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On Multivariate Hermitian Quadratic Forms

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Abstract

Multivariate Hermitian quadratic forms play an important role in the real quantifier elimination algorithm based on the computation of comprehensive Gröbner systems introduced by V. Weispfenning and further improved by us. Our algorithm needs the computation of a certain type of saturation ideal in a parametric polynomial ring. In this paper, we study multivariate Hermitian quadratic forms in more detail and show several facts which have special importance in a parametric polynomial ring. Our results enable us to have an efficient method to compute the saturation ideal, which brings us a drastic improvement of our real quantifier elimination software.

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Acknowledgements

This work was partially supported by JSPS KAKENHI Grant Numbers 17K12642 and 18K03426.

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Authors and Affiliations

  1. Tokyo University of Science, Tokyo, Japan

    Ryoya Fukasaku & Yosuke Sato

  2. Fujitsu Laboratories LTD/National Institute of Informatics, Kanagawa, Japan

    Hidenao Iwane

Authors
  1. Ryoya Fukasaku
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  2. Hidenao Iwane
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  3. Yosuke Sato
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Correspondence to Ryoya Fukasaku.

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Fukasaku, R., Iwane, H. & Sato, Y. On Multivariate Hermitian Quadratic Forms. Math.Comput.Sci. 13, 79–93 (2019). https://doi.org/10.1007/s11786-018-0387-8

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  • DOI: https://doi.org/10.1007/s11786-018-0387-8

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