This is a request for a gentle introduction to quaternions and quaternion calculus and their applications to problems in computer science and physics. I would also be obliged for any references on extensions of results in complex analysis, especially polynomial theory, to quarternions. Lastly, I would be grateful to know what the tools are for carrying out quarternion calculus calculations, both symbolic and numerical, preferably in python and mathematica. Thank you in advance for any links/references/tutorial/suggestions.
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I learnt the most about quaternions by taking spatial rotations as a starting point. This will help you to understand why $SU(2)$ is the double cover of $SO(3)$ which has a lot to do with spin in physics. If you find out how $i,j,k$ are related to the Pauli matrices you can easily program your own python tools. IMO this helps more than reading tons of books. – Kurt G. Sep 23 '22 at 06:45
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Note the spelling "quaternion". https://mathworld.wolfram.com/Quaternion.html – badjohn Sep 23 '22 at 06:57
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Thank you for your valuable comments – AgnostMystic Sep 23 '22 at 08:54
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A pretty good book could be Andrew J. Hanson, Visualizing Quaternions. – Kurt G. Sep 23 '22 at 08:58
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I mostly learned about 3d rotation stuff (and quaternions) by using them in a programming abomination I made. I had to compose a bunch of rotations in Euler angle format, and so I converted them to quaternions and did the multiplication. I think that I looked at this wikipedia page https://en.wikipedia.org/wiki/Rotation_formalisms_in_three_dimensions – gist076923 Sep 23 '22 at 14:27