#This file contains all the data needed to show $\pi_{ce}(B)$ is at most 0.60680 (see Section
#2.5.2). The calculation can be verified using the program "HypercubeEdgeDensityChecker".

#This file follows a similar format to those created for "DensityChecker". It has been
#commented to highlight the differences.

Program : HypercubeEdgeDensityChecker

#Instead of setting the order we instead the dimension of the hypercubes.
#The current implementation of HypercubeEdgeDensityChecker can only handle subcubes of
#dimension at most 4.
Dimension of subcubes H : 3

#Description of the forbidden family $\mathcal{F}$. Note that a red-blue edge-coloured 
#hypercube is represented by a number (indicating its *dimension*, n say) folowed by a colon
#then the set of its blue edges. We assume its vertices are labelled 0,1,...,2^n-1 such that
#ij is an edge if and only if i differs from j by precisely one digit in their binary
#representations. The current implementation of HypercubeEdgeDensityChecker can only read
#edge sets of hypercubes that have at most 8 vertices.
Number of forbidden hypercubes : 1
Forbidden hypercubes           :
2 : {01, 02, 13, 23}

Number of terms : 5


--- Term 1 ---

#We need only define the dimension of the type. The colouring  of its edges can be determined
#from the flags (see terms 2 and 4 for an example).
Dimension of type : 0

#The common dimension of the flags.
#Note that "dimension of flags"<=("dimension of type" + "dimension of subcubes H")/2 must
#hold. The current implementation of HypercubeEdgeDensityChecker can only handle flags of
#dimension at most 3.
Dimension of flags : 1

Number of flags    : 2
Matrix dimension   : 2

#The sets of blue coloured edges of the flags. (The dimension of the flags has already been
#defined.) The labelled vertices of the flag (which describe the type) are the vertices
#0,...,2^"dimension of type"-1. In this case there is only one labelled vertex: the vertex 0.
Flags :
F1 : {}
F2 : {01}

Basis :
B1 : (F1)
B2 : (F2)

Matrix :
 31114490449/1099511627776 -20162249079/1099511627776
-20162249079/1099511627776  13065175809/1099511627776


--- Term 2 ---

Dimension of type  : 1
Dimension of flags : 2
Number of flags    : 8
Matrix dimension   : 6

#The dimension of the type is 1, hence the labelled vertices are 0 and 1. By looking at flag
#F1 we can determine the type has no blue edges. 

Flags :
F1 : {}
F2 : {02}
F3 : {13}
F4 : {02, 13}
F5 : {23}
F6 : {02, 23}
F7 : {13, 23}
F8 : {02, 13, 23}

Basis :
B1 : (F1)
B2 : (F2)+(F3)
B3 : (F4)
B4 : (F5)
B5 : (F6)+(F7)
B6 : (F8)

Matrix :
636062076225/1099511627776 -498128397975/1099511627776 -675463495365/1099511627776 
292464059850/1099511627776 -245845746495/1099511627776 97873495200/1099511627776 
-498128397975/1099511627776 451385939434/1099511627776 555421434539/1099511627776 
-194531285627/1099511627776 228465878224/1099511627776 -127874467004/1099511627776 
-675463495365/1099511627776 555421434539/1099511627776 728710200985/1099511627776 
-295693234762/1099511627776 276576481667/1099511627776 -126035036224/1099511627776 
292464059850/1099511627776 -194531285627/1099511627776 -295693234762/1099511627776 
153911093381/1099511627776 -92804732257/1099511627776 16154468012/1099511627776 
-245845746495/1099511627776 228465878224/1099511627776 276576481667/1099511627776 
-92804732257/1099511627776 116092932698/1099511627776 -67866927364/1099511627776 
97873495200/1099511627776 -127874467004/1099511627776 -126035036224/1099511627776 
16154468012/1099511627776 -67866927364/1099511627776 57881051024/1099511627776


--- Term 3 ---

Dimension of type  : 1
Dimension of flags : 2
Number of flags    : 4
Matrix dimension   : 2

Flags :
F1 : {02}
F2 : {13}
F3 : {02, 23}
F4 : {13, 23}

Basis :
B1 : (F2)-(F1)
B2 : (F4)-(F3)

Matrix :
1691724239569/1099511627776 982367351966/1099511627776
 982367351966/1099511627776 824752243613/1099511627776


--- Term 4 ---

Dimension of type  : 1
Dimension of flags : 2
Number of flags    : 7
Matrix dimension   : 5

#The dimension of the type is 1, hence the labelled vertices are 0 and 1. By looking at flag
#F1 we can determine the type's blue edge set is {01}.

Flags :
F1 : {01}
F2 : {01, 02}
F3 : {01, 13}
F4 : {01, 02, 13}
F5 : {01, 23}
F6 : {01, 02, 23}
F7 : {01, 13, 23}

Basis :
B1 : (F1)
B2 : (F2)+(F3)
B3 : (F4)
B4 : (F5)
B5 : (F6)+(F7)

Matrix :
1834762357156/1099511627776 310923797962/1099511627776 -1328810044806/1099511627776 
18161591872/1099511627776 430023908980/1099511627776 310923797962/1099511627776 
52699848449/1099511627776 -225068391567/1099511627776 4575222504/1099511627776 
72784706850/1099511627776 -1328810044806/1099511627776 -225068391567/1099511627776 
963728338725/1099511627776 4367497860/1099511627776 -312474146742/1099511627776 
18161591872/1099511627776 4575222504/1099511627776 4367497860/1099511627776 
227626737860/1099511627776 -9156091576/1099511627776 430023908980/1099511627776 
72784706850/1099511627776 -312474146742/1099511627776 -9156091576/1099511627776 
101578160276/1099511627776


--- Term 5 ---

Dimension of type  : 1
Dimension of flags : 2
Number of flags    : 4
Matrix dimension   : 2

Flags :
F1 : {01, 02}
F2 : {01, 13}
F3 : {01, 02, 23}
F4 : {01, 13, 23}

Basis :
B1 : (F2)-(F1)
B2 : (F4)-(F3)

Matrix :
888873725601/1099511627776 322787721171/1099511627776
322787721171/1099511627776 150140915450/1099511627776

