library(MASS)
# vertices are extended by the constant 1 
dataVertices=read.table("stand-imset4-vertices.txt",header=FALSE,sep=",")
# the last coefficient is the negative of the right hand side value of the equality
dataEqualities=read.table("stand-imset4-equalities.txt",header=FALSE,sep=",")
# 185 x 12 matrix
V=data.matrix(dataVertices)
# 154 x 12 matrix
E=data.matrix(dataEqualities)
# 185 x 154 matrix - A[i,j] is 0 if vertex satisfies equality
A=V %*% t(E)
# 185 x 185 matrix - B[i1,i2]=1 if i1 and i2 are neighbours
B=matrix(0,nrow=nrow(A),ncol=nrow(A))
# 185 lists of neighbours 
NB=vector(mode="list",length=nrow(A))
for (i1 in 1:(nrow(A)-1)){
  for (i2 in (i1+1):nrow(A)){
    # print(c("i1=",i1,", i2=",i2),quote=FALSE)
    J=c()
    for (j in 1:ncol(A))
      if ((A[i1,j]==0) & (A[i2,j]==0)) J=append(J,j)
    # Now, J contains indexes of all inequalities satisfied by both i1 and i2
    # print(c("J=",J),quote=FALSE)
    if (length(J)>1){
      I=c()
      for (i in 1:nrow(A)){
        all=TRUE
        for (j in 1:length(J)){
          all=all & (A[i,J[j]]==0)
          if (!all) break
        }
        if (all) I=append(I,i)
      }
      # Now, I contains vertices that satisfy all inequalities from J
      # print(c("I=",I),quote=FALSE)
      # If there exactly two vertices in I then they are geometric neighbours.
      if (length(I)==2){
        B[i1,i2]=1
        B[i2,i1]=1
        NB[[i1]]=append(NB[[i1]],i2)
        NB[[i2]]=append(NB[[i2]],i1)
      }else{
        B[i1,i2]=0
        B[i2,i1]=0
      }
    }else{
      B[i1,i2]=0
      B[i2,i1]=0
    }
  }
}
# write.matrix(t(E), file="stand-imset4-equalities-transposed.txt", sep = ",")
write.matrix(A,file="stand-imset4-vertex-satisfies-equality.txt", sep = ",")
write.matrix(B, file = "stand-imset4-neigbourhood-matrix.txt", sep = ",")
write.matrix(NB, file = "stand-imset4-neigbourhood-list.txt", sep = ",")