The Complexity of the Quaternion Product
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Let X and Y be two quaternions over an arbitrary ring. Eight multiplications are necessary and sufficient for computing the product XY. If the ring is assumed to be commutative, at least seven multiplications are still necessary and eight are sufficient.
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1975-06
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Cornell University
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computer science; technical report
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http://techreports.library.cornell.edu:8081/Dienst/UI/1.0/Display/cul.cs/TR75-245
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technical report