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Univariate Polynomials with Long Unbalanced Coefficients as Bivariate Balanced Ones: A Toom–Cook Multiplication Approach

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Computer Algebra in Scientific Computing (CASC 2020)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 12291))

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Abstract

Multiplication of univariate dense polynomials with long integer unbalanced (having different lengths) coefficients is considered. By reducing the problem to the product of bivariate polynomials with balanced coefficients, Toom–Cook approach is shown, pointing out some optimizations in order to reduce the computational cost. As a byproduct, univariate sparse Toom–Cook is also sketched. Lastly, some experimental results concerning performance comparisons are presented.

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Notes

  1. 1.

    The same idea can, of course, be applied to the general case \(a(x^r)b(x^r)\).

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Acknowledgments

The authors would like to deeply thank all the referees for their precious comments that helped to improve the paper.

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Correspondence to Alberto Zanoni .

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Bodrato, M., Zanoni, A. (2020). Univariate Polynomials with Long Unbalanced Coefficients as Bivariate Balanced Ones: A Toom–Cook Multiplication Approach. In: Boulier, F., England, M., Sadykov, T.M., Vorozhtsov, E.V. (eds) Computer Algebra in Scientific Computing. CASC 2020. Lecture Notes in Computer Science(), vol 12291. Springer, Cham. https://doi.org/10.1007/978-3-030-60026-6_6

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  • DOI: https://doi.org/10.1007/978-3-030-60026-6_6

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