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Dom::Complex

Field of complex numbers

Use only in the MuPAD Notebook Interface.

This functionality does not run in MATLAB.

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

_mult — Multiplie numbers

_mult(x, y, …)

_plus — Add numbers

_plus(x, y, …)

diff — Differentiates

diff(z, <x, …>)

equal — Equations

equal(x, y)

random — Random number generation

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.

Conversion Methods

convert — Conversion into this domain

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 — Conversion to other domains

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.

See Also

MuPAD Domains

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