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 |
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 |
i4 : F=C1.fc_0_0 o4 = x 0 o4 : face with 1 vertex |
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 |
i6 : F=C1.fc_0_1 o6 = x 1 o6 : face with 1 vertex |
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 |
i8 : F=C1.fc_1_0 o8 = x x 0 1 o8 : face with 2 vertices |
i9 : deformationsFace(F,C1) x x 0 1 o9 = {----} x x 3 4 o9 : List |
i10 : F=C1.fc_2_0 o10 = x x x 0 1 3 o10 : face with 3 vertices |
i11 : deformationsFace(F,C1) o11 = {} o11 : List |
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 |
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 |
i16 : deformationsFace(F,C1) 2 x x x 1 1 1 o16 = {--, --, ----} x x x x 4 3 3 4 o16 : List |
i17 : F=C1.fc_1_1 o17 = x x 0 3 o17 : face with 2 vertices |
i18 : deformationsFace(F,C1) o18 = {} o18 : List |