17.2 Quaternion algebra elements

Module: sage.algebras.quaternion_algebra_element

Class: QuaternionAlgebraElement

class QuaternionAlgebraElement
QuaternionAlgebraElement( self, H, x)

Create the element x of the quaternion algebra H.

Functions: characteristic_polynomial,$  $ charpoly,$  $ conjugate,$  $ minimal_polynomial,$  $ minpoly,$  $ reduced_norm,$  $ reduced_trace

reduced_trace( self)

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$ .

Special Functions: _cmp_

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