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On the Radical of a Polynomial Ideal with Parameters

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Computer Algebra in Scientific Computing (CASC 2024)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 14938))

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Abstract

A parametric radical system is introduced as a new concept within parametric ideals. It is demonstrated that an algorithm for computing the radical of a non-parametric ideal can be generalized to its parametric version by utilizing several tools related to parametric ideals. The keys to this generalization are two types of comprehensive Gröbner systems.

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Acknowledgments

This work has been partly supported by JSPS Grant-in-Aid for Scientific Research(C)(No. 23K03076).

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Correspondence to Katsusuke Nabeshima .

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Kuramochi, R., Tanaka, K., Nabeshima, K. (2024). On the Radical of a Polynomial Ideal with Parameters. In: Boulier, F., Mou, C., Sadykov, T.M., Vorozhtsov, E.V. (eds) Computer Algebra in Scientific Computing. CASC 2024. Lecture Notes in Computer Science, vol 14938. Springer, Cham. https://doi.org/10.1007/978-3-031-69070-9_12

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  • DOI: https://doi.org/10.1007/978-3-031-69070-9_12

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-031-69069-3

  • Online ISBN: 978-3-031-69070-9

  • eBook Packages: Computer ScienceComputer Science (R0)

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