Let formula 57 be the discriminants of formula 58. There are explicit congruence conditions that give the set of fundamental discriminants. It can also be stated in terms of discriminants. Thus, all such integers are referred to as "discriminants" in this theory. In that paper, Cayley used it for in the theory of resultants and discriminants. Also, in many practical cases linear discriminants are not suitable. In summary, the same information can be deduced from these two discriminants. All these discriminants may be defined by the formula of . Their discriminants show that these curves are hyperbolas. The set of discriminants of quadratic fields is exactly the set of fundamental discriminants. As for the conic sections there are two discriminants that may be naturally defined. Two quadratic forms, and thus two discriminants may be associated to a conic section. Pick discriminants "D" in sequence of increasing "h"("D"). Fundamental discriminants may also be characterized by their factorization into positive and negative prime powers. Unlike K-d trees, in a relaxed K-d tree, the discriminants in each node are arbitrary.