Wolfram Function Repository
Instantuse addon functions for the Wolfram Language
Function Repository Resource:
Represent a quaternion object
ResourceFunction["Quaternion"][a,b,c,d] returns the quaternion number a+bⅈ+cⅉ+d𝕜. 
Get the quaternion 1+2ⅈ+3ⅉ+4𝕜:
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Add two quaternions:
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Use NonCommutativeMultiply (**) to multiply quaternions:
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This multiplication is noncommutative:
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In the conjugate of a quaternion, all the signs of the nonreal components are reversed:
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The sign of a quaternion is defined in the same way as the sign of a complex number. It is the “direction” of the quaternion:
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Get the standard Euclidean length:
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The exponential of a quaternion can be quite complicated:
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Just as with complex numbers, it is important to beware of branch cuts:
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A four‐dimensional analog of de Moivre’s theorem is used for calculating powers of quaternions:
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Round for quaternions returns a Quaternion in which either all components are integers or all components are odd multiples of :
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A quaternion is even if its norm is even:
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Just as with complex numbers, the quaternion Mod works:
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You can specify a quaternion as the modulus:
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