OxAsirDebug = 0$
OxVlist = [x,y,z]$

def ox_ptod(F) {
  extern OxVlist;
  extern OxAsirDebug;
  if (OxAsirDebug != 0) { print(["ox_ptod:", F, OxVlist]); } 
  if (type(F) == 4) return(map(ox_ptod,F));
  else if (type(F) == 2) return(dp_ptod(F,OxVlist));
  else return(F);
}

def ox_dtop(F) {
  extern OxVlist;
  extern OxAsirDebug;
  if (OxAsirDebug != 0) { print(["ox_dtop:", F, OxVlist]); } 
  if (type(F) == 4) return(map(ox_dtop,F));
  else if (type(F) == 9) return(dp_dtop(F,OxVlist));
  else return(F);
}

/***  From gbhg3/Int/solv1.asir ***/
/* solv1.asir  1999, 1/28.
   Finding rational number roots of systems of polynomials.
   Make a substitution.
*/

def sm1_solv1a(F) {
  V = var(F);
  if (deg(F,V) != 1) return([]);
  return([V,red(-coef(F,0)/coef(F,1))]);
}


def sm1_solv1(L,V) {
  N = length(L);
  Ans = newvect(length(V));
  for(J=0; J<length(V); J++) {
     Ans[J] = "?";
  }
  for (I=0; I<N; I++) {
    S = sm1_solv1a(L[I]);
    if (S == []) return([]);
    for (J=0; J<length(V); J++) {
      if (V[J] == S[0]) {
        Ans[J] = S[1];
      }
    }
  }
  return(Ans);
}

def sm1_rationalRoots(F,V) {
  F = primadec(F,V); 
  print(F);
  N = length(F);
  Ans = [ ];
  for (I=0; I<N; I++) {
    P = F[I][1];  /* associated prime */
    R = sm1_solv1(P,V);
    if (R != []) {
      Ans = append(Ans,[R]);
    }
  }
  return(Ans);
}

/* sm1_rationalRoots([x^2+y-2,x^2-1/9],[x,y]); */

def sm1_inner00(A,B) {
  P = 0;
  for (I=0; I<size(A)[0]; I++) {
    P = P + A[I]*B[I];
  }
  return(red(P));
}

def sm1_rationalRoots2(F,V,W) {
  print([F,V,W]);
  print(type(W[0]));
  R = sm1_rationalRoots(F,V);
  Ans = [ ];
  Ans2 = [ ];
  W = newvect(length(W),W);
  for (I=0; I<length(R); I++) {
     T = sm1_inner00(W,R[I]);
     if (dn(T) == 1) {
        Ans = append(Ans,[T]);
        Ans2 = append(Ans2,[R[I]]);
     }
  }
  print([Ans,Ans2]);
  return(Ans);
}

/* W is a weight vector */
/* sm1_rationalRoots2([(z-3)*(z^2+z+1),x^2+y-2,x^2-1/9],[x,y,z],[9,9,1]); */

def sm1_ptozp_subst(F,X,V) {
  /*  sm1_ptozp_subst(x*y-1,x,[1,2]);  ptozp(subst(x*y,x,1/2)) ;  */
  A=ptozp(subst(F,X,V[0]/V[1]));
  return(A);
}

/* A =  ((1/2)*x^2+(1/4)*x+1)/((1/5)*x^4+x^8);
   B= sm1_rat2plist( A); 
   print(red(A-B[0]/B[1]));
*/
def sm1_rat2plist(T) {
  T = red(T);
  T1 = nm(T); T1a = ptozp(T1); 
  T1b = red(T1a/T1);
  T2 = dn(T); 
  return([T1a*dn(T1b),T2*nm(T1b)]);
}

def sm1_rat2plist2(TT) {
  T = red(TT[0]/TT[1]);
  T1 = nm(T); T1a = ptozp(T1); 
  T1b = red(T1a/T1);
  T2 = dn(T); 
  return([T1a*dn(T1b),T2*nm(T1b)]);
}

  
  



end$