diff --git a/RF_NTT.R b/RF_NTT.R
deleted file mode 100644
index 4c705dd..0000000
--- a/RF_NTT.R
+++ /dev/null
@@ -1,142 +0,0 @@
-library("ape")
-library("phangorn")
-library("readtext")
-
-#Beta function
-Beta=function(m){
-  if(m<0){return(1)}
-  return(dfactorial(2*m+1))
-}
-
-# the function for computing the number of internal edges
-internaledges <- function(tree,ntip){
-  intedges=array(0,c(1,ntip-1))
-  edges=tree$edge
-  for (i in (2*ntip-1):(ntip+1)) {
-    children=which(edges[,1]==i)
-    child1=edges[children[1],2]
-    child2=edges[children[2],2]
-    if(child1 <= ntip&child2 <= ntip){intedges[i-ntip]=0}
-    else if(child1<= ntip & child2 > ntip){intedges[i-ntip]=intedges[child2-ntip]+1}
-    else if(child2<= ntip & child1 > ntip){intedges[i-ntip]=intedges[child1-ntip]+1}
-    else {intedges[i-ntip]=intedges[child2-ntip]+intedges[child1-ntip]+2}
-  }
-  return(intedges)
-}
-
-# the function for computing the number of internal children
-internalchildren <- function(tree,v,ntip){
-  edges=tree$edge
-  children=which(edges[,1]==v)
-  child1=edges[children[1],2]
-  child2=edges[children[2],2]
-  if(child1 > ntip & child2 > ntip){result=c(2,child1,child2)}
-  else if(child1 > ntip & child2 <= ntip){result=c(1,child1)}
-  else if(child2 > ntip & child1 <= ntip){result=c(1,child2)}
-  else {result=0}
-  return(result)
-}
-
-RF_Convolve=function(tree,n){
-  ntip=n-1
-  N=tree$Nnode
-  R=rep(list(matrix(0,(ntip-1),(ntip-1))),N)
-  edges=internaledges(tree,ntip)
-  B=c()
-  for (k in 0:(n-2)) {
-    B[k+1]=Beta(k)        
-  }
-  for (v in N:1) {
-    intchild=internalchildren(tree,v+ntip,ntip)
-    intedges=edges[v]
-    if(intchild[1]==0){
-      R[[v]][1,1]=1
-    }
-    else if(intchild[1]==1){
-      Rchild=R[[intchild[2]-ntip]]
-      R[[v]][1,intedges+1]=1
-      R[[v]][2:(ntip-1),1]=rowSums(t(t(Rchild[1:(ntip-2),])*B[1:(ntip-1)]))
-      R[[v]][2:(ntip-1),2:(ntip-1)]=Rchild[2:(ntip-1),1:((ntip-2))]
-    }
-    else {
-      Rchild1=R[[intchild[2]-ntip]]
-      Rchild2=R[[intchild[3]-ntip]]
-      R[[v]][1,intedges+1]=1
-      R[[v]][3,1]=sum(t(t(Rchild1[1,])*B[1:(ntip-1)]))*sum(t(t(Rchild2[1,])*B[1:(ntip-1)]))
-      for (s in 4:(ntip-1)) {
-        R[[v]][s,1]=sum(rowSums(t(t(Rchild1[1:(s-2),])*B[1:(ntip-1)]))*rowSums(t(t(Rchild2[(s-2):1,])*B[1:(ntip-1)])))
-      }
-      sum1=matrix(0,(ntip-2),(ntip-2))
-      sum1[1,1:(ntip-2)]=sum(t(t(Rchild1[1,])*B[1:(ntip-1)]))*Rchild2[1,1:(ntip-2)]
-      for (s in 3:(ntip-1)) {
-        temp=colSums(rowSums(t(t(Rchild1[1:(s-1),])*B[1:(ntip-1)]))*Rchild2[(s-1):1,1:(ntip-2)])
-        sum1[s-1,1:(ntip-2)]=temp
-      }
-      sum2=matrix(0,(ntip-2),(ntip-2))
-      sum2[1,1:(ntip-2)]=sum(t(t(Rchild2[1,])*B[1:(ntip-1)]))*Rchild1[1,1:(ntip-2)]
-      for (s in 3:(ntip-1)) {
-        temp=colSums(rowSums(t(t(Rchild2[1:(s-1),])*B[1:(ntip-1)]))*Rchild1[(s-1):1,1:(ntip-2)])
-        sum2[s-1,1:(ntip-2)]=temp
-      }
-      
-      R1=Rchild1[1:(ntip-1),1:(ntip-3)]
-      #R1aug=numeric(nrow(R1)*(2*ncol(R1)-1))
-      R1aug=numeric(2048)
-      t=1
-      for(i in 1:ncol(R1)){
-        R1aug[t:(t+nrow(R1)-1)]=R1[,i]
-        t=t+3*nrow(R1)
-      }
-      R2=Rchild2[1:(ntip-1),1:(ntip-3)]
-      #R2aug=numeric(nrow(R2)*(2*ncol(R2)-1))
-      R2aug=numeric(2048)
-      t=1
-      for(i in 1:ncol(R2)){
-        R2aug[t:(t+nrow(R2)-1)]=R2[,i]
-        t=t+3*nrow(R2)
-      }
-    
-      write(R1aug,"testNTT.txt",ncolumns=2048,append = TRUE)
-      write(R2aug,"testNTT.txt",ncolumns=2048,append = TRUE)
-     #read the output of mathematica
-      system("/Applications/Mathematica.app/Contents/MacOS/MathKernel -script  /Users/maryam/Desktop/NTT_fromR.wls")
-      U=as.matrix(read.csv("/Users/maryam/Google Drive/Research/RF_improvment/outNTT.txt",header = FALSE, sep="'", quote=""))
-      Matc=ceiling(length(R1aug)/(3*nrow(R1)))
-      sum3=matrix(c(U,numeric(Matc*3*nrow(R1)-length(R1aug))),nrow=3*nrow(R1))[1:nrow(R1),1:ncol(R1)]
-      sum3=cbind(array(0, dim=c(nrow(R1)-1,1)),sum3[2:nrow(R1),])
-      R[[v]][2:(ntip-1),2:(ntip-1)]=sum1+sum2+sum3
-      file.remove("testNTT.txt")
-    }
-  }
-  
-  return(R)
-}
-
-
-
-#==========================================
-RsT=function(R,n,s){
-  B=c()
-  for (k in 0:(n-2)) {
-    B[k+1]=Beta(k)        
-  }
-  rst =sum(t(t(R[[1]][s+1,1:(n-2-s)])*B[1:(n-2-s)]))
-  return(rst)
-}
-
-#Compute the value of q_m(T)
-qmT=function(R,n,m){
-  qmt=0
-  for (s in m:(n-3)) {
-    rst=RsT(R,n,s)
-    qmt=qmt+(factorial(s)/(factorial(m)*factorial(s-m)))*rst*(-1)^(s-m)
-  }
-  return(qmt)
-}
-
-polynomial=function(tree,n){
-  R=RF_Convolve(tree,n)
-  for (i in seq(0,2*(n-3),2)) {
-    print(qmT(R,n,n-3-(i/2)))
-  }
-}