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exp of quaternion

asked 2022-04-16 19:22:50 +0100

Andr gravatar image

updated 2022-04-16 19:23:50 +0100

I try

Q.<i,j,k> = QuaternionAlgebra(SR, -1, -1)

I get

TypeError: cannot coerce arguments: no canonical coercion from Quaternion Algebra (-1, -1) with base ring Symbolic Ring to Symbolic Ring

what means "-1,-1"? How to expand as demoivre() this?

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answered 2022-04-17 17:55:54 +0100

You can construct very general quaternion algebras in Sage, and the command QuaternionAlgebra(QQ, 2, 3) would construct an algebra with base field the rationals, with elements i and j such that i^2=2 and j^2=3. You've constructed a quaternion algebra over the "symbolic ring" SR with elements i and j such that i^2 = j^2 = -1.

Maybe because they are constructible in such generality, exponentials are not implemented for them. You can just use the formula on the wikipedia page ( General quaternion algebras have their own wikipedia page, too:

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answered 2022-04-23 01:25:43 +0100

AlanTStafford gravatar image

I have used quaternions a few times perhaps here notebooks could provide some guidance.

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Asked: 2022-04-16 19:22:50 +0100

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Last updated: Apr 23 '22