Remove conformance to AlgebraicField
on Quaternion
#229
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As of now,
Quaternion
conforms to theAlgebraicField
protocol defined inRealModule
. However quaternions are a non-commutative, associative algebra over the real numbers and thus, this is incorrect. Their structure is similiar to a field, but given that their multiplication is non-commutative they form a division algebra (division ring). This has no implications on the implementation ofAlgebraicField
onQuaternion
, but contradicts the mathematical definition – and the definition in theAlgebraicField
documentation noting that:I would like to propose to remove the conformance to
AlgebraicField
and replace it withSignedNumeric
, but to keep the implementation of the division operators andreciprocoal
, as these are well defined for quaternions.