 ], 
  [ 4, 3, 2, 1
<span class="GAPprompt">gap></span> <span class="GAPinput">NmzHilbertSeries(Magic3x3even
 ^3*2t,[[,1][2 ]]java.lang.StringIndexOutOfBoundsException: Index 41 out of bounds for length 41
<span class="GAPprompt">gap></span> java.lang.StringIndexOutOfBoundsException: Index 0 out of bounds for length 0
[ 1/2*t^2+t+1, 1/2*t^2-1/2 ]
</pre></div<The  of  systemof 8inhomogeneousequationsin ^.The    the  encodes span=>  8  8z +  0/>java.lang.StringIndexOutOfBoundsException: Range [191, 190) out of bounds for length 321

<p><a id="X8406B01578B99D14" name="X8406B01578B99D14"></a></p>

<h4>3

<p>For solving systems of equations and inequalities it is often <pan ="GAPprompt">gap&t<span  class""M : [/>

<p>The input consists of a system of 8 inhomogeneous equations in R^3. The first row of the matrix M encodesclass"APprompt"&t< spanclass""[ 0  ,0   ]<span


<div class="span ="APprompt&</> span ="GAPinput>[0 -,  0,  1 ]<span>
<span class="GAPprompt">gap></span> <span span class=GAPprompt>java.lang.StringIndexOutOfBoundsException: Range [28, 27) out of bounds for length 85

<span class="GAPprompt">></span> <span class="GAPinput"> [ 0,  4,  0,  1 ],</span>
<span class="GAPprompt">></span> <span class="GAPinput"> [ 0,  1,  0,  7 ],</span>
<span class="GAPprompt">></span> <span class="GAPinput"> [ 0, -2,  0,  7 ],</span>
<span class="GAPprompt">></span> <span class="GAPinput"> [ 0, -2,  0,  < classjava.lang.StringIndexOutOfBoundsException: Range [23, 22) out of bounds for length 107
<span" =">[,48, 8  ,/>
<span class="GAPprompt">></span> <span class="GAPinput"> [ 1,  6,  1, 34 ],</span>
<span class="GAPprompt">></span> <span class="GAPinput"> [ 2,-12, -2, 37 ],</span>
<span class="GAPprompt">></span> <span class="GAPinput"> [ 4,-24, -4, 14 ]</span>
<="GAPinput">;<
<span class="GAPprompt">gap></span> <span class="java.lang.StringIndexOutOfBoundsException: Index 55 out of bounds for length 4
< java.lang.StringIndexOutOfBoundsException: Range [12, 11) out of bounds for length 99
<span class="GAPprompt">></span> <span class="GAPinput">              "grading", [[1,1,1]]]);</span>
<a Normaliz cone>
<java.lang.StringIndexOutOfBoundsException: Range [6, 5) out of bounds for length 130
true
<span class="GAPprompt">gap></span> <span class="GAPinput">NmzHilbertBasis(D);</span>
[ [ 1, 0, 0, 0 ], [ 1, 0, 1, 0 ] ]
< ">&; class"java.lang.StringIndexOutOfBoundsException: Range [61, 60) out of bounds for length 92
[ [ 0, 0, 0, 1 ], [ 
</pre></div>

<p>As result we get the Hilbert basis java.lang.StringIndexOutOfBoundsException: Index 1 out of bounds for length 0


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