solvelib::cartesianPower

Cartesian power of a set

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Syntax

Domain Creation

solvelib::cartesianPower()
solvelib::cartesianPower(S, n)

Description

solvelib::cartesianPower is the domain of all cartesian powers of subsets of the complex numbers.

solvelib::cartesianPower(S, n) returns the set of all n-tuples of elements of S.

solvelib::cartesianPower(S, n) returns the n-fold cartesian product of S with itself, that is, the set of all vectors of length n whose components are elements of S.

S must represent a subset of the complex numbers; see solve for an overview of the different kinds of sets in MuPAD®.

The set of one-tuples of elements of S consists of vectors and therefore differs from the set S in the same way as matrices of type matrix with one row and one column are different from numbers.

Superdomain

Dom::BaseDomain

Categories

Cat::Set

Examples

Example 1

A cartesian power of a finite set of numbers is a finite set of vectors:

A:= solvelib::cartesianPower({1, 2, I}, 3)

We can select those vectors with all components real as follows:

A intersect solvelib::cartesianPower(R_, 3)

Example 2

Cartesian powers of the set of complex numbers may occur as the result of a call to solve if every n-tuple of complex numbers is a solution of the given system:

solve([x+y = x+y], [x, y], VectorFormat)

Parameters

S

Set

n

Positive integer

Methods

expand all

Access Methods

base(A)

dimension(A)

Technical Methods

print(A)