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In three dimensions a multivector is any sum of a scalar, vector, bivector, and a trivector.

$ Multivector M = \sum_{r=0}^{n} \langle M \rangle _r $ for i=0 to n where n is the number of dimensions.

〈M〉0 = scalar
〈M〉1 = vector
〈M〉2 = bivector
〈M〉3 = trivector


$ M^{+} = \langle M \rangle _0 + \langle M \rangle _2 + \langle M \rangle _4 + \cdots $
$ M^{-} = \langle M \rangle _1 + \langle M \rangle _3 + \langle M \rangle _5 + \cdots $
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