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Polynomial Algebra: an Application of the Fast Fourier Transform

Nature volume 222, page 1302 (28 June 1969) | Download Citation

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Abstract

MUCH use is made in combinatorial problems of generating functions in the form of polynomials and infinite power series, these being obtained by the manipulation of other algebraic expressions. In order to save time and improve accuracy in the evaluation of the coefficients, one can, of course, make use of computer programs for doing algebra1,2. But it is often easier to use the following method which relies only on arithmetical operations available in all programming languages.

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References

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    , , and , Nature, 178, 1208 (1956).

  2. 2.

    , in Machine Intelligence, II (edit. by Dale, E., and Michie, D.), 47 (Oliver and Boyd, Edinburgh and London, 1968).

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    , The Theory of Groups and Quantum Mechanics, 34 (Methuen, London, 1931).

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    , Biometrika, 17, 185 (1950); Proc. Camb. Phil. Soc., 47, 756 (1951); ibid., 51, 385 (1955); J. Roy. Stat. Soc. B, 20, 361 (1958); ibid., 22, 372 (1960); Amer. Math. Monthly, 69, 259 (1962).

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    IEEE Trans. Audio Electronics, AU-15, No. 2 (June 1967).

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    , Ann. Math. Stat., 28, 861 (1957); ibid., 32, 535 (1961).

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Affiliations

  1. Virginia Polytechnic Institute, Blacksburg, Virginia.

    • I. J. GOOD

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https://doi.org/10.1038/2221302a0

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