Continued fractions for some algebraic numbers.
暂无分享,去创建一个
where <*! = 2 cos — =is a root of x -\x — 2x — l, #2 is a root of x — χ — l, OCB = j/2~+ j/3"is a root of X — 9z — 4# + 27z — 36z — 23. The first numbers were chosen s cubic irrationalities, oc1 s being totally real, and we picked a2, OCB at random to be non cubic. The original motivation was to see if computations for algebraic numbers would be in line with some conjectures made in [3] and [4], and to observe whatever eise might come up.
[1] S. Lang. Report on Diophantine approximations , 1965 .
[2] R. F. Churchhouse,et al. Continued Fractions, Algebraic Numbers and Modular Invariants , 1969 .
[3] D. H. Lehmer. Euclid's Algorithm for Large Numbers , 1938 .