Bland's Finite Pivoting Method is often used as the standard pivoting rule in simplical optimization for linear programs. However, some literature conflicts - for maximization, some state that only the denominator (the coefficient in the tableau) need be positive, while others (see step 9) suggest that only the ratio need be positive. The competing possabilities:
$\forall const, coeff : \mathbb{Q} | coeff > 0. \frac{const}{coeff}$
vs.
$\forall const, coeff : \mathbb{Q} | \frac{const}{coeff} > 0. \frac{const} {coeff}$
I could see how the denominator's restriction could be more logical; as it avoids division by zero. However, I still can't rule out the other case, due to the number of books and tutorials I've seen that abuse this edge case.
Edit:
I am actually entirely incorrect about this - this ratio is canonical for all simplex methods, and Bland's rule is merely oriented on the assumption of indicies identifying the row and columns of coefficients in the tableau.
I've found an authoritative source that explicitly show's that the second option is the correct one - Linear Programming and Extensions, by Dantzig (the original pioneer of simplex method):
$\forall const, coeff : \mathbb{Q} | coeff > 0, const \ge 0. \frac{const}{coeff}$
Edit:
Again as stated in the question - this rule is for all simplex methods - this measure captures the amount of allowable growth until breaking the positivity restriction on the entry variable you pivot over - such that this is the distance increased in the matroid.