Documentation |
Field of real numbers
This functionality does not run in MATLAB.
Dom::Real(x)
Dom::Real is the field of real numbers represented by elements of the kernel domains DOM_INT, DOM_RAT, DOM_FLOAT, and DOM_EXPR.
Dom::Real is the domain of real numbers represented by expressions of type DOM_INT, DOM_RAT or DOM_FLOAT. An expression of type DOM_EXPR is considered as a real number if it is of type Type::Arithmetical and if it contains no indeterminates which are not of type Type::ConstantIdents and if it contains no imaginary part. See Example 2.
Dom::Real has category Cat::Field due to practical reasons. This domain actually is not a field because bool(1.0 = 1e100 + 1.0 - 1e100) returns FALSE for example.
Elements may not have an unique representation, for example bool(0 = sin(2)^2 + cos(2)^2 - 1) returns FALSE.
Elements of Dom::Real 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::Real is a façade domain which creates elements of domain type DOM_INT, DOM_RAT, DOM_FLOAT, or DOM_EXPR.
Dom::Real has no normal representation, because 0 and 0.0 both represent zero.
Viewed as a differential ring, Dom::Real is trivial, it contains constants only.
Dom::Real has the domain Dom::Complex as its super domain, i.e., it inherits each method which is defined by Dom::Complex and not re-implemented by Dom::Real. Methods described below are re-implemented by Dom::Real.
Ax::systemRep, Ax::canonicalOrder, Ax::efficientOperation("_divide"), Ax::efficientOperation("_mult"), Ax::efficientOperation("_invert")
The following lines demonstrate how to generate elements of Dom::Real. The rational and the floating-point numbers are elements of the real numbers:
Dom::Real(2/3)
Dom::Real(0.5666)
The numbers PI and sin(2) are real numbers whereas sin(2/3 * I) + 3 and sin(x) for general symbolic x are not real numbers. If we try to create the elements Dom::Real(sin(2/3 * I) + 3) and Dom::Real(sin(x)) an error message is produced.
Dom::Real(PI)
Dom::Real(sin(2))
Dom::Real(sin(2/3 * I) + 3)
Error: The arguments are invalid. [Dom::Real::new]
Dom::Real(sin(x))
Error: The arguments are invalid. [Dom::Real::new]
x |
An expression of type DOM_INT, DOM_RAT, or DOM_FLOAT. An expression of type DOM_EXPR is also allowed if it is of type Type::Arithmetical and if it contains no indeterminates which are not of type Type::ConstantIdents and if it contains no imaginary part. |