Compute the homogeneous (i.e., degree(FirstOrderDeformation) zero) deformations associated to a face F of the complex C.
The additional parameter I should be the Stanley-Reisner ideal of C and can be given to avoid computation of the Stanley-Reisner ideal if it is already known. Usually this is not necessary: Once I is computed it is stored in C.ideal, so deformationsFace(F,C,I) is equivalent to deformationsFace(F,C). Note also that all methods producing a complex from an ideal (like idealToComplex) store the ideal in C.ideal.
The deformations and C are stored in F.deform = C, deformations. Note that usually C is not ofComplex F.
i1 : R=QQ[x_0..x_4] o1 = R o1 : PolynomialRing |
i2 : I=ideal(x_0*x_1*x_2,x_3*x_4)
o2 = ideal (x x x , x x )
0 1 2 3 4
o2 : Ideal of R
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i3 : C1=idealToComplex I
o3 = 2: x x x x x x x x x x x x x x x x x x
0 1 3 0 2 3 1 2 3 0 1 4 0 2 4 1 2 4
o3 : complex of dim 2 embedded in dim 4 (printing facets)
equidimensional, simplicial, F-vector {1, 5, 9, 6, 0, 0}, Euler = 1
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i4 : F=C1.fc_0_0
o4 = x
0
o4 : face with 1 vertex
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i5 : deformationsFace(F,C1)
2 2
x x x x x x
0 0 0 0 0 0
o5 = {--, --, --, --, ----, ----}
x x x x x x x x
4 3 2 1 3 4 1 2
o5 : List
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i6 : F=C1.fc_0_1
o6 = x
1
o6 : face with 1 vertex
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i7 : deformationsFace(F,C1)
2 2
x x x x x x
1 1 1 1 1 1
o7 = {--, --, --, --, ----, ----}
x x x x x x x x
4 3 2 0 3 4 0 2
o7 : List
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i8 : F=C1.fc_1_0
o8 = x x
0 1
o8 : face with 2 vertices
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i9 : deformationsFace(F,C1)
x x
0 1
o9 = {----}
x x
3 4
o9 : List
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i10 : F=C1.fc_2_0
o10 = x x x
0 1 3
o10 : face with 3 vertices
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i11 : deformationsFace(F,C1)
o11 = {}
o11 : List
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i12 : R=QQ[x_0..x_4] o12 = R o12 : PolynomialRing |
i13 : I=ideal(x_0*x_1,x_1*x_2,x_2*x_3,x_3*x_4,x_4*x_0)
o13 = ideal (x x , x x , x x , x x , x x )
0 1 1 2 2 3 3 4 0 4
o13 : Ideal of R
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i14 : C1=idealToComplex I
o14 = 1: x x x x x x x x x x
0 2 0 3 1 3 1 4 2 4
o14 : complex of dim 1 embedded in dim 4 (printing facets)
equidimensional, simplicial, F-vector {1, 5, 5, 0, 0, 0}, Euler = -1
|
i15 : F=C1.fc_0_1
o15 = x
1
o15 : face with 1 vertex
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i16 : deformationsFace(F,C1)
2
x x x
1 1 1
o16 = {--, --, ----}
x x x x
4 3 3 4
o16 : List
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i17 : F=C1.fc_1_1
o17 = x x
0 3
o17 : face with 2 vertices
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i18 : deformationsFace(F,C1)
o18 = {}
o18 : List
|