Abstract
Let O be a real quadratic order of discriminant Δ. For elements α in O we develop a compact representation whose binary length is polynomially bounded in log log H(α), log N(α) and log Δ where H(α) is the height of α and N(α) is the norm of α. We show that using compact representations we can in polynomial time compute norms, signs, products, and inverses of numbers in O and principal ideals generated by numbers in O. We also show how to compare numbers given in compact representation in polynomial time.
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© 1995 Springer Science+Business Media Dordrecht
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Buchmann, J., Thiel, C., Williams, H. (1995). Short Representation of Quadratic Integers. In: Bosma, W., van der Poorten, A. (eds) Computational Algebra and Number Theory. Mathematics and Its Applications, vol 325. Springer, Dordrecht. https://doi.org/10.1007/978-94-017-1108-1_12
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DOI: https://doi.org/10.1007/978-94-017-1108-1_12
Publisher Name: Springer, Dordrecht
Print ISBN: 978-90-481-4560-7
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