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Mathematics of Computation

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The optimal algorithm to evaluate $ x\sp{n}$ using elementary multiplication methods


Author: D. P. McCarthy
Journal: Math. Comp. 31 (1977), 251-256
MSC: Primary 68A20
MathSciNet review: 0428791
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Abstract: The optimality of the binary algorithm to evaluate $ {x^n}$ is established where x is an integer or a completely dense polynomial modulo m, n is a positive integer, and the multiplications are done using a simple improvement on the naive algorithm.


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DOI: https://doi.org/10.1090/S0025-5718-1977-0428791-X
Keywords: Symbolic algebraic manipulation, computational complexity, optimal multiplication chains
Article copyright: © Copyright 1977 American Mathematical Society