GROUP THEORY TUTORIAL

Working with Quaternions

Although Mathematica provides a package for working with quaternions the Group Theory Package includes some basic functions for working with quaternions represented as a list.

{w,{x,y,z}}w + i x + j y + k z
Let's get started by loading the Group Theory Package
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We obtain the quaternion representation of the symmetry element C3z (three-fold rotation about the z-axis) by using GTGetQuaternion.
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GTQuaternionQ[q]gives True if q is a quaternion.
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a⋄bmultiplication of two quaternions a and b.
GTQInverse[quaternion]gives the inverse quaternion of a quaternion.
GTQConjugate[quaternion]gives the conjugate quaternion of a quaternion.
The multiplication of two quaternions can be calculated with ⋄
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Quaternions form a division ring hence for every quaternion there exists a multiplicative inverse element. Use GTQInverse...
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Obtain the conjugate quaternion by GTQConjugate...
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GTQAbs[quaternion]gives the absolute value of a quaternion.
GTQPolar[quaternion]gives the polar angle of a quaternion.
The absolute value of a quaternion can be calculated by GTQAbs...
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The polar angle of a quaternion can be calculated by GTQPolar...
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