31.4 Quaternion order elements

Module: sage.algebras.quaternion_order_element

Quaternion order elements

Author: David Kohel, 2005-09

Class: QuaternionOrderElement

class QuaternionOrderElement
QuaternionOrderElement( self, A, x, [check=True])

Create the element x of the quaternion order A.

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

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: __eq__,$ \,$ __init__

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