MODE R = REAL;
MODE S = STRUCT(R c, [~]R m);
OP * = (R s, []R r)[]R: (
      INT n = UPB r; [n]R t; FOR j TO n DO t[j] := s*r[j] OD; t);
PROC c = ([]R a)S: (INT n = UPB a;
  S bt = (R p:=1, b := 0; FOR j TO n DO p *:= a[j]*j; b +:= a[j]**2 OD;
             (1/p, ([n]R t; FOR j TO n DO t[j] := 1/(p*a[j]*(n+1)) OD; t)));
  PROC r = (R b, INT j)S: (b<0 | (0, ~) | (j=0
      | R t = b**n; (t*c OF bt, b*t*m OF bt)
      | S s0 = r(b, j-1), s1 = r(b - a[j], j-1); (c OF s1 = 0 | s0 |
         (c OF s0 - c OF s1, ([n]R t; FOR k TO n
             DO t[k] := (m OF s0)[k] - (m OF s1)[k] OD;
             t[j] -:= c OF s1; t))))); r(1, n));

PROC cn = ([]R a)S: (INT n = UPB a; INT q := 0;
  FOR j TO n DO (a[j] < 0 | q := j) OD;
  IF q = 0 THEN c(a)
  ELSE [n]R na;
       FOR j TO n DO na[j] := (j=q | a[j]/(a[j]-1) | a[j]/(1-a[q])) OD;
       S s = cn(na);
       (c OF s, ([n]R nm := m OF s; nm[q] := c OF s - (m OF s)[q]; nm))
  FI);

(0=0 | print(("S= ", cn( (1, 1/3, 1/4) ))) |
 
    MODE TC =  STRUCT([~]R t, S a);
    PROC ts = (R t)TC: #0<t<1#
        ((t, 1), (1 - t/2, (1/2 - t/3, 1/2 - t/2 + t*t/6)));
    PROC tc = (R u, v)TC: #0<u<1, 0<u<1, u+v<1#
         ((1, u, v), (1 - u/2 - v/2,
            (1/2 - u/3 - v/3, 1/2 - u/6 - v/3, 1/2 - u/2 + u*u/6)));
    []TC t = (
     ((1), (1, (1/2))),
     ((2, 2), (1/8, (1/48, 1/48))),
     ((2, -2), (7/8, (19/48, 23/48))),
     ((-2, 2), (7/8, (23/48, 19/48))),
     ((-2, -2), (1, (1/2, 1/2))),
     ((1/7, 8/7), (13/16, (19/48, 127/384))),
     ((-1/6, 4/3), (13/16, (5/12, 127/384))),
     ((4, -2), (1/2, (13/96, 7/24))),
     ((1, 1, 1), (1/6, (1/24, 1/24, 1/24))),
     ts(1/3), ts(1/25), ts(1/60), ts(1/100),
     tc(1/10, 3/10));

FOR j TO UPB t DO []R tc = t OF t[j];
   FOR k TO UPB tc DO print(tc[k]) OD; print(newline);
     (S s = cn(tc); print(("c = ", c OF s));
     FOR k TO UPB m OF s DO print((m OF s)[k]) OD; print(newline);
     IF (ABS (c OF s - c OF a OF  t[j])) > 1.e-14
       THEN print(("Foul c: ", j, c OF s,  c OF a OF  t[j], newline)) FI;
     FOR k TO UPB m OF s DO IF ABS ((m OF s)[k] - (m OF a OF t[j])[k]) > 1.e-13
       THEN print(("Foul m: ", j, k, (m OF s)[k], (m OF a OF t[j])[k], newline))FI OD) OD)