Field of numbers
This functionality does not run in MATLAB.
Dom::Numerical is the field of numbers.
Dom::Numerical 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.
Dom::Numerical are usually not
created explicitly. However, if one creates elements using the usual
syntax, it is checked whether the input expression can be converted
into a number (see below).
This means that
Dom::Numerical is a façade
domain which creates elements of domain type
Every system function dealing with numbers can be applied, and computations
in this domain are performed efficiently.
Dom::Numerical has no normal representation,
0.0 both represent
Viewed as a differential ring,
trivial. It only contains constants.
Dom::Numerical(2), Dom::Numerical(2/3), Dom::Numerical(3.141), Dom::Numerical(2 + 3*I)
Constant arithmetical expressions are converted into a real
and complex floating-point number, respectively, i.e., into an element
of the domain
DOM_COMPLEX (see the function
float for details):
Dom::Numerical(exp(5)), Dom::Numerical(sin(2/3*I) + 3)
Note that the elements of this domain are elements of kernel
domains, there are no elements of the domain type
An error message is issued for non-constant arithmetical expressions:
Error: The arguments are invalid. [Dom::Numerical::new]
Dom::Numerical is regarded as a field, and
it therefore can be used as a coefficient ring of polynomials or as
a component ring of matrices, for example.
We create the domain of matrices of arbitrary size (see
Dom::Matrix) with numerical
MatN := Dom::Matrix(Dom::Numerical)
Next we create a banded matrix, such as:
A := MatN(4, 4, [-PI, 0, PI], Banded)
and a row vector with four components as a 1 ×4 matrix:
v := MatN([[2, 3, -1, 0]])
Vector-matrix multiplication can be performed with the standard
v * A
Finally we compute the determinant of the matrix
using the function
See the function
D for details and further calling sequences.
See the function
details and further calling sequences.