polar

polarDeg

polarRev

Complex number in polar form with rational magnitude and
 rational angle as a cyclotomic number.

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

polar function

<dl><dt>r</dt>
<dd>magnitude, an integer number, a gmp rational number, or a
fraction given as a character string (e.g. <code>"2/7"</code>)</dd>
<dt>theta</dt>
<dd>angle, an integer number, a gmp rational number, or a
fraction given as a character string (e.g. <code>"2/7"</code>); for
<code>polarDeg</code> the angle is given in degrees and for <code>polarRev</code>
it is given in revolutions</dd></dl>

Arguments

Polar complex number with rational magnitude and angle — polar

<dl>

<dt>r</dt>
<dd>magnitude, an integer number, a gmp rational number, or a
fraction given as a character string (e.g. <code>"2/7"</code>)</dd>


<dt>theta</dt>
<dd>angle, an integer number, a gmp rational number, or a
fraction given as a character string (e.g. <code>"2/7"</code>); for
<code>polarDeg</code> the angle is given in degrees and for <code>polarRev</code>
it is given in revolutions</dd>

</dl>

polar: Polar complex number with rational magnitude and angle

Description

Usage

Value

Arguments

Examples