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Dom::Complex

Field of complex numbers

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Syntax

Dom::Complex(x)

Description

Dom::Complex is the domain of complex constants represented by expressions of type DOM_INT, DOM_RAT, DOM_FLOAT or DOM_COMPLEX. An expression of type DOM_EXPR is considered a complex number if it is of type Type::Arithmetical and if it contains only indeterminates which are of type Type::ConstantIdents or if it contains no indeterminates, cf. Example 2.

Dom::Complex is of category Cat::Field due to pragmatism. This domain actually is not a field because bool(1.0 = float(3) / float(3)) returns FALSE, for example.

Elements of Dom::Complex are usually not created explicitly. However, if one creates elements using the usual syntax, it is checked whether the input expression can be converted to a number. This means Dom::Complex is a facade domain which creates elements of domain type DOM_INT, DOM_RAT, DOM_FLOAT, DOM_COMPLEX or DOM_EXPR.

Dom::Complex has no normal representation, because 0 and 0.0 both represent the zero.

Viewed as a differential ring, Dom::Complex is trivial. It only contains constants.

Dom::Complex has the domain Dom::BaseDomain as its super domain, i.e., it inherits each method which is defined by Dom::BaseDomain and not re-implemented by Dom::Complex. Methods described below are re-implemented by Dom::Complex.

Examples

Example 1

Creating some complex numbers using Dom::Complex:

Dom::Complex(2/3)

Dom::Complex(2/3 + 4*I)

Example 2

It's also possible to use expressions or constants for creating an element of Dom::Complex:

Dom::Complex(PI)

Dom::Complex(sin(2))

Dom::Complex(sin(2/3*I) + 3)

If the expression cannot be converted to an element of Dom::Complex we will get an error message:

Dom::Complex(sin(x))
Error: The arguments are invalid. [Dom::Complex::new]

Parameters

x

An expression of type DOM_INT, DOM_RAT, DOM_FLOAT, DOM_COMPLEX. An expression of type DOM_EXPR is also possible if it is of type Type::Arithmetical and if it contains only indeterminates which are of type Type::ConstantIdents or if it contains no indeterminates.

Entries

"characteristic"

the characteristic of this field is 0.

"one"

the unit element; it equals 1.

"zero"

The zero element; it equals 0.

Methods

expand all

Mathematical Methods

_divide(x, y)

_invert(x)

_mult(x, y, …)

_negate(x)

_plus(x, y, …)

_power(x, y)

_unequal(x, y)

conjugate(x)

D(x)

diff(z, <x, …>)

equal(x, y)

expr(x)

iszero(x)

norm(x)

random()

random(n)

random(m .. n)

random(n) returns a random number generator which creates complex random numbers where the real parts and the imaginary parts are positive integers between 0 and n - 1.

random(m..n) returns a random number generator which creates complex random numbers where the real parts and the imaginary parts are positive integers between m and n.

unequal(x, y)

Conversion Methods

convert(x)

An arithmetical expression can be converted if it only contains subexpression of the types just mentioned.

If the conversion fails, FAIL is returned.

convert_to(x, T)

If the conversion fails, FAIL is returned.

The following domains are allowed for T: DOM_INT, Dom::Integer, DOM_RAT, Dom::Rational, DOM_FLOAT, Dom::Float, Dom::Numerical, DOM_COMPLEX and DOM_EXPR.

normal(x)

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