Real floating-point numbers

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Dom::Float is the set of real floating-point numbers represented by elements of the domain DOM_FLOAT.

Dom::Float is the domain of real floating point numbers represented by expressions of type DOM_FLOAT.

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

Elements of Dom::Float are usually not created explicitly. However, if one creates elements using the usual syntax, it is checked whether the input expression may be converted to a floating point number. This means Dom::Float is a facade domain which creates elements of domain type DOM_FLOAT.

Viewed as a differential ring Dom::Float is trivial, it contains constants only.

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




Example 1

Creating some floating-point numbers using Dom::Float. This example also shows that Dom::Float is a facade domain.

Dom::Float(2.3); domtype(%)

Dom::Float(sin(2/3*PI) + 3)

Error: Invalid arguments. [Dom::Float::new]

Example 2

By tracing the method Dom::Float::testtypeDom we can see the interaction between testtype and Dom::Float::testtypeDom.

delete x:
testtype(x, Dom::Float);
testtype(3.4, Dom::Float);
enter Dom::Float::testtypeDom(x, Dom::Float)
computed FAIL

enter Dom::Float::testtypeDom(3.4, Dom::Float)
computed TRUE



An expression which can be converted to a DOM_FLOAT by the function float.



the unit element; it equals 1.0.


The zero element; it equals 0.0.


expand all

Mathematical Methods


This method is called if this domain is used as the component ring of a matrix domain to perform Gaussian elimination.


Conversion Methods


In general, if float(x) evaluates to a real floating-point number of type DOM_FLOAT, this number is the result of the conversion.

convert_to(x, T)

The following domains are allowed for T: DOM_FLOAT, Dom::Float and Dom::Numerical.

testtype(x, T)

In general this method is called from the function testtype and not directly by the user. Example 2 demonstrates this behavior.