Complex Numbers
The Complex constructor implements
complex objects over a commutative ring R. Typically, the ring R is
Integer,
Fraction Integer,
Float,
DoubleFloat,
R can also be a symbolic type, like
Polynomial Integer.
For more information about the numerical and graphical aspects of
complex numbers, see
Numeric Functions
in section 8.1.
Complex objects are created by the
complex operation
The standard arithmetic operations are available.
If R is a field, you can also divide the complex objects.
Use a conversion
(see Conversion in
section 2.7) to view the last object as a fraction of complex
integers.
The predefined macro %i is defined to be complex(0,1).
You can also compute the
conjugate and
norm of a complex number.
The real and
imag operations are provided to
extract the real and imaginary parts, respectively.
The domain
Complex Integer
is also called the Gaussian integers. If R is the integers (or, more
generally, a
Euclidean Domain),
you can compute greatest common divisors.
You can also compute least common multiples
You can factor Gaussian integers.
