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<head><title>Working with fans - Part 2</title>
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<div><h1>Working with fans - Part 2</h1>
<div>Now we construct a new fan to show some other functions.<table class="examples"><tr><td><pre>i1 : C1 = posHull matrix {{1,1,-1,-1},{1,-1,1,-1},{1,1,1,1}};</pre>
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<tr><td><pre>i2 : C2 = posHull matrix {{1,1,1},{0,1,-1},{-1,1,1}};</pre>
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<tr><td><pre>i3 : C3 = posHull matrix {{-1,-1,-1},{0,1,-1},{-1,1,1}};</pre>
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<tr><td><pre>i4 : C4 = posHull matrix {{1,-1},{0,0},{-1,-1}};</pre>
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<tr><td><pre>i5 : F = fan {C1,C2,C3,C4}
o5 = {ambient dimension => 3 }
number of generating cones => 4
number of rays => 6
top dimension of the cones => 3
o5 : Fan</pre>
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This is not a ''very nice'' fan, as it is neither complete nor
of pure dimension:<table class="examples"><tr><td><pre>i6 : isComplete F
o6 = false</pre>
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<tr><td><pre>i7 : isPure F
o7 = true</pre>
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If we add two more cones the fan becomes complete.<table class="examples"><tr><td><pre>i8 : C5 = posHull matrix {{1,-1,1,-1},{-1,-1,0,0},{1,1,-1,-1}};</pre>
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<tr><td><pre>i9 : C6 = posHull matrix {{1,-1,1,-1},{1,1,0,0},{1,1,-1,-1}};</pre>
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<tr><td><pre>i10 : F = addCone({C5,C6},F)
o10 = {ambient dimension => 3 }
number of generating cones => 5
number of rays => 6
top dimension of the cones => 3
o10 : Fan</pre>
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<tr><td><pre>i11 : isComplete F
o11 = true</pre>
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For a complete fan we can check if it is projective:<table class="examples"><tr><td><pre>i12 : isPolytopal F
o12 = true</pre>
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If the fan is projective, the function returns a polyhedron such that
the fan is its normal fan, otherwise it returns the empty polyhedron. This means
our fan is projective.</div>
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