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 Hh, where H is the division ring of real Hamiltonians, otherwise A is indefinite.
A quaternion algebra A over Fq(X) is called definite if the place corresponding to the degree valuation is ramified.
Given a quaternion algebra A over a number field, Q or Fq(X) with q odd, returns true if and only if A is a (totally) definite or indefinite quaternion algebra, respectively.