# Test cases for Find_F6:




# Test cases:     f:= (x^3+3*a*x^2+b*x+c)^2/(x^2+2*a*x+d)^3;

# P4:= (x^2+1)^3/(13*x^4-22*x^2-15+8*x^3-40*x) ; (x^2+10*x+1)^3/(88*x^4+1218*x^3+398*x^2-10*x-15);    #### (x^2+1)^3/(x^3+x^2-1)^2;

# P5:= -125*(-4+4*x+5*x^2)^3/((9375*x^4-21250*x^3+8050*x^2-900*x+929)*(5*x-3)^2); -64*(115+44*x+4*x^2)^3/((1166129+1154800*x+417952*x^2+65920*x^3+3840*x^4)*(4*x+17)^2);

# P5:= (5+11*x)^3*(29+77*x)^3/((4963299*x^4+8800572*x^3+5836314*x^2+1718156*x+189499)*(4+11*x)^2);(program returns 3 maps for this example)

# a=0:  (x^3+3-3*x)^2/(x^2-11)^3; #P4 , -(-239+81*x^3-351*x^2+504*x)^2/(175+99*x^2-264*x)^3; #P5

# a=b=0: (x^3+3)^2/(x^2-11)^3; #P4,  -(-1028+6591*x^3-10647*x^2+5733*x)^2/(538+1859*x^2-2002*x)^3; # P5

# c=0: x^2*(x^2+6*x-3)^2/(x^2+4*x-11)^3; # P4, -(1/27)*(-4+27*x^2)^2/(2+18*x+33*x^2)^3; # P5

# d=0: (x^3+6*x^2-3*x+5)^2/(x^3*(x+4)^3); # P4, (-7083+24531*x-28392*x^2+10985*x^3)^2/(-43+52*x)^3; #P5