Efficient polynomial substitutions of a sparse argument

Efficient polynomial substitutions of a sparse argument

Methods are presented for taking powers of symbolic polynomials and substituting them into univariate polynomials with scalar coefficients. It is shown that the size of the result is a sharp lower bound on the number of coefficient multiplications required to raise a completely sparse polynomial to...

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Veröffentlicht in:SIGSAM bulletin 1981-08, Vol.15 (3), p.17-23
1. Verfasser: Rowan, William H.
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creator Rowan, William H.
description Methods are presented for taking powers of symbolic polynomials and substituting them into univariate polynomials with scalar coefficients. It is shown that the size of the result is a sharp lower bound on the number of coefficient multiplications required to raise a completely sparse polynomial to a power. Other theoretical results prove the optimality or near-optimality of the methods given, in terms of numbers of coefficient operations, under the condition of complete sparsity of the argument.
doi_str_mv 10.1145/1089263.1089266
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title Efficient polynomial substitutions of a sparse argument
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