vb -- Option whether to print intermediate results.

i1 : R=QQ[y_0..y_2];

i2 : I=ideal(y_0^2 + 3*3*43*y_1^2 -2*2*2*2*11*41*y_2^2)

            2       2        2
o2 = ideal(y  + 387y  - 7216y )
            0       1        2

o2 : Ideal of R

i3 : p=rationalPointOnConic(I,vb=>1)
(Input: 1548, ,-17291729664)
(a,b,c) = (1,43,-451)
(a,b,c) = (1,43,-451)
(R1,R2,R2) = (298,8,0)
(alpha,beta,gamma) = (-153,43,2)
(a,b,c) = (1,-13,43)
(R1,R2,R2) = (20,3,0)
(alpha,beta,gamma) = (20,-13,3)
(a,b,c) = (1,1,-13)
(R1,R2,R2) = (5,0,0)
(alpha,beta,gamma) = (5,1,1)
(a,b,c) = (1,1,-2)
(R1,R2,R2) = (1,0,0)
(alpha,beta,gamma) = (-1,1,1)

o3 = | 502 50 -13 |

              1        3
o3 : Matrix QQ  <--- QQ