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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 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.

IsDefinite(A) : AlgQuat -> BoolElt
IsIndefinite(A) : AlgQuat -> BoolElt
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.
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Version: V2.19 of Wed Apr 24 15:09:57 EST 2013