cyclotomic: The Field of Cyclotomic Numbers (original) (raw)

The cyclotomic numbers are complex numbers that can be thought of as the rational numbers extended with the roots of unity. They are represented exactly, enabling exact computations. They contain the Gaussian rationals (complex numbers with rational real and imaginary parts) as well as the square roots of all rational numbers. They also contain the sine and cosine of all rational multiples of pi. The algorithms implemented in this package are taken from the 'Haskell' package 'cyclotomic', whose algorithms are adapted from code by Martin Schoenert and Thomas Breuer in the 'GAP' project (<https://www.gap-system.org/>). Cyclotomic numbers have applications in number theory, algebraic geometry, algebraic number theory, coding theory, and in the theory of graphs and combinatorics. They have connections to the theory of modular functions and modular curves.

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