9.3.4.1 QuaternionOrderElement Objects

class QuaternionOrderElement
QuaternionOrderElement( A, x)

Create the element x of the quaternion order A.

Instances of class QuaternionOrderElement have the following methods (in addition to inherited methods and special methods):

characteristic_polynomial,$  $ charpoly,$  $ conjugate,$  $ minimal_polynomial,$  $ minpoly,$  $ reduced_norm,$  $ reduced_trace,$  $ vector

Further documentation:

reduced_trace( )

Return the reduced trace of this element.

Note: In a quaternion algebra $ A$ , every element $ x$ is quadratic over the center, thus $ x^2 = \Tr (x)*x - \Nr (x)$ , so we solve for a linear relation $ (1,-\Tr (x),\Nr (x))$ among $ [x^2, x, 1]$ for the reduced trace of $ x$ .

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