#  Test cases for Find_F4:

#NN.///  f:= (x-a)^3*(x-p3)/(x^2+b1*x+b0)^2.

###  p3 at infinity: (i.e input comes from poles of f only.)

#  all non-zero:  P4:= (x+6)^3/(x^4-5*x^3+19*x^2+132*x+232);  P5:= (2*x-5)*(-29+12*x)^3/(3712*x^4-36064*x^3+131356*x^2-212590*x+129001);

#  a=0:           P4:= x^3/(x^4-3*x^3+14*x^2-20*x+25);        P5:= (3*x+1)/(17+195*x+936*x^2+2160*x^3+2025*x^4);  # (a = infty in this case)

#  b1=0:          P4:= (x-3)^3/(x^4+x^2-2+x^3+27*x);          P5:= (2*(2*x+1))*(3*x+1)^3/(-7-70*x^2-38*x+8*x^4-38*x^3);

#  b0=0:          P4:= (x-3)^3/(x^4-x^3-8*x^2+27*x-27);       P5:= (2*(2*x-3))*(-5+3*x)^3/(1709*x^2-1846*x+746-702*x^3+108*x^4);

# a= b1= 0:       P4:= x^3/(x^4-6*x^2+9+x^3);                 P5:= (2*x-1)/(3+192*x^2-46*x+144*x^4-288*x^3);

# p3=0:           P5:= 2*(x-2)^3*x/(3*x^4-14*x^3+19*x^2-10*x+9);



### pole of f is at infinity (i.e input has the form (x-p3)*P3):    P4:=  -(x-3)^3*(4*x-3)/(x*(35*x^2-98*x+171)) ;

# all non-zero:   P4:= (x-2)^3*(x-8)/(-16*x^3+77*x^2-120*x+2*x^4+128);        P5:= (27*(5+9*x))*(2*x+1)^3/(7128*x^4+17388*x^3+16191*x^2+6819*x+1096);

# a=0:            P4:= (x-3)*x^3/(-5*x^3-3*x^2+4*x+4+2*x^4);                  P5:= -(4+3*x)/(32*x^4+208*x^3+498*x^2+517*x+196);