 QUATERNION ALGEBRAS - Maple Application Center
Application Center Applications QUATERNION ALGEBRAS

## QUATERNION ALGEBRAS This Application runs in Maple. Don't have Maple? No problem!
This worksheet presents some procedures in order to make computations in a quaternion algebra B defined over the field of rational numbers Q . Quaternion algebra means something more general than the algebra of Hamilton's quaternions (for which there exists already a Maple package) . To give a quaternion algebra B is equivalent to give a pair (a,b) of non-zero rational numbers so that B is defined as the Q-algebra of basis {1,i,j,k} where the elements i,j of B verify the relations i^2=a, j^2=b, ij=-ji and k=ij. It can be very useful to define new procedures ProdQuat, InvQ, TrQ, NormQ in Maple which return the product of two elements of B, the inverse of a non-zero-element of B, the reduced trace of an element of B and the reduced norm of an element of B. Moreover, since the places of Q where B is ramified determine B up to isomorphism as an algebra, it can be very useful to give a procedure Discriminant which computes the reduced discriminant of a quaternion algebra B=(a,b).

#### Application Details

Publish Date: November 02, 2007
Created In: Maple 10
Language: English

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