Compute the faces of a simplicial Complex C. The result is a List L. The j-th entry L#j of L is a list of the faces of C of dimension j.
If the second argument d is specificed then a list of the faces of dimension d is returned.
i1 : K=QQ; |
i2 : R=K[x_0..x_4] o2 = R o2 : PolynomialRing |
i3 : I=ideal(x_0*x_1,x_1*x_2,x_2*x_3,x_3*x_4,x_4*x_0)
o3 = ideal (x x , x x , x x , x x , x x )
0 1 1 2 2 3 3 4 0 4
o3 : Ideal of R
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i4 : C=idealToComplex I
o4 = {x x , x x , x x , x x , x x }
2 4 0 3 0 2 1 3 1 4
o4 : complex with 5 facets on the vertices x x x x x
0 1 2 3 4
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i5 : faces(C)
o5 = {{{}}, {x , x , x , x , x }, {x x , x x , x x , x x , x x
1 0 3 2 4 1 4 1 3 2 4 0 2 0 3
------------------------------------------------------------------------
}, {}, {}, {}}
o5 : List
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i6 : K=QQ; |
i7 : R=K[x_0..x_4] o7 = R o7 : PolynomialRing |
i8 : I=ideal(x_0*x_1,x_2*x_3*x_4)
o8 = ideal (x x , x x x )
0 1 2 3 4
o8 : Ideal of R
|
i9 : C=idealToComplex I
o9 = {x x x , x x x , x x x , x x x , x x x , x x x }
0 2 3 1 2 3 1 3 4 1 2 4 0 3 4 0 2 4
o9 : complex with 6 facets on the vertices x x x x x
0 1 2 3 4
|
i10 : faces(C)
o10 = {{{}}, {x , x , x , x , x }, {x x , x x , x x , x x , x
4 1 2 0 3 0 4 2 4 2 3 3 4 1
-----------------------------------------------------------------------
x , x x , x x , x x , x x }, {x x x , x x x , x x x ,
2 1 3 0 2 0 3 1 4 0 2 4 0 3 4 1 2 4
-----------------------------------------------------------------------
x x x , x x x , x x x }, {}, {}}
1 2 3 1 3 4 0 2 3
o10 : List
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i11 : faces(C,1)
o11 = {x x , x x , x x , x x , x x , x x , x x , x x , x x
0 4 2 4 2 3 3 4 1 2 1 3 0 2 0 3 1 4
-----------------------------------------------------------------------
}
o11 : List
|