Abstract
This paper proposes a new representation for ideals of any order in an algebraic number field. This representation is compact and highly readable; for example, (95, x+65)(2216) and (7, x 2+4)(95, x+46) are two ideals of Z[x]/(x 4−x 3+7x 2−11x+5), with sum (19, x+8). Arithmetic on ideals in this form is generally much faster than arithmetic in the Z-basis or two-element representations.
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References
Daniel J. Bernstein, Computing coprime bases in essentially linear time, preprint.
Henri Cohen, A course in computational algebraic number theory, Springer-Verlag, Berlin, 1993.
Hideyuki Matsumura, Commutative ring theory, Cambridge University Press, Cambridge, 1986.
Michael E. Pohst, Computational algebraic number theory, Birkhaüser, Basel, 1993.
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© 1996 Springer-Verlag Berlin Heidelberg
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Bernstein, D.J. (1996). Fast ideal arithmetic via lazy localization. In: Cohen, H. (eds) Algorithmic Number Theory. ANTS 1996. Lecture Notes in Computer Science, vol 1122. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-61581-4_38
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DOI: https://doi.org/10.1007/3-540-61581-4_38
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Online ISBN: 978-3-540-70632-8
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