Predicates on Algebras

A quaternion algebra A over a number field F with [F:Q]=h is definite (or totally definite) if F is totally real and A tensor _Q R isomorphic to H^h, where H is the division ring of real Hamiltonians, otherwise A is indefinite.

A quaternion algebra A over F_q(X) is called definite if the place corresponding to the degree valuation is ramified.

IsDefinite(A) : AlgQuat -> BoolElt

IsIndefinite(A) : AlgQuat -> BoolElt

Given a quaternion algebra A over a number field, Q or F_q(X) with q odd, returns true if and only if A is a (totally) definite or indefinite quaternion algebra, respectively.