/* cloitrem */
define t(x,m){
auto f

   f=int((m+1)*x,m)
   g=f%2
   if(g==0){
     return(f/2)
   }else{
     return((3*f+1)/2)
   }
}

/* This determines the matrix Q(d) for the d-branched mapping F_m.
   Here d=2m or ma, according as m is even or odd.
 */
define matrixq(m){
auto i,j,mm[],d,g,r
 if(m%2==0){
   d=2*m
 }else{
   d=m
 }
 for(i=0;i<m;i++){
   if(i%2==0){
     mm[i]=m+1
   }else{
     mm[i]=3*(m+1)
   }
 }
 for(i=m;i<d;i++){
   if(i%2==0){
     mm[i]=3*(m+1)
   }else{
     mm[i]=m+1
   }
 }
    print "\n"
 for(i=0;i<d;i++){
    for (j=0;j<d;j++){
       r=t(i,m)
       g=gcd(mm[i],d)
       if((r-j)%g==0){
         if(d==g){
            print "1 "
         }else{
            print 1,"/",d/g," "
         }
       }else{
         print "0 "
       }
    }
    print "\n"
 }
}

/*  This function prints the F_m function as a 2m or m-branched mapping
 * in two ways, the second being in the form F_m(x)=int(m[i]x/d)+x[i] if x (mod d) = i.
 */
define function(m){
auto i,a,b,s,x,y,r,d

   if(m%2==0){
      s=2*m
   }else{
      s=m
   }
   for(i=0;i<s;i++){
     x=t(i,m)
     y=t(i+s,m)
     a=y-x
     b=(s+i)*x-i*y
     d=a*i
     r=int(d,s)
     c=(d+b)/s-r
     if(b==0){
        print "T(x)=",a,"x/",s,"=int(",a,"x/",s,")+",c,"\n"
     }
     if(b>0){
        print "T(x)=(",a,"x+",b,")/",s,"=int(",a,"x/",s,")+",c,"\n"
     }
     if(b<0){
        print "T(x)=(",a,"x",b,")/",s,"=int(",a,"x/",s,")+",c,"\n"
     }
   }
}

/* traj(x,m,n) prints the first n iterates of x under t(x,m) */
define traj(x,m,n){
   auto i
   for(i=0;i<n;i++){
     print x,"\n"
     x=t(x,m)
   }
   return
}