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Inversion in P-Computable Fields

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Twenty Years of Theoretical and Practical Synergies (CiE 2024)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 14773))

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Abstract

We consider fields computable in polynomial time (P-computable). We prove that under some assumptions about a P-computable field \( (A, +, \cdot ) \) of characteristic 0, there exists a P-computable field \( (B, +, \cdot ) \cong (A, +, \cdot ) \), in which \(x^{-1}\) is not a primitive recursive function. In particular, this holds for the field \( \mathbb Q \) of rational numbers.

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References

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Acknowledgments

This study was supported by the Russian Science Foundation (grant No. 23-11-00170), https://rscf.ru/project/23-11-00170.

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Correspondence to Pavel Alaev .

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Alaev, P. (2024). Inversion in P-Computable Fields. In: Levy Patey, L., Pimentel, E., Galeotti, L., Manea, F. (eds) Twenty Years of Theoretical and Practical Synergies. CiE 2024. Lecture Notes in Computer Science, vol 14773. Springer, Cham. https://doi.org/10.1007/978-3-031-64309-5_9

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  • DOI: https://doi.org/10.1007/978-3-031-64309-5_9

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-031-64308-8

  • Online ISBN: 978-3-031-64309-5

  • eBook Packages: Computer ScienceComputer Science (R0)

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