1. Transitivity however, depends on the definition of the set of elementary operations . 2. What is important is that each elementary operation has a constant cost. 3. Is not in closed form because the summation entails an infinite number of elementary operations . 4. The generator matrices of equivalent codes can be obtained from one another via the following elementary operations : 5. Computer processors have well-defined elementary operations . 6. Hence the universe of sets under ZFC is not closed under the elementary operations of the algebra of sets. 7. Alternatively, a sequence of elementary operations that reduces a single row may be viewed as multiplication by a Frobenius matrix. 8. A set of elementary operations which will be used in the algorithm is chosen and their costs are arbitrarily set to 1. 9. Early programs had to be painstakingly crafted using the instructions ( elementary operations ) of the particular machine, often in binary notation. 10. Thus, the amount of time taken and the number of elementary operations performed by the algorithm differ by at most a constant factor.
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