Prime Numbers

5.6 Binary quadratic forms 241
so our restriction is not so severe. Another way of putting these restrictions
is to say we are only considering forms (a, b, c) withb 2 − 4ac < 0anda>0.
Note that these conditions then force c>0.
We say that a form (a, b, c) of negative discriminant is reduced if
−a 0.
This algorithm constructs a reduced quadratic form equivalent to (A, B, C).
1. [Replacement loop]
while(A >C or B>Aor B ≤−A) {
if(A >C) (A, B, C) =(C, −B,A); // ‘Type (1)’ move.
if(A ≤ C and (B >Aor B ≤−A)) {
Find B ∗ ,C ∗ such that the three conditions:
}
}
−A