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It is possible to do the symbolic multiplication $qq^*$ of a quaternion $q=a+bi+cj+dk$ by its conjugate $q^*=a-bi-cj-dk$ using Mathematica? It seems that Quaternion package only works with numeric entries.

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    $\begingroup$ Use ** instead of * to "multiply" 2 quaternions. $\endgroup$ – Carl Woll Nov 19 '18 at 17:19
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    $\begingroup$ Try a new package named GTPack. $\endgroup$ – Αλέξανδρος Ζεγγ Nov 20 '18 at 2:53
  • $\begingroup$ Thanks for all the relevant contributions! $\endgroup$ – robson denke Nov 28 '18 at 20:01
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Needs["Quaternions`"]
q = Quaternion[a, b, c, d];
q ** Conjugate[q]

Quaternion[a^2 + b^2 + c^2 + d^2, 0, 0, 0]

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The following links might be helpful to you:

https://www.mathematica-journal.com/2018/05/computational-aspects-of-quaternionic-polynomials/

https://www.mathematica-journal.com/2018/07/computational-aspects-of-quaternionic-polynomials-2/

http://blog.wolframalpha.com/2011/08/25/quaternion-properties-and-interactive-rotations-with-wolframalpha/

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    $\begingroup$ Please keep in mind that answers which provide only links are discouraged. Try to summarized the contents of the linked articles in the answer, so that if a link ever goes dead the answer will still be of use. $\endgroup$ – silvascientist Nov 19 '18 at 23:55

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