zeta

For example, `zeta(4) = i` is the primitive 4th root of unity,
 and `zeta(5) = exp(2*pi*i/5)` is the primitive 5th root of unity.
 In general, `zeta(n) = exp(2*pi*i/n)`.

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.

Stc3<a9>phane Laurent

cyclotomic

The Field of Cyclotomic Numbers

Stéphane Laurent

Scott N. Walck

zeta function

<dl><dt>n</dt>
<dd>a positive integer</dd></dl>

Arguments

The primitive n-th root of unity. — zeta

<dl>

<dt>n</dt>
<dd>a positive integer</dd>

</dl>

zeta: The primitive n-th root of unity.

Description

Usage

Value

Arguments

Examples