For any hyperplane arrangement $A$ and any flat $F$ in $A$, this methods creates a new hyperplane arrangement formed by the hyperplanes in $A$ that contain the linear subspace associated to the flat $A$.
i1 : S = QQ[w, x, y, z];
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i2 : A3 = typeA(3, S)
o2 = {w - x, w - y, w - z, x - y, x - z, y - z}
o2 : Hyperplane Arrangement
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i3 : F1 = flat(A3, {3,4,5})
o3 = {3, 4, 5}
o3 : Flat of {w - x, w - y, w - z, x - y, x - z, y - z}
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i4 : A3' = subArrangement(A3, F1)
o4 = {x - y, x - z, y - z}
o4 : Hyperplane Arrangement
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i5 : assert(ring A3 === ring A3')
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i6 : subArrangement flat(A3, {0, 5})
o6 = {w - x, y - z}
o6 : Hyperplane Arrangement
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i7 : F2 = flat(A3, {0, 1, 3})
o7 = {0, 1, 3}
o7 : Flat of {w - x, w - y, w - z, x - y, x - z, y - z}
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i8 : assert(typeA(2, S) == A3_F2)
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i9 : assert(A3 === subArrangement flat(A3, {0,1,2,3,4,5}))
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i10 : B = arrangement("bracelet", S);
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i11 : B' = arrangement({w+x+y+z} | hyperplanes B)
o11 = {w + x + y + z, w, x, y, w + z, x + z, y + z, w + x + z, w + y + z, x + y + z}
o11 : Hyperplane Arrangement
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i12 : subArrangement flat(B', {0,1,2,6,8,9})
o12 = {w + x + y + z, w, x, y + z, w + y + z, x + y + z}
o12 : Hyperplane Arrangement
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i13 : subArrangement flat(B', {0,1,3,5,7,9})
o13 = {w + x + y + z, w, y, x + z, w + x + z, x + y + z}
o13 : Hyperplane Arrangement
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i14 : subArrangement flat(B', {0,2,3,4,7,8})
o14 = {w + x + y + z, x, y, w + z, w + x + z, w + y + z}
o14 : Hyperplane Arrangement
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